Lacunae: A Software for Lacunarity Analysis of Digital Images

Lacunae: A Software for Lacunarity Analysis of Digital Images | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Lacunae: A Software for Lacunarity Analysis of Digital Images Mauro Normando Macêdo Barros Filho, Eanes Torres Pereira, Lucas Khalil Azevedo Dantas, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6812524/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This paper aims to present the main features and functionalities of LACUNAE, a software for analyzing lacunarity of digital images, which represents an advance in the application of Fractal Geometry by implementing innovations in relation to other software of this nature already used by the scientific community. A satellite image sample, characterized by the presence of formal and informal areas in the city of Recife, Brazil, was used to validate LACUNAE, using Discriminant Analysis to investigate the software's ability to distinguish spatial patterns between formal and informal urban areas. The lacunarity results obtained showed consistently different canonical means for groups of cells with different urban forms, with the advantage of performing the calculation on a batch of images. This type of development has the potential to subsidize spatial analyses that consider lacunarity as the main texture metric, and its implementation logic can be replicated for other indicators useful in distinguishing urban morphological patterns in digital images. lacunarity software images urban areas Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 INTRODUCTION In the 1980s, investigations into the geometric complexity of natural forms, which were not properly understood by Euclidean geometry, inaugurated the field of Fractal Geometry. The term “fractal”, coined by Benoit Mandelbrot (1982), comes from the Latin “fractus” and means “fraction”. The nomenclature refers to the main characteristic of Fractal Geometry: self-similarity, which occurs when a given spatial pattern can be visualized at multiple scales and its “fractions” being similar to its totality. Some models seek to reproduce the self-similarity of fractals, such as Sierpinski's Triangle, Koch's Snowflake, Mandelbrot's Set, among others. However, studies on fractals have sought not only to understand the modus operandi of their principles, but also to measure them in order to distinguish different spatial patterns. At first, studies involved in measuring fractal patterns, with the intention of distinguishing them, began to be applied in Physics (Plotnick et al. 1996), Biology (Smith Junior et al. 1996), Neurosciences (Karperien, 2011) and other areas of Medicine (Yasar et al. 2005; Borys et al . 2008) that evaluate texture patterns in digital images such as those capture by X-rays and CT scans. Later, applications of fractals emerged in the fields of Remote Sensing (Su & Krummel, 1996), Geomorphology (Kambesis et al. 2016), Environment (Sampurno et al. 2018) and Urban Planning (Batty & Longley, 1994; Frankhauser, 1997). Lacunarity comes from the Latin “lacuna”, meaning “void”. It is a property of fractals that allows us to evaluate the distribution of “voids” in a spatial structure, at different scales. In urban planning, lacunarity makes it possible to analyze the dispersion, density, packing and permeability of the urban fabric (Barros Filho & Sobreira, 2005). Lacunarity may be obtained by calculating Sliding Boxes, which can be applied to both binary images (Allain & Cloitre, 1991) and grayscale images (Dong, 2000). The result is a numerical value ranging from 1 to infinity. In general, more homogeneous texture patterns have values closer to 1 (Myint & Lam, 2005). Fractal dimension and lacunarity are among the most widely used metrics for investigating the fractal patterns of digital images in urban areas. Some studies discuss the existence of a synergy between them (Kilic & Abiyev, 2011; Yadav et al. 2024). This paper focuses on lacunarity, as applications of this measure in urban areas have proven to be more efficient in distinguishing spatial patterns compared to the Fractal Dimension (Barros Filho, 2006). In urban studies, lacunarity has already been correlated with various indicators, such as Principal Component Analysis (PCA) (Pereira et al ., 2023), Line Detection (Kit et al. , 2012), Visual Graph Analysis (Amorim & Barros Filho, 2017), Urban Density (Veiga et al. , 2024), Habitability (Simões & Barros Filho, 2022; Barros Filho, 2006) and Normalized Difference Vegetation Index (NDVI) (Han et al. , 2012). In addition, lacunarity has contributed as an indicator in the construction of models and classifiers, especially in studies engaged in the identification and classification of informal areas at multiple intra-urban scales (Barros Filho & Sobreira, 2005, Mahabir et al. , 2017; Pereira et al. , 2023). There are many softwares that perform the lacunarity calculation proposed by Dong (2000), such as FRACLAC (Karperien, 2012) and PASSaGE (Rosemberg & Anderson, 2011). Several studies also use MATLAB to calculate lacunarity (Scott et al., 2022; Roy & Sivaji, 2022), as well as plugins for GIS software (ArcGIS, QGIS) and implementations in programming languages such as Python (Murueta-Goyena, 2021). This paper aims to present LACUNAE, a software under development which proposes to calculate lacunarity of urban areas, by manipulating a significant amount of images and generating a wide range of results, which can later be analyzed in GIS software and support urban studies. To validate the results, the lacunarity values obtained by LACUNAE in a satellite image of an urban area located in the city of Recife, Brazil, were compared with the lacunarity values obtained by another reference software, FRACLAC, in the same spatial area. In this method, Discriminant Analysis (Fávero et al., 2009; Hair et al. , 2005) was applied in order to assess the potential of the lacunarity generated by LACUNAE to distinguish groups of values previously labeled as belonging to formal and informal urban areas. Thus, before describing the main features and functionalities of LACUNAE, as well as its advances in lacunarity analysis of urban areas, it is worth highlighting the features, possibilities and limitations of FRACLAC for this purpose. FRACLAC: POSSIBILITIES AND LIMITATIONS IN LACUNARITY ANALYSIS OF URBAN AREAS Developed by Charles Sturt University in Australia, FRACLAC 1 is a plugin for the ImageJ software (Schneider et al., 2012), which is available free of charge and which is used to process images. As it is open source, the ImageJ user community can create plugins with additional functionalities. FRACLAC is an established tool for studying fractal and lacunarity patterns, and it has been usually applied at medical, physical and biological areas associated with microscopy. The FRACLAC portal 2 provides a large set of 73 experiments that took place mainly between 2002 and 2013 (Jelinek et al., 2002; Captur et al., 2013). Since the 2000’s, many studies have used FRACLAC to calculate the fractal dimension and lacunarity of urban areas. Mahabir et al. (2018) refer to Barros Filho and Sobreira (2005) as the first experiment to discriminate informal urban areas based on their multiscale properties. The authors (2005) used FRACLAC to analyze three binary images with urban configurations characterized by formality and informality. These high-resolution images were captured by the IKONOS satellite in the city of Campinas, Brazil. The fractal dimension and lacunarity were calculated and it was found that there was a high degree of similarity between the fractal patterns measured by the fractal dimension. However, the lacunarity values made it possible to distinguish different texture patterns in the cells. They concluded that lacunarity complemented fractal analysis by revealing the particularities behind fractal complexities. Subsequently, Barros Filho (2006) used FRACLAC to carry out experiments in the city of Recife, Brazil, with binary images obtained from high spatial resolution satellite images and showed that it was possible to distinguish texture patterns in urban areas of the city with different habitability conditions. The lacunarity values obtained from these images were strongly correlated with the values of a Habitability Index (HI) constructed with data from the 2000 Demographic Census. Urban areas with better habitability conditions had higher gap values than urban areas with poorer conditions. These differences, however, tend to decrease when these areas are analyzed at larger scales. The methodology applied by Barros Filho (2006) consisted of selecting 30 cells based on a visual interpretation of the original satellite image, 15 of which belonged to urban areas with a high level of habitability and 15 to areas with a low level of habitability. The same size was set for all the cells to enable a comparison of the lacunarity values between them. By associating the black and white pixels of these sub-images with the city's built and unbuilt spaces, it was possible to deduce that, at all the scales analyzed, the unbuilt spaces are smaller and more evenly distributed in the areas with the poorest living conditions in the city. This can be explained by the density and irregular occupation of the land in informal areas, generating a large number of small voids, while in formal areas occupation is more sparse and conforms to the parameters of the urban planning legislation in force. Binary images do not represent the real textures of the original images. Some valuable information about the spatial arrangement of the gray levels in these images can be lost during the process of converting an 8-bit gray-level image into a binary image with only 1 bit (Dong, 2000; Myint & Lam, 2005). Later results also obtained in FRACLAC with the same cells analyzed by Barros Filho (2006) in the city of Recife - by applying the Gliding-Box and Differential Box-Counting algorithms to binary images and images with 256 gray levels, respectively - revealed that the latter is capable of improving the percentage of images correctly classified as belonging to urban areas with low and high habitability conditions by up to 40% (Barros Filho & Sobreira, 2008). In addition to distinguishing slums from non-slums in Recife, another experiment carried out by Amorim, Barros Filho and Cruz (2014) using FRACLAC on images with 256 gray levels also made it possible to distinguish texture patterns in cells representing four specific neighborhoods in the same city, originating from very different occupation processes, revealing the potential of lacunarity measures in morphological studies. Lacunarity analyses with FRACLAC have been tested on a variety of scales, manipulating images with different extensions, granulations and spatial resolutions, and sliding boxes with different sizes and spacings (Alves Junior & Barros Filho, 2006; Barros Filho & Sobreira, 2008). These include the application of discriminant analysis techniques (Barros Filho et al. , 2022; Simões et al., 2024) and the interpolation of lacunarity values by Ordinary Kriging (Barros Filho, 2009; Barros Filho et al., 2024). Brazil has concentrated a large number of these studies, which were inspired mainly by the international discussions on fractals that have impacted on various areas of knowledge. In this way, many experiments have also been carried out in other countries, whose methodologies, when observed under the current context of computational development, could be improved (Owen & Wong, 2013; Greenhill et al., 2006). Leão (2011) used FRACLAC to analyze the city of Canela, in the state of Rio Grande do Sul, Brazil. The author (2011) proposed a model that associated lacunarity data, based on a map of buildings, with income and infrastructure indexes, in order to estimate different housing standards. The model achieved high correlation values between the variables involved. However, even though the image was partitioned into 1,009 sections, it was necessary to select representative cells for pre-established groups, resulting in a total of 67 cells, a much lower number. This procedure is mainly linked to the difficulty in finding tools that could perform the lacunarity calculation on a large number of cells. As mentioned before, FRACLAC has been applied to various areas of knowledge, and the software is not exclusively dedicated to urban analysis, generating a series of limitations that made some studies unfeasible, especially those that considered a large amount of data. Lacunarity analysis in urban areas should start with the following question: How many image cells are needed for a robust lacunarity analysis in an urban area? An experiment conducted by Wang et al. (2018), considering the spatial heterogeneity present in urban digital remote sensing images, as well as the laws of scale and anisotropy to which objects and patterns are subject, evaluated the importance of calibrating parameters related to granulations, extensions and directions. In general, the cells used did not go beyond the scale of neighborhoods and, in some cases, the scale of a city, requiring a large number of cells to assess the texture of the entire area. Despite all advances with FRACLAC in the discrimination of urban areas, the following functions are not properly provided by the software: (i) creation of grids in images, a useful resource when the user starts from a satellite image of the entire urban area of a city and wants the lacunarity to be calculated in each cell 3 of a pre-established grid, tools such as FRACLAC only accept one input at a time, making it impossible to calculate the lacunarity in several cells in a single process, substantially increasing the research time; (ii) support for the . geotiff format, FRACLAC focuses on .jpeg and .png formats, the loss of georeferencing information makes it impossible to represent the lacunarity values in geographical space and cross-reference them with other indicators; (iii) representation of the results, as it does not support georeferenced data, the result is made available in tabular and numerical format for each imported image cell, requiring the use of complementary GIS software to create maps and classify the results; (iv) consulting specific areas of the image, FRACLAC only generates a lacunarity value for the entire imported image, not taking into account the assessment of lacunarity in partitions within the image. Methodological limitations in current applications reduce the possibility of lacunarity being used more widely, as well as studies already carried out being widely replicated in other areas by other researchers and discussed in the scientific community. Therefore, in all of these previously reported experiments with FRACLAC, the image selection process was conducted manually, considering only a small number of cells, and it was unable to detect the great diversity of urban textures that exist in these cities. In this context, recent research based on the application of Machine Learning approaches, which allows a large number of cells to be manipulated for the automatic detection of image texture patterns, is becoming increasingly important. This type of study has already used various indicators to train automatic classification algorithms (Pereira et al., 2023; Reuß, 2017; Kit et al., 2012). To this end, the next sections describe the methodology used to develop LACUNAE and validate its results. LACUNAE: IMPROVING LACUNARITY ANALYSIS OF URBAN AREAS LACUNAE is a registered software under development at Federal University of Campina Grande. The initiative of developing the software arose in 2019 from a scientific initiation project carried out at the Urban Open Spaces Laboratory (LELU) with the collaboration of the Computer Perception Laboratory (LPC). LACUNAE applies a Machine Learning algorithm for the automatic detection of urban areas, considering exclusively the texture patterns of the images. It uses a Python code, which automated the calculation of lacunarity, facilitating both the import and parameterization of input images and the generation of output tables, maps and graphs. It is currently being improved through a scientific and technological development initiation project (PIBITI). The first stage of LACUNAE's development consisted of constructing a Python code based on experiments done by Simões and Barros Filho (2022), Pereira et al. (2023) and Barros Filho et al. (2024). Simões and Barros Filho (2022) confronted the challenge of evaluating the entire urban area of Campina Grande, a medium-sized city in the state of Paraíba, Brazil. An experimental code partitioned a Sentinel-2 image of the municipality into 19,044 cells and calculated the lacunarity of each of them, the results were then spatially associated with the assistance of GIS software. Pereira et al. (2023) detect deprived urban areas in six cities in the Brazilian semi-arid region using Sentinel-2 images and census data. The results obtained were more than 90% accurate, making an important contribution to slum mapping in cities lacking cartographic and sociodemographic bases. Barros Filho et al. (2024) applied the same code to distinguish socio-spatial patterns in João Pessoa. From these experiments, a desktop application was developed, using the PySide 6 library and basic knowledge of UX Design. The development flow can be synthesized in the flowchart below (Fig 1): The operation of the software can be described as follow: (i) importing an image (tif, geotiff, tiff, png, jpg, bmp) obtained previously, the software redirects the user to the Google Earth Engine catalog, a platform on which the user can select the location and sensor from pre-established codes; (ii) definition of an image partitioning grid (Cells Size), sliding to maximize the number of partitions (Overlap) and manipulation of the parameters of the Gliding Box (Dong, 2000), such as the number of boxes, the size of the first box in pixels and the progression to the largest box on a linear or exponential scale; (iii) visualization of the results on the imported image, which can be configured in multiple forms of interpolation, color palette and transparency. Interpolation was applied because it was able to continuously represent the lacunarity values of each cell initially partitioned from the image, and the value of each was linked to its respective centroid; (iv) the possibility of generating basic statistics, represented numerically or in graphs, for specific areas of the image, unit cells or transepts of cells; and (v) exporting the lacunarity results for each cell in a table and georeferenced image, whose files can later be manipulated in GIS software, making it possible to cross-reference them with other databases. APPLYING LACUNAE TO DISCRIMINATE FORMAL FROM INFORMAL URBAN AREAS LACUNAE was applied to calculate lacunarity of an image sample located in the city of Recife, Brazil, which includes two informal areas (Brasília Teimosa and Pina/Encanta Moça) separated to each other by a formal urban area (Fig. 2). This image was chosen because it was used in a previous paper which applied FRACLAC to differentiate lacunarity patterns between and within these informal areas (Barros Filho, 2009). Brasília Teimosa is located on a peninsula formed by the meeting of the Atlantic Ocean and the Pina River, an area of high real estate value in the city of Recife. Since its initial occupation at the end of the 1940s, Brasília Teimosa has suffered several threats of removal, which were minimized after the area was recognized by the Recife City Land Use and Occupation Law (Law n. 14.511 of 1983) as a Special Zone of Social Interest - ZEIS, officially recognizing the occupation and protecting it from the formal estate market. According to the National Register of Addresses for Statistical Uses, the result of the IBGE's 2022 Brazilian Census, there are 9,182 addresses in Brasília Teimosa, ranging from households to services and institutions. Considering its area of 5.27 hectares, there is an estimated density of 1,742 households per hectare. LACUNAE's home screen is shown in Fig. 3. Three main functions are highlighted in color: “Open” (to import the satellite image, highlighted in red); “Run” (to process the imported image, highlighted in green); and “Results” (to display the results, highlighted in blue). If the user has already processed an image, it is possible to import the resulting table and view the results at any time without the need for reprocessing. In addition, the “Open” option can also redirect the user to the Google Earth Engine image catalog, from which they can obtain various free options, such as the Sentinel, Planet and Landsat sensors, with the possibility of filtering out clouds. On the processing screen (Fig. 3), the user can see the spatial resolution of the imported image and the number of resulting cells when they define the resolution of the cells that will be sectioned from the initial image, a parameter manipulated in the “Sample Size” option. The screen also provides the estimated time for the algorithm to run, based on the parameters configured by the user. The Overlap parameter, which is intended to maximize the number of cells, can substantially increase processing time when the user opts for low sliding rates 4 . After setting the parameters for partitioning the main image, the user must define the parameters for calculating the lacunarity (Gliding Box). As proposed by Dong (2000), the gliding boxes calculate the lacunarity of each cell, each of which slides over it, calculating the average pixel intensity and the mass frequency distribution of the boxes. LACUNAE allows you to configure the number of boxes (N° Boxes), the size of the initial box (First Size) and the way subsequent boxes are generated (Size Ratio). The values can also progress following an arithmetic (Linear) or geometric (Geometric) progression. The “Back to Default” option returns the settings to a pre-established initial default. "Run” proceeds to processing and “Run, saving samples in folder” saves the cells obtained as an image in a user-defined folder. After processing the image, the screen highlighted in blue (Fig. 4) shows the user the interpolated results superimposed on the initial image (input), alongside basic statistics considering all the calculated cells. Details regarding the interval (Min and Max) of the classification, transparency and type of interpolation can be manipulated. The possibility of modifying the classification interval, generated automatically from the lacunarity values obtained, is useful for mitigating possible distortions in the classification caused by outlier values. The “Edit Colormap” button presented in the “viewing results” screen shown in Fig. 3 opens a dialog box (Fig. 4) to simulate a progression from 2 to 1,000 classes, also demonstrating different types of interpolations using the image of the study area as an example. Initial, final and intermediate colors can also be customized by the user. In the example, the “custom” color map is the default option, but it is also possible to apply ready-made palettes, such as the “Accent” and “CMRmap”. The “Save” button (Fig. 3) saves the results in three different formats: a PNG file with the RGB bands; a TXT file with the parameters used; a copy of the original image; and a XLSX file with the lacunarity values organized in matrix format, i.e. breaking down the row and column of the matrix that generated the interpolation. In the case of georeferenced images, a fourth artifact is made available, with the image in geotiff whose lacunarity values are the only band in the image. Fig. 5 shows two functionalities available in the “Plot Data” button on the “viewing results” screen in Fig. 3. The user can create line graphs and box plots based on the selection of cells, with three possibilities: selection of a square, selection of a cell, and selection of a transept between two cells. The “Transept” option was implemented based on Farr's (2013) concept, inspired by Alexander Von Humboldt and appropriated by Duany Plater-Zyberk, intended to reveal a sequence of land occupation patterns in a transition from urban to rural areas. This feature is useful for evaluating the behavior of lacunarity as the cell moves away from one location to another. The boxplot graph makes it possible to compare the lacunarity values of different selections drawn on the image. In a test carried out (Fig. 5), it can be seen that the lacunarity values decrease as the cells enter into Brasília Teimosa; however, they suddenly increase as the cells approach a marina at the tip of the peninsula, a region with a greater amount of open spaces. VALIDATING LACUNAE BASED ON FRACLAC RESULTS In order to validate LACUNAE, its lacunarity values were compared with those obtained by Barros Filho (2009) using FRACLAC for the same image, considering the same parameters. In the study carried out by Barros Filho (2009), lacunarity values were obtained from a Quickbird image with 0.60m spatial resolution, sectioned into two grids: 150m x 150m cells and 75m x 75m cells (Fig. 6). 5 The results were generated by FRACLAC and classified using a k-means algorithm. The author (2009) observed that the slum areas had much lower lacunarity values than the formal areas. This was subsequently followed by an analysis of lacunarity in a more recent image of the area, collected between 2023 and 2024 on the Google Earth Engine platform. This image refers to the Planet sensor which has a spatial resolution of 5 meters and only the 150m x 150m scenario was partitioned in LACUNAE, equivalent in this case to 30 x 30 pixels 6 . The cells were processed using the Gliding Box algorithm (Dong, 2000), considering boxes with the following pixel sizes: 2, 4, 6, 8, 10 and 12. Despite the differences between the Quickbird and Planet images, the purpose of this increment is to verify the accuracy of LACUNAE considering images with lower granulation, i.e. worse spatial resolutions. Summarizing, lacunarity data were analyzed for two groups (formal and informal urban areas) considering the Quickbird sensor scenario for 150m x 150m and 75m x 75m cells, generated by both FRACLAC and LACUNAE, totaling four analyses. For the Planet sensor, a single Discriminant Analysis was conducted considering the 150m x 150m cells. The cell sizes and their respective labels are shown in Figure 6. In the statistical evaluation, Discriminant Analysis (Fávero et al., 2009; Hair et al., 2005) was used to calculate the difference between the lacunarity values of the two pre-established scenarios (formal and informal areas). The difference is calculated by a linear discriminant function based on the overlap of the data from each cell. For each of the pre-established groups, the method calculates a canonical mean, which refers to the average of the variables in a canonical space. The average represents the linear combinations of the variables that best distinguish the groups, in this case, lacunarity is the variable evaluated. The more distant the canonical averages are, the better the discrimination between the groups. The results of the Discriminant Analysis obtained with FRACLAC and LACUNAE software for each group are shown in Table 1. Table 1 - Canonical mean of the discriminant analysis groups Software Sensors Grid Discriminant analysis groups Difference of averages Informal Cells Formal Cells FRACLAC Quickbird 150m x 150m 0,01 -0,13 0,14 Quickbird 75m x 75m -0,12 -0,12 0,0 LACUNAE Quickbird 150m x 150m -0,10 -0,08 0,02 Quickbird 75m x 75m -0,09 0,19 0,28 Planet 150m x 150m 0,20 -0,14 0,36 Results obtained using OriginPro and SPSS statistical software Comparing the difference in the canonical mean reveals which of the software and sensors performs best in this distinction. From the results in Table 1, it can be seen that the FRACLAC experiment in 150m x 150m cells was able to distinguish the slum and non-slum groups more accurately than LACUNAE, with a difference of 0.12 between the experiments. In the experiment on 75m x 75m cells, it was not possible to detect differences between the groups in FRACLAC, while it was possible to detect a significant difference of 0.28 in LACUNAE. The Planet sensor experiment at LACUNAE, whose resolution is lower than the Quickbird sensor, showed a better distinction between the averages. Despite the differences on discrimination capabilities between LACUNAE and FRACLAC, the experiments conducted in this research provide evidence that the data extracted using LACUNAE allows patterns to be differentiated from lacunarity just as well as FRACLAC, since the lacunarity values generated by FRACLAC have already proved effective in distinguishing different urban digital images (Barros Filho, 2006; Barros Filho et al., 2022). Moreover, LACUNAE also allows different parameters to be processed and the usage of more accessible images than those from the Quickbird sensor. Using data from the Quickbird sensor scenarios, it was not possible to reproduce the same results, even importing the same parameters and using the lacunarity calculation. This is because, although the logic of the calculation is based on Dong (2000), each software has its own unique way of implementing it, sometimes using different programming languages, as well as other minor issues that make it unlikely that the results will be the same. In short, even if the code and parameters are the same, different codes imply different lacunarity results. These features that differentiate LACUNAE from FRACLAC need to be investigated further, however, LACUNAE offers a greater possibility of maximizing the volume of data, establishing smaller windows and box sliding, as well as performing the calculations over a much shorter period of time. In addition, LACUNAE allows better analysis and comparison of patterns from a single image, through the square and transept options, making it innovative in this respect. The diversity of results also reproduces what was found by Wang (2018), that urban texture indicators are ruled by the laws of scale and anisotropy. In this context, there are many distinctions in the parameters, such as the size of the window and the resolution of the sensor, which will imply different results. In this case, the Planet sensor proved to be superior to the Quickbird sensor, despite its lower spatial resolution, in distinguishing slum areas from non-slum areas. This type of finding can help studies on the identification of precarious settlements using Machine Learning (Kuffer et al., 2016; Kohli et al., 2012), since investing in better resolution images does not necessarily imply greater accuracy in the results. Finally, it should be highlighted that there are geographic limitations in the study area, which was selected in order to compare it with previous studies by Barros Filho (2009). Most of the cells after the image intersection refer to the ocean and were not used in the discriminant analysis. If they had been used, the difference between the groups would certainly have been much greater, as can be seen from the classifications shown in Fig. 4. Lacunarity analysis is more accurate at distinguishing occupied and unoccupied areas than slum areas from non-slum areas, as there is no consensus that all slum areas will have low lacunarity or that all non-slum areas will have higher lacunarity. Simões and Barros Filho (2022) found the existence of slums with different texture patterns. In this context, LACUNAE should be further tested in order to differentiate between groups that may have similar characteristics at certain cut-off points and scales. CONCLUSIONS LACUNAE has proven to be a promising application for automating the analysis of lacunarity in geospatial images, and its development contributes to the scientific community interested in analyzing and comparing different morphological patterns in cities. The approach with which LACUNAE was implemented could be a model to drive projects to automate indicators related to remote sensing, such as other texture measures based or not on fractal logic. Different from the software already widespread in the academic community, LACUNAE's great advantage is the possibility of multiplying the amount of data by sectioning images into smaller cells and comparing the results of different areas of the image with each other, using descriptive statistics and graphs. It also represents the results under the image using different interpolation methods. All these features avoid the use of other software for these purposes and simplify geoprocessing methodologies. Adapting these applications into an intuitive interface can make lacunarity analysis more accessible to the academic community, especially those who are not yet adept at manipulating programming codes, as it was once necessary in previous experiments (Simões & Barros Filho, 2022 ). LACUNAE is not yet openly available, as it is currently under development, minimizing possible bugs, perfecting operations and adding new tools. Other studies should be carried out to demonstrate the potential of this software to distinguish urban patterns and develop studies in the field of urban and regional planning. Future versions of LACUNAE will bring its API version, allowing its library to be linked to other software based on texture pattern recognition. Research of this nature is important because it combines urban spatial analysis with current computational knowledge, strengthening methods already established in the literature and reverberating in the research economy. In this case, the main saving was in terms of time, since calculating the lacunarity cell by cell in the entire urban area of cities, especially the larger ones, would be unfeasible. Research scales such as these will later be the subject of LACUNAE research. Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials The data used to generate the results of this article can be made available by the authors. Competing interests The authors have no relevant financial or non-financial interests to disclose. Funding This study was funded by CNPq (National Council for Scientific and Technological Development) by Institutional Scholarship Program for Technological Development and Innovation Initiation (PIBITI). Despite funding during the course of the research, this paper does not have the availability of funds to pay for publication in open access. And due to the difficulties in raising funds, given the geographical location of the authors, we request the support of funds to enable this publication, if necessary. Authors' contributions Mauro Normando Macêdo Barros Filho, Eanes Torres Pereira, Matheus Batista Simões also helped with the writing of the article and the conceptual development of LACUNAE, Lucas Khalil Azevedo Dantas contributed specifically to the programming of LACUNAE. Acknowledgements The authors would like to thank CNPq (National Council for Scientific and Technological Development) for funding the research through the Institutional Scholarship Program for Initiation in Technological Development and Innovation (PIBITI). References Allain, C., & Cloitre, M. (1991). Characterizing the lacunarity of random and deterministic fractal sets, Physics Review A, 44, 3552-8. Alves Junior, S., & Barros Filho, M. N. M. (2006). Enhancing urban analysis through lacunarity multiscale measurement. CASA Working Paper Series , 97 08 | 05. Amorim, L. M., Barros Filho, M. N. M., & Cruz, D. (2014). Urban texture and space configuration: An essay on integrating socio-spatial analytical techniques. Cities . 39, 58–67. http://dx.doi.org/10.1016/j.cities.2014.02.001 Amorim, L. M., & Barros Filho, M. (2017). Convergência de métodos de descrição da forma urbana: análise de textura de imagens de satélite e análise gráfica visual. Revista De Morfologia Urbana , 5 (2), 65–81. https://doi.org/10.47235/rmu.v5i2.3 Barros Filho, M. N. M. (2009). Detecção de padrões morfológicos intra-urbanos a partir da interpolação por Krigagem Ordinária dos valores de lacunaridade obtidos em imagens de satélite de alta resolução espacial. In: Simpósio Brasileiro de Sensoriamento Remoto. Natal. Barros Filho, M. N. M. (2006). As múltiplas escalas da diversidade intra-urbana: uma análise de padrões socioespaciais no Recife. Thesis, Universidade Federal de Pernambuco, Recife. Barros Filho, M. N. M., & Sobreira, F. (2005). Assessing Texture Pattern in Slum Across Scales An Unsupervised Approach. CASA Working Paper Series , 87 03 | 05. Barros Filho, M. N. M., & Sobreira, F. (2007). Urban Textures: A Multiscale Analysis of socio-spatial patterns. 10th International Conference on Computers in Urban Planning and Urban Management (CUPUM) , Reviewed Paper. Barros Filho, M. N. M., Simões, M. B., & Silva, Y. S. A. (2022). Medidas de densidade e lacunaridade na discriminação da forma urbana: o caso das Zeis em Campina Grande, PB. Paisagem E Ambiente , 33 (49), e190642. Barros Filho, M. N. M., & Monteiro, C. M. G. (2011). "Chapter 7 Segmented Cities with Fuzzy Walls: Changes in Informal Settlements as Seen Through a Multiscale Analysis", Perrone, C., Manella, G. and Tripodi, L. (Ed.) Everyday Life in the Segmented City (Research in Urban Sociology, Vol. 11), Emerald Group Publishing Limited, Leeds, pp. 143-167. https://doi.org/10.1108/S1047-0042(2011)0000011010 Batty, M., & Longley, P. (1994). Fractal cities: a geometry of form and function . Academic Press, London. Borys, P., Krasowska, M., Grzywna, Z., Djamgoz, M. B. A., & Mycielska, M. E. (2008). Lacunarity as a novel measure of cancer cells behavior. Biosystems , 94(3). Captur, G., Muthurangu, V., Cook, C., et al. ( ). Quantification of Left Ventricular Trabeculae Using Fractal Analysis. Journal of cardiovascular magnetic resonance . 15:36. Dong, P. (2000) Test of a new lacunarity estimation method for image texture analysis. International Journal of Remote Sensing . 21(17), 3369-73. Farr, D. (2013). Urbanismo Sustentável: Desenho Urbano com a Natureza. Porto Alegre: Bookman. Fávero, L. P. L., Belfiore, P. P.; Silva, Fabiana L. da., & Chan, B. L. (2009) . Análise de Dados: Modelagem Multivariada para tomada de decisões. Elsevier. Frankhauser, P. (1997). “Fractal analysis of urban structures” In: Holm, E. (Ed). Modeling space and networks: Progress in theoretical and quantitative geography (Gerum Kulturgeografi, Umea) 145-181. Greenhill, D., Ripke, L.T., Hitchman, A.P., Jones, G.A., & Wilkinson, G. G. (2003) Use of Lacunarity index to characterize suburban areas for land use planning using IKONOS-2 multispectral imagery. In: 2nd GRS/ISPRS Joint Workshop on Remote Sensing and Data Fusion over Urban Areas . Berlin, Germany. Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (2005). Análise Multivariada de Dados. 5ª edição, Porto Alegre: Bookman. Han, N., Wu, J., Tahmassebi, A. R. S., Xu, H., & Wang, K. (2011). NDVI-Based Lacunarity Texture for Improving Identification of Torreya Using Object-Oriented Method. Agricultural Sciences in China , 10(9), pp. 1431–1444. Jelinek, H. F. A., Karperien, D., Cornforth, R. M. Jr. C., J. Leandro. (2002). "Micromod—an LSystems Approach to Neuron Modelling". In: Sixth Australia-Japan Joint Workshop on Intelligent and Evolutionary Systems AJJWIES '02. Sarker, R., Mckay, B., Gen, M., & Namatame, A. editors. Australian National University, Canberra, Australia. Kambesis, P. N., Larson, E. B., & Mylroie, J. E. (2016). Morphometric analysis of cave patterns using fractal indices. The Geological Society of America , Special Paper, 516. Karperien, A. (2012). FracLac to ImageJ , version 2.5. Karperien, A., Jelinek, H. F., & Milosević, N. T. (2011). Reviewing Lacunarity Analysis and Classification of Microglia in Neuroscience. Proceedings of the 8th European Conference on Mathematical and Theoretical Biology , ESMTB. Kit, O., Lüdeke, M., & Reckien, D. (2012). Texture-based identification of urban slums in Hyderabad, India using remote sensing data. Applied Geography (Sevenoaks, England) , 32(2), 660-667. http://dx.doi.org/10.1016/j.apgeog.2011.07.016 Kilic, K., & Abiyev, R. (2011). Exploiting the synergy between fractal dimension and lacunarity for improved texture recognition. Signal Processing . 91. 2332-2344. 10.1016/j.sigpro.2011.04.018. Kohli, D., Sliuzas, R., Kerle, N., & Stein, A. (2012). An ontology of slums for image-based classification. Computers, Environment and Urban Systems , 36(2), pp. 154–163. Kuffer, M., Pfeffer, K., & Sliuzas, R. (2016). Slums from Space - 15 Years of Slum Mapping Using Remote Sensing. MDPI , [S. l.], p. 1-29, 27. Leão, D. Z. (2011). Análise da Textura Urbana para mapeamento da precariedade habitacional. Dissertação de mestrado, Programa de Pós-Graduação em Planejamento Urbano e Regional. Universidade Federal do Rio Grande do Sul. Leao, S., & Leao, D. (2011). Targeting Housing Problems through Urban Texture Analysis. In: Proceedings of the 12th International Conference on Computers in Urban Planning and Urban Management , Lake Louise, AB, Canada, 5–8 July. Mandelbrot, B. (1995). Measures of fractal lacunarity: Minkowski content and alternatives. Progress in Probability, 37, 15–42. Mandelbrot, B. B. (1982). The fractal geometry of nature (Freeman, New York). Mahabir, R., Croitru, A., Crooks, A., Agouris, P., & Stefanidis, A. (2017). A Critical Review of High andVery High-Resolution Remote Sensing Approaches for Detecting and Mapping Slums: Trends, Challenges And Emerging Opportunities. Urban Scienc e 2(1), 1–38. Murueta-Goyena, A., Barrenechea, M., Erramuzpe, A., Teijeira-Portas, S., Pengo, M., Ayala, U., Romero-Bascones, D., Acera, M., Del Pino, R., Gómez-Esteban, JC., & Gabilondo, I. (2021). Foveal Remodeling of Retinal Microvasculature in Parkinson’s Disease. Front. Neurosci. 15:708700. doi: 10.3389/fnins.2021.708700 Myint, S., & Lam, N. (2005). A study of lacunarity-based texture analysis approaches to improve urban image classification, Computer, Environment and Urban Systems 21, 501-523. Owen, K. K., & Wong, D. W. (2013). An approach to differentiate informal settlements using spectral, texture, geomorphology and road accessibility metrics. Applied Geography , 38, 107–118. Pereira, E. T., Barros Filho, M. N. M., Simões, M. B.; & Bezerra Neto, J. A. (2022). Automatic detection of deprived urban areas using Google EarthTM images of cities from the Brazilian semi-arid region. city. Revista Brasileira de Gestão Urbana (URBE) , 14, e20210209. Plotnick, R., Gardner, R., Hasgrove, W., & Prestegaard, K. (1996). Lacunarity analysis: a general technique for the analysis of spatial patterns, Physical Review 55(5), 5461-68. Reuß, F. (2017). Detection of favelas in Brazil using texture parameters and machine learning . Rosenberg, M. S., & Anderson, C. D. (2011). PASSaGE: Pattern Analysis, Spatial Statistics and Geographic Exegesis. Version 2. Methods in Ecology and Evolution , 2: 229-232. https://doi.org/10.1111/j.2041-210X.2010.00081.x Roy, A., & Sivaji, L. (2022). Quantifying Connectivity of Fracture Networks: A Lacunarity Approach. 3rd International Discrete Fracture Network Engineering Conference , Santa Fe, New Mexico, USA. doi: https://doi.org/10.56952/ARMA-DFNE-22-0049 Sampurno, J., Apriansyah, A., Adriat, R., & Srigutomo, W. (2018). Fractal analysis of land surface temperature for geothermal and non-geothermal sites characterization. Journal of Physics: Conference Series. 1028. 012198. 10.1088/1742-6596/1028/1/012198. Schneider, C. A., Rasband, W. S., & Eliceiri, K. W. (2012). NIH Image to ImageJ: 25 years of image analysis. Nature Methods , 9 (7), 671–675. doi:10.1038/nmeth.2089 Simões, M. B., & Barros Filho, M. N. M. (2022). Da textura orbital à superfície social: investigando padrões socioespaciais através da lacunaridade e habitabilidade. Revista De Morfologia Urbana , 10 (2). https://doi.org/10.47235/rmu.v10i2.241 Simões, M. B., Anjos, K. L. dos., & Barros Filho, M. N. M. (2024). Investigando a fragmentação socioespacial a partir de assentamentos precários designados como Zonas Especiais de Interesse Social. Revista De Morfologia Urbana , 12 (2). https://doi.org/10.47235/rmu.v12i2.403 Simões, M. B., Anjos, K. L. dos., & Barros Filho, M. N. M. (2024). Quais os limites da segregação socioespacial? Contribuições metodológicas para classificação de Zonas Especiais de Interesse Social (ZEIS). Caderno de Geografia. 34(78). https://doi.org/10.5752/p.2318-2962.2024v3,4n78p846 Su, H., & Krummel, J. Lacunarity as a Texture Measure for a Tropical Forest Landscape. (1996). Environment Assessment Division , ERDAS Users Group Meeting, January 25. Scott, R., Kadum, H., Salmaso, G., Calaf, M., & Cal, R. B. (2022). A lacunarity-based index for spatial heterogeneity. Earth and Space Science , 9, e2021EA002180. https://doi.org/10.1029/2021EA002180 Smith, T. G., Jr, Lange, G. D., & Marks, W. B. (1996). Fractal methods and results in cellular morphology--dimensions, lacunarity and multifractals. Journal of neuroscience methods , 69 (2), 123–136. https://doi.org/10.1016/S0165-0270(96)00080-5 Veiga, M. E. B. da, Simões, M. B., Barros Filho, M. N. M., & Galvão, C. de O. (2024). A suscetibilidade às inundações em extremos climáticos: o papel da morfologia urbana revelado por análise multicriterial. Paranoá , 17 , e47439. https://doi.org/10.18830/1679-09442024v17e47439 Wang, J., Kuffer, M., & Pfeffer, K. (2018). The role of spatial heterogeneity in detecting urban slums. Computers, Environment and Urban Systems , v. 73, pp. 95-107. https://doi.org/10.1016/j.compenvurbsys.2018.08.007 Yadav N., Mohanty A. V. A., & Tiwari V. (2024). Fractal dimension and lacunarity measures of glioma subcomponents are discriminative of the grade of gliomas and IDH status. NMR in Biomedicine . 37(12):e5272. doi:10.1002/nbm.5272 Yasar, F., & Akgünlü, F. (2005). Fractal dimension and lacunarity analysis of dental radiographs. Dento maxillo facial radiology , 34 (5), 261–267. https://doi.org/10.1259/dmfr/85149245 Footnotes FRACLAC for ImageJ, version 2.5. Available at: https://imagej.net/ij/plugins/fraclac/FLHelp/Introduction.htm . Accessed on: Feb. 10, 2024. Citations to FRACLAC. Available at: https://imagej.net/ij/plugins/fraclac/FLHelp/FLCitations.htm . Accessed on: Feb. 10, 2024. In this paper, we will use the term sample or image for the image under study, and cell for each unit of the partitioning of this image, a process that was carried out in the LACUNAE software. When the Overlap is 0%, it implies that the cells will be analyzed in a juxtaposed manner, with no overlap between them. These cells were processed using the Gliding Box algorithm (Dong, 2000 ), considering in the case of the 150m x 150m (250 x 250 pixels) cells, 6 box sizes with the following pixel sizes: 2, 4, 8, 16, 32 and 64. And in the case of 75m x 75m (125 x 125 pixels) cells, 5 box sizes with the following pixel sizes: 2, 4, 8, 16, 32. The reduction by one box is justified in order to preserve sliding. Subsequently, the average lacunarity was calculated for all the box sizes, and this value was taken into account in the discriminant analysis. It was decided not to run the scenario with 75m x 75m cells in the case of the Planet Sensor, since it is not possible to clearly distinguish morphological aspects of slums and non-slums areas in so few pixels. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 02 Jul, 2025 Reviews received at journal 02 Jul, 2025 Reviews received at journal 14 Jun, 2025 Reviewers agreed at journal 12 Jun, 2025 Reviewers agreed at journal 12 Jun, 2025 Reviewers invited by journal 12 Jun, 2025 Editor assigned by journal 11 Jun, 2025 Submission checks completed at journal 11 Jun, 2025 First submitted to journal 03 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6812524","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471201208,"identity":"942e687e-5e0d-4624-ba23-6ab236c62daf","order_by":0,"name":"Mauro Normando Macêdo Barros Filho","email":"","orcid":"","institution":"Federal University of Campina Grande","correspondingAuthor":false,"prefix":"","firstName":"Mauro","middleName":"Normando Macêdo Barros","lastName":"Filho","suffix":""},{"id":471201209,"identity":"3d5f4637-12e9-4f91-8df4-f15cf0b2eacc","order_by":1,"name":"Eanes Torres Pereira","email":"","orcid":"","institution":"Federal University of Campina Grande","correspondingAuthor":false,"prefix":"","firstName":"Eanes","middleName":"Torres","lastName":"Pereira","suffix":""},{"id":471201210,"identity":"8de773d2-bd17-4c29-a67e-827a7c55629d","order_by":2,"name":"Lucas Khalil Azevedo Dantas","email":"","orcid":"","institution":"Federal University of Campina Grande","correspondingAuthor":false,"prefix":"","firstName":"Lucas","middleName":"Khalil Azevedo","lastName":"Dantas","suffix":""},{"id":471201211,"identity":"b3156bc3-f55c-47a9-80c7-56f58dd1b0ce","order_by":3,"name":"Matheus Batista Simões","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYHACNgjFDCZtGNgbYGycgBlFSxoDzwGitUDAYcJadNvPH3vwsa2OQb6dO/HBhz/nE3ukmw8wF+7BrcXsTDK74cy2wwwGh3k3Axm3E3tkjiUwz3iGR8uBZDZp3rYDDAbMvNukeRtuJ+6XyDFgBrkOp5bzj9mk/4Ic1gzU8ufPucQeifwP+LXcANrC2Ab072GgFga2A0AtOQwEtDw2k+w5d5gH7JfetmRjoF8MDs/A67DEZxI/yurk5PvPbnzw44+dLDDEHj4uwKMFBngQTAkGBiI0oAAJEtWPglEwCkbBsAcAhCFQwL9Y+QcAAAAASUVORK5CYII=","orcid":"","institution":"Federal University of Pernambuco","correspondingAuthor":true,"prefix":"","firstName":"Matheus","middleName":"Batista","lastName":"Simões","suffix":""}],"badges":[],"createdAt":"2025-06-03 14:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6812524/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6812524/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84779532,"identity":"0d71662e-e972-4ae8-aa2e-2cf74fb051f8","added_by":"auto","created_at":"2025-06-17 09:22:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":61991,"visible":true,"origin":"","legend":"\u003cp\u003eLACUNAE’s operating flowchart. Source: Authors (2025).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/c8c486e666821346c341714f.png"},{"id":84781033,"identity":"1c324df4-60d1-44b1-ac51-153d5e6faabd","added_by":"auto","created_at":"2025-06-17 09:30:39","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":481683,"visible":true,"origin":"","legend":"\u003cp\u003eSelected image and its location in the city of Recife, Brazil. Source: Authors (2025).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/cb4961b2da9602925f8c3a5a.png"},{"id":84779533,"identity":"607f4d02-349f-495a-a6a5-163771cb3f8a","added_by":"auto","created_at":"2025-06-17 09:22:39","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":310056,"visible":true,"origin":"","legend":"\u003cp\u003eLACUNAE's main functions. Source: Authors (2025).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/9156337e13592d78c13ef340.png"},{"id":84779536,"identity":"d2cec221-e887-4217-8a54-7a985385546d","added_by":"auto","created_at":"2025-06-17 09:22:39","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":301623,"visible":true,"origin":"","legend":"\u003cp\u003ePossibilities for viewing LACUNAE results. Source: Authors (2025).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/6c0f57e8ff9a724dce3ce7bc.png"},{"id":84781038,"identity":"9cf2169e-a086-4c5d-8648-42828c5cd056","added_by":"auto","created_at":"2025-06-17 09:30:39","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":241376,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of lacunarity in specific areas of the image. Source: Authors (2025).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/404e1e3a7dae5bfee4b63525.png"},{"id":84779538,"identity":"04fa2586-eeb9-4aaa-8eff-5f4f7310b640","added_by":"auto","created_at":"2025-06-17 09:22:39","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":330599,"visible":true,"origin":"","legend":"\u003cp\u003eGrids with 75m x 75m and 150m x 150m cells, according to Barros Filho (2009).\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/b8fac072a99915582954d62f.png"},{"id":84782628,"identity":"619db7cd-1034-4da4-9a7a-ab643b6981db","added_by":"auto","created_at":"2025-06-17 09:46:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2471771,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6812524/v1/1df04371-2cb7-4856-8e35-a523676911e2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eLacunae: A Software for Lacunarity Analysis of Digital Images\u003c/p\u003e","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eIn the 1980s, investigations into the geometric complexity of natural forms, which were not properly understood by Euclidean geometry, inaugurated the field of Fractal Geometry. The term \u0026ldquo;fractal\u0026rdquo;, coined by Benoit Mandelbrot (1982), comes from the Latin \u0026ldquo;fractus\u0026rdquo; and means \u0026ldquo;fraction\u0026rdquo;. The nomenclature refers to the main characteristic of Fractal Geometry: self-similarity, which occurs when a given spatial pattern can be visualized at multiple scales and its \u0026ldquo;fractions\u0026rdquo; being similar to its totality. Some models seek to reproduce the self-similarity of fractals, such as Sierpinski\u0026apos;s Triangle, Koch\u0026apos;s Snowflake, Mandelbrot\u0026apos;s Set, among others. However, studies on fractals have sought not only to understand the modus operandi of their principles, but also to measure them in order to distinguish different spatial patterns.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAt first, studies involved in measuring fractal patterns, with the intention of distinguishing them, began to be applied in Physics (Plotnick \u003cem\u003eet al.\u003c/em\u003e 1996), Biology (Smith Junior \u003cem\u003eet al.\u003c/em\u003e 1996), Neurosciences (Karperien, 2011) and other areas of Medicine (Yasar \u003cem\u003eet al.\u0026nbsp;\u003c/em\u003e2005; Borys \u003cem\u003eet al\u003c/em\u003e. 2008) that evaluate texture patterns in digital images such as those capture by X-rays and CT scans. Later, applications of fractals emerged in the fields of Remote Sensing (Su \u0026amp; Krummel, 1996), Geomorphology (Kambesis \u003cem\u003eet al.\u0026nbsp;\u003c/em\u003e2016), Environment (Sampurno\u003cem\u003e\u0026nbsp;et al.\u0026nbsp;\u003c/em\u003e2018) and Urban Planning (Batty \u0026amp; \u0026nbsp;Longley, 1994; Frankhauser, 1997).\u003c/p\u003e\n\u003cp\u003eLacunarity comes from the Latin \u0026ldquo;lacuna\u0026rdquo;, meaning \u0026ldquo;void\u0026rdquo;. It is a property of fractals that allows us to evaluate the distribution of \u0026ldquo;voids\u0026rdquo; in a spatial structure, at different scales. In urban planning, lacunarity makes it possible to analyze the dispersion, density, packing and permeability of the urban fabric (Barros Filho \u0026amp; Sobreira, 2005). Lacunarity may be obtained by calculating Sliding Boxes, which can be applied to both binary images (Allain \u0026amp; Cloitre, 1991) and grayscale images (Dong, 2000). The result is a numerical value ranging from 1 to infinity. In general, more homogeneous texture patterns have values closer to 1 (Myint \u0026amp; Lam, 2005).\u003c/p\u003e\n\u003cp\u003eFractal dimension and lacunarity are among the most widely used metrics for investigating the fractal patterns of digital images in urban areas. Some studies discuss the existence of a synergy between them (Kilic \u0026amp; Abiyev, 2011; Yadav \u003cem\u003eet al.\u003c/em\u003e 2024). This paper focuses on lacunarity, as applications of this measure in urban areas have proven to be more efficient in distinguishing spatial patterns compared to the Fractal Dimension (Barros Filho, 2006). In urban studies, lacunarity has already been correlated with various indicators, such as Principal Component Analysis (PCA) (Pereira \u003cem\u003eet al\u003c/em\u003e., 2023), Line Detection (Kit \u003cem\u003eet al.\u003c/em\u003e, 2012), Visual Graph Analysis (Amorim \u0026amp; Barros Filho, 2017), Urban Density (Veiga \u003cem\u003eet al.\u003c/em\u003e, 2024), Habitability (Sim\u0026otilde;es \u0026amp; Barros Filho, 2022; Barros Filho, 2006) and Normalized Difference Vegetation Index (NDVI) (Han \u003cem\u003eet al.\u003c/em\u003e, 2012). In addition, lacunarity has contributed as an indicator in the construction of models and classifiers, especially in studies engaged in the identification and classification of informal areas at multiple intra-urban scales (Barros Filho \u0026amp; Sobreira, 2005, Mahabir \u003cem\u003eet al.\u003c/em\u003e, 2017; Pereira \u003cem\u003eet al.\u003c/em\u003e, 2023).\u003c/p\u003e\n\u003cp\u003eThere are many softwares that perform the lacunarity calculation proposed by Dong (2000), such as FRACLAC (Karperien, 2012) and PASSaGE (Rosemberg \u0026amp; Anderson, 2011). Several studies also use MATLAB to calculate lacunarity (Scott \u003cem\u003eet al.,\u003c/em\u003e 2022; Roy \u0026amp; Sivaji, 2022), as well as plugins for GIS software (ArcGIS, QGIS) and implementations in programming languages such as Python (Murueta-Goyena, 2021). This paper aims to present LACUNAE, a software under development which proposes to calculate lacunarity of urban areas, by manipulating a significant amount of images and generating a wide range of results, which can later be analyzed in GIS software and support urban studies.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo validate the results, the lacunarity values obtained by LACUNAE in a satellite image of an urban area located in the city of Recife, Brazil, were compared with the lacunarity values obtained by another reference software, FRACLAC, in the same spatial area. In this method, Discriminant Analysis (F\u0026aacute;vero \u003cem\u003eet al.,\u0026nbsp;\u003c/em\u003e2009; Hair \u003cem\u003eet al.\u003c/em\u003e, 2005) was applied in order to assess the potential of the lacunarity generated by LACUNAE to distinguish groups of values previously labeled as belonging to formal and informal urban areas. Thus, before describing the main features and functionalities of LACUNAE, as well as its advances in lacunarity analysis of urban areas, it is worth highlighting the features, possibilities and limitations of FRACLAC for this purpose.\u0026nbsp;\u003c/p\u003e"},{"header":"FRACLAC: POSSIBILITIES AND LIMITATIONS IN LACUNARITY ANALYSIS OF URBAN AREAS","content":"\u003cp\u003eDeveloped by Charles Sturt University in Australia, FRACLAC\u003ca href=\"#_ftn1\" name=\"_ftnref1\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e1\u003c/sup\u003e is a plugin for the ImageJ software (Schneider \u003cem\u003eet al.,\u003c/em\u003e 2012), which is available free of charge and which is used to process images. As it is open source, the ImageJ user community can create plugins with additional functionalities. FRACLAC is an established tool for studying fractal and lacunarity patterns, and it has been usually applied at medical, physical and biological areas associated with microscopy. The FRACLAC portal\u003ca href=\"#_ftn2\" name=\"_ftnref2\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e2\u003c/sup\u003e provides a large set of 73 experiments that took place mainly between 2002 and 2013 (Jelinek \u003cem\u003eet al.,\u0026nbsp;\u003c/em\u003e2002; Captur \u003cem\u003eet al.,\u003c/em\u003e 2013).\u003c/p\u003e\n\u003cp\u003eSince the 2000\u0026rsquo;s, many studies have used FRACLAC to calculate the fractal dimension and lacunarity of urban areas. Mahabir \u003cem\u003eet al.\u003c/em\u003e (2018) refer to Barros Filho and Sobreira (2005) as the first experiment to discriminate informal urban areas based on their multiscale properties. The authors (2005) used FRACLAC to analyze three binary images with urban configurations characterized by formality and informality. These high-resolution images were captured by the IKONOS satellite in the city of Campinas, Brazil. The fractal dimension and lacunarity were calculated and it was found that there was a high degree of similarity between the fractal patterns measured by the fractal dimension. However, the lacunarity values made it possible to distinguish different texture patterns in the cells. They concluded that lacunarity complemented fractal analysis by revealing the particularities behind fractal complexities.\u003c/p\u003e\n\u003cp\u003eSubsequently, Barros Filho (2006) used FRACLAC to carry out experiments in the city of Recife, Brazil, with binary images obtained from high spatial resolution satellite images and showed that it was possible to distinguish texture patterns in urban areas of the city with different habitability conditions. The lacunarity values obtained from these images were strongly correlated with the values of a Habitability Index (HI) constructed with data from the 2000 Demographic Census. Urban areas with better habitability conditions had higher gap values than urban areas with poorer conditions. These differences, however, tend to decrease when these areas are analyzed at larger scales. The methodology applied by Barros Filho (2006) consisted of selecting 30 cells based on a visual interpretation of the original satellite image, 15 of which belonged to urban areas with a high level of habitability and 15 to areas with a low level of habitability. The same size was set for all the cells to enable a comparison of the lacunarity values between them. By associating the black and white pixels of these sub-images with the city\u0026apos;s built and unbuilt spaces, it was possible to deduce that, at all the scales analyzed, the unbuilt spaces are smaller and more evenly distributed in the areas with the poorest living conditions in the city. This can be explained by the density and irregular occupation of the land in informal areas, generating a large number of small voids, while in formal areas occupation is more sparse and conforms to the parameters of the urban planning legislation in force.\u003c/p\u003e\n\u003cp\u003eBinary images do not represent the real textures of the original images. Some valuable information about the spatial arrangement of the gray levels in these images can be lost during the process of converting an 8-bit gray-level image into a binary image with only 1 bit (Dong, 2000; Myint \u0026amp; Lam, 2005). Later results also obtained in FRACLAC with the same cells analyzed by Barros Filho (2006) in the city of Recife - by applying the Gliding-Box and Differential Box-Counting algorithms to binary images and images with 256 gray levels, respectively - revealed that the latter is capable of improving the percentage of images correctly classified as belonging to urban areas with low and high habitability conditions by up to 40% (Barros Filho \u0026amp; Sobreira, 2008). In addition to distinguishing slums from non-slums in Recife, another experiment carried out by Amorim, Barros Filho and Cruz (2014) using FRACLAC on images with 256 gray levels also made it possible to distinguish texture patterns in cells representing four specific neighborhoods in the same city, originating from very different occupation processes, revealing the potential of lacunarity measures in morphological studies.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eLacunarity analyses with FRACLAC have been tested on a variety of scales, manipulating images with different extensions, granulations and spatial resolutions, and sliding boxes with different sizes and spacings (Alves Junior \u0026amp; Barros Filho, 2006; Barros Filho \u0026amp; Sobreira, 2008). These include the application of discriminant analysis techniques (Barros Filho \u003cem\u003eet al.\u003c/em\u003e, 2022; Sim\u0026otilde;es \u003cem\u003eet al.,\u003c/em\u003e 2024) and the interpolation of lacunarity values by Ordinary Kriging (Barros Filho, 2009; Barros Filho \u003cem\u003eet al.,\u003c/em\u003e 2024). Brazil has concentrated a large number of these studies, which were inspired mainly by the international discussions on fractals that have impacted on various areas of knowledge. In this way, many experiments have also been carried out in other countries, whose methodologies, when observed under the current context of computational development, could be improved (Owen \u0026amp; Wong, 2013; Greenhill \u003cem\u003eet al.,\u003c/em\u003e 2006).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eLe\u0026atilde;o (2011) used FRACLAC to analyze the city of Canela, in the state of Rio Grande do Sul, Brazil. The author (2011) proposed a model that associated lacunarity data, based on a map of buildings, with income and infrastructure indexes, in order to estimate different housing standards. The model achieved high correlation values between the variables involved. However, even though the image was partitioned into 1,009 sections, it was necessary to select representative\u0026nbsp;cells for pre-established groups, resulting in a total of 67 cells, a much lower number. This procedure is mainly linked to the difficulty in finding tools that could perform the lacunarity calculation on a large number of cells. As mentioned before, FRACLAC has been applied to various areas of knowledge, and the software is not exclusively dedicated to urban analysis, generating a series of limitations that made some studies unfeasible, especially those that considered a large amount of data.\u003c/p\u003e\n\u003cp\u003eLacunarity analysis in urban areas should start with the following question: How many image cells are needed for a robust lacunarity analysis in an urban area? An experiment conducted by Wang \u003cem\u003eet al.\u0026nbsp;\u003c/em\u003e(2018), considering the spatial heterogeneity present in urban digital remote sensing images, as well as the laws of scale and anisotropy to which objects and patterns are subject, evaluated the importance of calibrating parameters related to granulations, extensions and directions. In general, the cells used did not go beyond the scale of neighborhoods and, in some cases, the scale of a city, requiring a large number of cells to assess the texture of the entire area.\u003c/p\u003e\n\u003cp\u003eDespite all advances with FRACLAC in the discrimination of urban areas, the following functions are not properly provided by the software: (i) creation of grids in images, a useful resource when the user starts from a satellite image of the entire urban area of a city and wants the lacunarity to be calculated in each cell\u003ca href=\"#_ftn3\" name=\"_ftnref3\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e3\u003c/sup\u003e of a pre-established grid, tools such as FRACLAC only accept one input at a time, making it impossible to calculate the lacunarity in several cells in a single process, substantially increasing the research time; (ii) support for the . geotiff format, FRACLAC focuses on .jpeg and .png formats, the loss of georeferencing information makes it impossible to represent the lacunarity values in geographical space and cross-reference them with other indicators; (iii) representation of the results, as it does not support georeferenced data, the result is made available in tabular and numerical format for each imported image cell, requiring the use of complementary GIS software to create maps and classify the results; (iv) consulting specific areas of the image, FRACLAC only generates a lacunarity value for the entire imported image, not taking into account the assessment of lacunarity in partitions within the image. Methodological limitations in current applications reduce the possibility of lacunarity being used more widely, as well as studies already carried out being widely replicated in other areas by other researchers and discussed in the scientific community.\u003c/p\u003e\n\u003cp\u003eTherefore, in all of these previously reported experiments with FRACLAC, the image selection process was conducted manually, considering only a small number of cells, and it was unable to detect the great diversity of urban textures that exist in these cities. In this context, recent research based on the application of Machine Learning approaches, which allows a large number of cells to be manipulated for the automatic detection of image texture patterns, is becoming increasingly important. This type of study has already used various indicators to train automatic classification algorithms (Pereira \u003cem\u003eet al.,\u003c/em\u003e 2023; Reu\u0026szlig;, 2017; Kit \u003cem\u003eet al.,\u0026nbsp;\u003c/em\u003e2012). To this end, the next sections describe the methodology used to develop LACUNAE and validate its results. \u0026nbsp;\u003c/p\u003e"},{"header":"LACUNAE: IMPROVING LACUNARITY ANALYSIS OF URBAN AREAS","content":"\u003cp\u003eLACUNAE is a registered software under development at Federal University of Campina Grande. The initiative of developing the software arose in 2019 from a scientific initiation project carried out at the Urban Open Spaces Laboratory (LELU) with the collaboration of the Computer Perception Laboratory (LPC). LACUNAE applies a Machine Learning algorithm for the automatic detection of urban areas, considering exclusively the texture patterns of the images. It uses a Python code, which automated the calculation of lacunarity, facilitating both the import and parameterization of input images and the generation of output tables, maps and graphs. It is currently being improved through a scientific and technological development initiation project (PIBITI).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe first stage of LACUNAE\u0026apos;s development consisted of constructing a Python code based on experiments done by Sim\u0026otilde;es and Barros Filho (2022), Pereira\u003cem\u003e\u0026nbsp;et al.\u003c/em\u003e (2023) and Barros Filho \u003cem\u003eet al.\u003c/em\u003e (2024). Sim\u0026otilde;es and Barros Filho (2022) confronted the challenge of evaluating the entire urban area of Campina Grande, a medium-sized city in the state of Para\u0026iacute;ba, Brazil. An experimental code partitioned a Sentinel-2 image of the municipality into 19,044 cells and calculated the lacunarity of each of them, the results were then spatially associated with the assistance of GIS software. Pereira et al. (2023) detect deprived urban areas in six cities in the Brazilian semi-arid region using Sentinel-2 images and census data. The results obtained were more than 90% accurate, making an important contribution to slum mapping in cities lacking cartographic and sociodemographic bases. Barros Filho \u003cem\u003eet al.\u0026nbsp;\u003c/em\u003e(2024) applied the same code to distinguish socio-spatial patterns in Jo\u0026atilde;o Pessoa. From these experiments, a desktop application was developed, using the PySide 6 library and basic knowledge of UX Design. The development flow can be synthesized in the flowchart below (Fig 1):\u003c/p\u003e\n\u003cp\u003eThe operation of the software can be described as follow: (i) importing an image (tif, geotiff, tiff, png, jpg, bmp) obtained previously, the software redirects the user to the Google Earth Engine catalog, a platform on which the user can select the location and sensor from pre-established codes; (ii) definition of an image partitioning grid (Cells Size), sliding to maximize the number of partitions (Overlap) and manipulation of the parameters of the Gliding Box (Dong, 2000), such as the number of boxes, the size of the first box in pixels and the progression to the largest box on a linear or exponential scale; (iii) visualization of the results on the imported image, which can be configured in multiple forms of interpolation, color palette and transparency. Interpolation was applied because it was able to continuously represent the lacunarity values of each cell initially partitioned from the image, and the value of each was linked to its respective centroid; (iv) the possibility of generating basic statistics, represented numerically or in graphs, for specific areas of the image, unit cells or transepts of cells; and (v) exporting the lacunarity results for each cell in a table and georeferenced image, whose files can later be manipulated in GIS software, making it possible to cross-reference them with other databases. \u0026nbsp;\u003c/p\u003e"},{"header":"APPLYING LACUNAE TO DISCRIMINATE FORMAL FROM INFORMAL URBAN AREAS","content":"\u003cp\u003eLACUNAE was applied to calculate lacunarity of an image sample located in the city of Recife, Brazil, which includes two informal areas (Bras\u0026iacute;lia Teimosa and Pina/Encanta Mo\u0026ccedil;a) separated to each other by a formal urban area (Fig. 2). This image was chosen because it was used in a previous paper which applied FRACLAC to differentiate lacunarity patterns between and within these informal areas (Barros Filho, 2009).\u003c/p\u003e\n\u003cp\u003eBras\u0026iacute;lia Teimosa is located on a peninsula formed by the meeting of the Atlantic Ocean and the Pina River, an area of high real estate value in the city of Recife. Since its initial occupation at the end of the 1940s, Bras\u0026iacute;lia Teimosa has suffered several threats of removal, which were minimized after the area was recognized by the Recife City Land Use and Occupation Law (Law n. 14.511 of 1983) as a Special Zone of Social Interest - ZEIS, officially recognizing the occupation and protecting it from the formal estate market. According to the National Register of Addresses for Statistical Uses, the result of the IBGE\u0026apos;s 2022 Brazilian Census, there are 9,182 addresses in Bras\u0026iacute;lia Teimosa, ranging from households to services and institutions. Considering its area of 5.27 hectares, there is an estimated density of 1,742 households per hectare.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eLACUNAE\u0026apos;s home screen is shown in Fig. 3. Three main functions are highlighted in color: \u0026ldquo;Open\u0026rdquo; (to import the satellite image, highlighted in red); \u0026ldquo;Run\u0026rdquo; (to process the imported image, highlighted in green); and \u0026ldquo;Results\u0026rdquo; (to display the results, highlighted in blue). If the user has already processed an image, it is possible to import the resulting table and view the results at any time without the need for reprocessing. In addition, the \u0026ldquo;Open\u0026rdquo; option can also redirect the user to the Google Earth Engine image catalog, from which they can obtain various free options, such as the Sentinel, Planet and Landsat sensors, with the possibility of filtering out clouds.\u003c/p\u003e\n\u003cp\u003eOn the processing screen (Fig. 3), the user can see the spatial resolution of the imported image and the number of resulting cells when they define the resolution of the cells that will be sectioned from the initial image, a parameter manipulated in the \u0026ldquo;Sample Size\u0026rdquo; option. The screen also provides the estimated time for the algorithm to run, based on the parameters configured by the user. The Overlap parameter, which is intended to maximize the number of cells, can substantially increase processing time when the user opts for low sliding rates\u003ca href=\"#_ftn4\" name=\"_ftnref4\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e4\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAfter setting the parameters for partitioning the main image, the user must define the parameters for calculating the lacunarity (Gliding Box). As proposed by Dong (2000), the gliding boxes calculate the lacunarity of each cell, each of which slides over it, calculating the average pixel intensity and the mass frequency distribution of the boxes. LACUNAE allows you to configure the number of boxes (N\u0026deg; Boxes), the size of the initial box (First Size) and the way subsequent boxes are generated (Size Ratio). The values can also progress following an arithmetic (Linear) or geometric (Geometric) progression. The \u0026ldquo;Back to Default\u0026rdquo; option returns the settings to a pre-established initial default. \u0026quot;Run\u0026rdquo; proceeds to processing and \u0026ldquo;Run, saving samples in folder\u0026rdquo; saves the cells obtained as an image in a user-defined folder.\u003c/p\u003e\n\u003cp\u003eAfter processing the image, the screen highlighted in blue (Fig. 4) shows the user the interpolated results superimposed on the initial image (input), alongside basic statistics considering all the calculated cells. Details regarding the interval (Min and Max) of the classification, transparency and type of interpolation can be manipulated. The possibility of modifying the classification interval, generated automatically from the lacunarity values obtained, is useful for mitigating possible distortions in the classification caused by outlier values.\u003c/p\u003e\n\u003cp\u003eThe \u0026ldquo;Edit Colormap\u0026rdquo; button presented in the \u0026ldquo;viewing results\u0026rdquo; screen \u0026nbsp;shown in Fig. 3 opens a dialog box (Fig. 4) to simulate a progression from 2 to 1,000 classes, also demonstrating different types of interpolations using the image of the study area as an example. Initial, final and intermediate colors can also be customized by the user. In the example, the \u0026ldquo;custom\u0026rdquo; color map is the default option, but it is also possible to apply ready-made palettes, such as the \u0026ldquo;Accent\u0026rdquo; and \u0026ldquo;CMRmap\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003eThe \u0026ldquo;Save\u0026rdquo; button (Fig. 3) saves the results in three different formats: a PNG file with the RGB bands; a TXT file with the parameters used; a copy of the original image; and a XLSX file with the lacunarity values organized in matrix format, i.e. breaking down the row and column of the matrix that generated the interpolation. In the case of georeferenced images, a fourth artifact is made available, with the image in geotiff whose lacunarity values are the only band in the image.\u003c/p\u003e\n\u003cp\u003eFig. 5 shows two functionalities available in the \u0026ldquo;Plot Data\u0026rdquo; button on the \u0026ldquo;viewing results\u0026rdquo; screen in Fig. 3. The user can create line graphs and box plots based on the selection of cells, with three possibilities: selection of a square, selection of a cell, and selection of a transept between two cells. The \u0026ldquo;Transept\u0026rdquo; option was implemented based on Farr\u0026apos;s (2013) concept, inspired by Alexander Von Humboldt and appropriated by Duany Plater-Zyberk, intended to reveal a sequence of land occupation patterns in a transition from urban to rural areas. This feature is useful for evaluating the behavior of lacunarity as the cell moves away from one location to another. The boxplot graph makes it possible to compare the lacunarity values of different selections drawn on the image. In a test carried out (Fig. 5), it can be seen that the lacunarity values decrease as the cells enter into Bras\u0026iacute;lia Teimosa; however, they suddenly increase as the cells approach a marina at the tip of the peninsula, a region with a greater amount of open spaces.\u003c/p\u003e"},{"header":"VALIDATING LACUNAE BASED ON FRACLAC RESULTS","content":"\u003cp\u003eIn order to validate LACUNAE, its lacunarity values were compared with those obtained by Barros Filho (2009) using FRACLAC for the same image, considering the same parameters. In the study carried out by Barros Filho (2009), lacunarity values were obtained from a Quickbird image with 0.60m spatial resolution, sectioned into two grids: 150m x 150m cells and 75m x 75m cells (Fig. 6).\u003ca href=\"#_ftn5\" name=\"_ftnref5\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e5\u003c/sup\u003e The results were generated by FRACLAC and classified using a k-means algorithm. The author (2009) observed that the slum areas had much lower lacunarity values than the formal areas.\u003c/p\u003e\n\u003cp\u003eThis was subsequently followed by an analysis of lacunarity in a more recent image of the area, collected between 2023 and 2024 on the Google Earth Engine platform. This image refers to the Planet sensor which has a spatial resolution of 5 meters and only the 150m x 150m scenario was partitioned in LACUNAE, equivalent in this case to 30 x 30 pixels\u003ca href=\"#_ftn6\" name=\"_ftnref6\" title=\"\"\u003e\u003c/a\u003e\u003csup\u003e6\u003c/sup\u003e. The cells were processed using the Gliding Box algorithm (Dong, 2000), considering boxes with the following pixel sizes: 2, 4, 6, 8, 10 and 12. Despite the differences between the Quickbird and Planet images, the purpose of this increment is to verify the accuracy of LACUNAE considering images with lower granulation, i.e. worse spatial resolutions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSummarizing, lacunarity data were analyzed for two groups (formal and informal urban areas) considering the Quickbird sensor scenario for 150m x 150m and 75m x 75m cells, generated by both FRACLAC and LACUNAE, totaling four analyses. For the Planet sensor, a single Discriminant Analysis was conducted considering the 150m x 150m cells. The cell sizes and their respective labels are shown in Figure 6.\u003c/p\u003e\n\u003cp\u003eIn the statistical evaluation, Discriminant Analysis (F\u0026aacute;vero \u003cem\u003eet al.,\u0026nbsp;\u003c/em\u003e2009; Hair \u003cem\u003eet al.,\u0026nbsp;\u003c/em\u003e2005) was used to calculate the difference between the lacunarity values of the two pre-established scenarios (formal and informal areas). The difference is calculated by a linear discriminant function based on the overlap of the data from each cell. For each of the pre-established groups, the method calculates a canonical mean, which refers to the average of the variables in a canonical space. The average represents the linear combinations of the variables that best distinguish the groups, in this case, lacunarity is the variable evaluated. The more distant the canonical averages are, the better the discrimination between the groups. The results of the Discriminant Analysis obtained with FRACLAC and LACUNAE software for each group are shown in Table 1.\u003c/p\u003e\n\u003cp\u003eTable 1 - Canonical mean of the discriminant analysis groups\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"617\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSoftware\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 93px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSensors\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 105px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eGrid\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 223px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDiscriminant analysis groups\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" style=\"width: 102px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDifference of averages\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 109px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eInformal Cells\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 114px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp; \u0026nbsp; Formal Cells\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 94px;\"\u003e\n \u003cp\u003eFRACLAC\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 93px;\"\u003e\n \u003cp\u003eQuickbird\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003e150m x 150m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e0,01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003e-0,13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 102px;\"\u003e\n \u003cp\u003e0,14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 93px;\"\u003e\n \u003cp\u003eQuickbird\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003e75m x 75m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e-0,12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003e-0,12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 102px;\"\u003e\n \u003cp\u003e0,0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 94px;\"\u003e\n \u003cp\u003eLACUNAE\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 93px;\"\u003e\n \u003cp\u003eQuickbird\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003e150m x 150m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e-0,10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003e-0,08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 102px;\"\u003e\n \u003cp\u003e0,02\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 93px;\"\u003e\n \u003cp\u003eQuickbird\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003e75m x 75m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e-0,09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003e0,19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 102px;\"\u003e\n \u003cp\u003e0,28\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 93px;\"\u003e\n \u003cp\u003ePlanet\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 105px;\"\u003e\n \u003cp\u003e150m x 150m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 109px;\"\u003e\n \u003cp\u003e0,20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 114px;\"\u003e\n \u003cp\u003e-0,14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 102px;\"\u003e\n \u003cp\u003e0,36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cem\u003eResults obtained using OriginPro and SPSS statistical software\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eComparing the difference in the canonical mean reveals which of the software and sensors performs best in this distinction. From the results in Table 1, it can be seen that the FRACLAC experiment in 150m x 150m cells was able to distinguish the slum and non-slum groups more accurately than LACUNAE, with a difference of 0.12 between the experiments. In the experiment on 75m x 75m cells, it was not possible to detect differences between the groups in FRACLAC, while it was possible to detect a significant difference of 0.28 in LACUNAE. The Planet sensor experiment at LACUNAE, whose resolution is lower than the Quickbird sensor, showed a better distinction between the averages.\u003c/p\u003e\n\u003cp\u003eDespite the differences on discrimination capabilities between LACUNAE and FRACLAC, the experiments conducted in this research provide evidence that the data extracted using LACUNAE allows patterns to be differentiated from lacunarity just as well as FRACLAC, since the lacunarity values generated by FRACLAC have already proved effective in distinguishing different urban digital images (Barros Filho, 2006; Barros Filho \u003cem\u003eet al.,\u003c/em\u003e 2022). Moreover, LACUNAE also allows different parameters to be processed and the usage of more accessible images than those from the Quickbird sensor.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eUsing data from the Quickbird sensor scenarios, it was not possible to reproduce the same results, even importing the same parameters and using the lacunarity calculation. This is because, although the logic of the calculation is based on Dong (2000), each software has its own unique way of implementing it, sometimes using different programming languages, as well as other minor issues that make it unlikely that the results will be the same. In short, even if the code and parameters are the same, different codes imply different lacunarity results.\u003c/p\u003e\n\u003cp\u003eThese features that differentiate LACUNAE from FRACLAC need to be investigated further, however, LACUNAE offers a greater possibility of maximizing the volume of data, establishing smaller windows and box sliding, as well as performing the calculations over a much shorter period of time. In addition, LACUNAE allows better analysis and comparison of patterns from a single image, through the square and transept options, making it innovative in this respect.\u003c/p\u003e\n\u003cp\u003eThe diversity of results also reproduces what was found by Wang (2018), that urban texture indicators are ruled by the laws of scale and anisotropy. In this context, there are many distinctions in the parameters, such as the size of the window and the resolution of the sensor, which will imply different results. In this case, the Planet sensor proved to be superior to the Quickbird sensor, despite its lower spatial resolution, in distinguishing slum areas from non-slum areas. This type of finding can help studies on the identification of precarious settlements using Machine Learning (Kuffer \u003cem\u003eet al.,\u003c/em\u003e 2016; Kohli \u003cem\u003eet al.,\u0026nbsp;\u003c/em\u003e2012), since investing in better resolution images does not necessarily imply greater accuracy in the results.\u003c/p\u003e\n\u003cp\u003eFinally, it should be highlighted that there are geographic limitations in the study area, which was selected in order to compare it with previous studies by Barros Filho (2009). Most of the cells after the image intersection refer to the ocean and were not used in the discriminant analysis. If they had been used, the difference between the groups would certainly have been much greater, as can be seen from the classifications shown in Fig. 4. Lacunarity analysis is more accurate at distinguishing occupied and unoccupied areas than slum areas from non-slum areas, as there is no consensus that all slum areas will have low lacunarity or that all non-slum areas will have higher lacunarity. Sim\u0026otilde;es and Barros Filho (2022) found the existence of slums with different texture patterns. In this context, LACUNAE should be further tested in order to differentiate between groups that may have similar characteristics at certain cut-off points and scales.\u003c/p\u003e"},{"header":"CONCLUSIONS","content":"\u003cp\u003eLACUNAE has proven to be a promising application for automating the analysis of lacunarity in geospatial images, and its development contributes to the scientific community interested in analyzing and comparing different morphological patterns in cities. The approach with which LACUNAE was implemented could be a model to drive projects to automate indicators related to remote sensing, such as other texture measures based or not on fractal logic.\u003c/p\u003e \u003cp\u003eDifferent from the software already widespread in the academic community, LACUNAE's great advantage is the possibility of multiplying the amount of data by sectioning images into smaller cells and comparing the results of different areas of the image with each other, using descriptive statistics and graphs. It also represents the results under the image using different interpolation methods. All these features avoid the use of other software for these purposes and simplify geoprocessing methodologies. Adapting these applications into an intuitive interface can make lacunarity analysis more accessible to the academic community, especially those who are not yet adept at manipulating programming codes, as it was once necessary in previous experiments (Sim\u0026otilde;es \u0026amp; Barros Filho, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eLACUNAE is not yet openly available, as it is currently under development, minimizing possible bugs, perfecting operations and adding new tools. Other studies should be carried out to demonstrate the potential of this software to distinguish urban patterns and develop studies in the field of urban and regional planning. Future versions of LACUNAE will bring its API version, allowing its library to be linked to other software based on texture pattern recognition.\u003c/p\u003e \u003cp\u003eResearch of this nature is important because it combines urban spatial analysis with current computational knowledge, strengthening methods already established in the literature and reverberating in the research economy. In this case, the main saving was in terms of time, since calculating the lacunarity cell by cell in the entire urban area of cities, especially the larger ones, would be unfeasible. Research scales such as these will later be the subject of LACUNAE research.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data used to generate the results of this article can be made available by the authors.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was funded by CNPq (National Council for Scientific and Technological Development) by Institutional Scholarship Program for Technological Development and Innovation Initiation (PIBITI). Despite funding during the course of the research, this paper does not have the availability of funds to pay for publication in open access. And due to the difficulties in raising funds, given the geographical location of the authors, we request the support of funds to enable this publication, if necessary.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMauro Normando Mac\u0026ecirc;do Barros Filho, Eanes Torres Pereira, Matheus Batista Sim\u0026otilde;es also helped with the writing of the article and the conceptual development of LACUNAE, Lucas Khalil Azevedo Dantas contributed specifically to the programming of LACUNAE.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank CNPq (National Council for Scientific and Technological Development) for funding the research through the Institutional Scholarship Program for Initiation in Technological Development and Innovation (PIBITI).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAllain, C., \u0026amp; Cloitre, M. (1991). Characterizing the lacunarity of random and deterministic fractal sets, \u003cem\u003ePhysics Review A,\u003c/em\u003e 44, 3552-8. \u003c/li\u003e\n\u003cli\u003eAlves Junior, S., \u0026amp; Barros Filho, M. N. M. (2006). Enhancing urban analysis through lacunarity multiscale measurement. \u003cem\u003eCASA Working Paper Series\u003c/em\u003e, 97 08 | 05.\u003c/li\u003e\n\u003cli\u003eAmorim, L. M., Barros Filho, M. N. M., \u0026amp; Cruz, D. (2014). Urban texture and space configuration: An essay on integrating socio-spatial analytical techniques. \u003cem\u003eCities\u003c/em\u003e. 39, 58\u0026ndash;67. http://dx.doi.org/10.1016/j.cities.2014.02.001\u003c/li\u003e\n\u003cli\u003eAmorim, L. M., \u0026amp; Barros Filho, M. (2017). Converg\u0026ecirc;ncia de m\u0026eacute;todos de descri\u0026ccedil;\u0026atilde;o da forma urbana: an\u0026aacute;lise de textura de imagens de sat\u0026eacute;lite e an\u0026aacute;lise gr\u0026aacute;fica visual. \u003cem\u003eRevista De Morfologia Urbana\u003c/em\u003e, \u003cem\u003e5\u003c/em\u003e(2), 65\u0026ndash;81. https://doi.org/10.47235/rmu.v5i2.3\u003c/li\u003e\n\u003cli\u003eBarros Filho, M. N. M. (2009). Detec\u0026ccedil;\u0026atilde;o de padr\u0026otilde;es morfol\u0026oacute;gicos intra-urbanos a partir da interpola\u0026ccedil;\u0026atilde;o por Krigagem Ordin\u0026aacute;ria dos valores de lacunaridade obtidos em imagens de sat\u0026eacute;lite de alta resolu\u0026ccedil;\u0026atilde;o espacial. In:\u003cem\u003e Simp\u0026oacute;sio Brasileiro de Sensoriamento Remoto.\u003c/em\u003e Natal.\u003c/li\u003e\n\u003cli\u003eBarros Filho, M. N. M. (2006). \u003cem\u003eAs m\u0026uacute;ltiplas escalas da diversidade intra-urbana: uma an\u0026aacute;lise de padr\u0026otilde;es socioespaciais no Recife.\u003c/em\u003e Thesis, Universidade Federal de Pernambuco, Recife.\u003c/li\u003e\n\u003cli\u003eBarros Filho, M. N. M., \u0026amp; Sobreira, F. (2005). Assessing Texture Pattern in Slum Across Scales An Unsupervised Approach. \u003cem\u003eCASA Working Paper Series\u003c/em\u003e, 87 03 | 05.\u003c/li\u003e\n\u003cli\u003eBarros Filho, M. N. M., \u0026amp; Sobreira, F. (2007). Urban Textures: A Multiscale Analysis of socio-spatial patterns. \u003cem\u003e10th International Conference on Computers in Urban Planning and Urban Management (CUPUM)\u003c/em\u003e, Reviewed Paper.\u003c/li\u003e\n\u003cli\u003eBarros Filho, M. N. M., Sim\u0026otilde;es, M. B., \u0026amp; Silva, Y. S. A. (2022). Medidas de densidade e lacunaridade na discrimina\u0026ccedil;\u0026atilde;o da forma urbana: o caso das Zeis em Campina Grande, PB. \u003cem\u003ePaisagem E Ambiente\u003c/em\u003e, \u003cem\u003e33\u003c/em\u003e(49), e190642.\u003c/li\u003e\n\u003cli\u003eBarros Filho, M. N. M., \u0026amp; Monteiro, C. M. G. (2011). \u0026quot;Chapter 7 Segmented Cities with Fuzzy Walls: Changes in Informal Settlements as Seen Through a Multiscale Analysis\u0026quot;, Perrone, C., Manella, G. and Tripodi, L. (Ed.) Everyday Life in the Segmented City (Research in Urban Sociology, Vol. 11), Emerald Group Publishing Limited, Leeds, pp. 143-167. https://doi.org/10.1108/S1047-0042(2011)0000011010\u003c/li\u003e\n\u003cli\u003eBatty, M., \u0026amp; Longley, P. (1994).\u003cem\u003e Fractal cities: a geometry of form and function\u003c/em\u003e. Academic Press, London.\u003c/li\u003e\n\u003cli\u003eBorys, P., Krasowska, M., Grzywna, Z., Djamgoz, M. B. A., \u0026amp; Mycielska, M. E. (2008). Lacunarity as a novel measure of cancer cells behavior. \u003cem\u003eBiosystems\u003c/em\u003e, 94(3).\u003c/li\u003e\n\u003cli\u003eCaptur, G., Muthurangu, V., Cook, C., \u003cem\u003eet al.\u003c/em\u003e ( ). Quantification of Left Ventricular Trabeculae Using Fractal Analysis. \u003cem\u003eJournal of cardiovascular magnetic resonance\u003c/em\u003e. 15:36.\u003c/li\u003e\n\u003cli\u003eDong, P. (2000) Test of a new lacunarity estimation method for image texture analysis. \u003cem\u003eInternational Journal of Remote Sensing\u003c/em\u003e. 21(17), 3369-73. \u003c/li\u003e\n\u003cli\u003eFarr, D. (2013). \u003cem\u003eUrbanismo Sustent\u0026aacute;vel: Desenho Urbano com a Natureza.\u003c/em\u003e Porto Alegre: Bookman.\u003c/li\u003e\n\u003cli\u003eF\u0026aacute;vero, L. P. L., Belfiore, P. P.; Silva, Fabiana L. da., \u0026amp; Chan, B. L. (2009)\u003cem\u003e. An\u0026aacute;lise de Dados: Modelagem Multivariada para tomada de decis\u0026otilde;es.\u003c/em\u003e Elsevier. \u003c/li\u003e\n\u003cli\u003eFrankhauser, P. (1997). \u0026ldquo;Fractal analysis of urban structures\u0026rdquo; In: Holm, E. (Ed). \u003cem\u003eModeling space and networks: Progress in theoretical and quantitative geography \u003c/em\u003e(Gerum Kulturgeografi, Umea) 145-181.\u003c/li\u003e\n\u003cli\u003eGreenhill, D., Ripke, L.T., Hitchman, A.P., Jones, G.A., \u0026amp; Wilkinson, G. G. (2003) Use of Lacunarity index to characterize suburban areas for land use planning using IKONOS-2 multispectral imagery. In: \u003cem\u003e2nd GRS/ISPRS Joint Workshop on Remote Sensing and Data Fusion over Urban Areas\u003c/em\u003e. Berlin, Germany. \u003c/li\u003e\n\u003cli\u003eHair, J. F., Anderson, R. E., Tatham, R. L., \u0026amp; Black, W. C. (2005).\u003cem\u003e An\u0026aacute;lise Multivariada de Dados.\u003c/em\u003e 5\u0026ordf; edi\u0026ccedil;\u0026atilde;o, Porto Alegre: Bookman.\u003c/li\u003e\n\u003cli\u003eHan, N., Wu, J., Tahmassebi, A. R. S., Xu, H., \u0026amp; Wang, K. (2011). NDVI-Based Lacunarity Texture for Improving Identification of Torreya Using Object-Oriented Method. \u003cem\u003eAgricultural Sciences in China\u003c/em\u003e, 10(9), pp. 1431\u0026ndash;1444.\u003c/li\u003e\n\u003cli\u003eJelinek, H. F. A., Karperien, D., Cornforth, R. M. Jr. C., J. Leandro. (2002). \u0026quot;Micromod\u0026mdash;an LSystems Approach to Neuron Modelling\u0026quot;. In: \u003cem\u003eSixth Australia-Japan Joint Workshop on Intelligent and Evolutionary Systems AJJWIES\u003c/em\u003e\u0026apos;02. Sarker, R., Mckay, B., Gen, M., \u0026amp; Namatame, A. editors. Australian National University, Canberra, Australia.\u003c/li\u003e\n\u003cli\u003eKambesis, P. N., Larson, E. B., \u0026amp; Mylroie, J. E. (2016). Morphometric analysis of cave patterns using fractal indices. \u003cem\u003eThe Geological Society of America\u003c/em\u003e, Special Paper, 516.\u003c/li\u003e\n\u003cli\u003eKarperien, A. (2012). \u003cem\u003eFracLac to ImageJ\u003c/em\u003e, version 2.5. \u003c/li\u003e\n\u003cli\u003eKarperien, A., Jelinek, H. F., \u0026amp; Milosević, N. T. (2011). Reviewing Lacunarity Analysis and Classification of Microglia in Neuroscience. \u003cem\u003eProceedings of the 8th European Conference on Mathematical and Theoretical Biology\u003c/em\u003e, ESMTB.\u003c/li\u003e\n\u003cli\u003eKit, O., L\u0026uuml;deke, M., \u0026amp; Reckien, D. (2012). Texture-based identification of urban slums in Hyderabad, India using remote sensing data. \u003cem\u003eApplied Geography (Sevenoaks, England)\u003c/em\u003e, 32(2), 660-667. http://dx.doi.org/10.1016/j.apgeog.2011.07.016\u003c/li\u003e\n\u003cli\u003eKilic, K., \u0026amp; Abiyev, R. (2011). Exploiting the synergy between fractal dimension and lacunarity for improved texture recognition. \u003cem\u003eSignal Processing\u003c/em\u003e. 91. 2332-2344. 10.1016/j.sigpro.2011.04.018.\u003c/li\u003e\n\u003cli\u003eKohli, D., Sliuzas, R., Kerle, N., \u0026amp; Stein, A. (2012). An ontology of slums for image-based classification. \u003cem\u003eComputers, Environment and Urban Systems\u003c/em\u003e, 36(2), pp. 154\u0026ndash;163.\u003c/li\u003e\n\u003cli\u003eKuffer, M., Pfeffer, K., \u0026amp; Sliuzas, R. (2016). Slums from Space - 15 Years of Slum Mapping Using Remote Sensing. \u003cem\u003eMDPI\u003c/em\u003e, [S. l.], p. 1-29, 27. \u003c/li\u003e\n\u003cli\u003eLe\u0026atilde;o, D. Z. (2011). \u003cem\u003eAn\u0026aacute;lise da Textura Urbana para mapeamento da precariedade habitacional.\u003c/em\u003e Disserta\u0026ccedil;\u0026atilde;o de mestrado, Programa de P\u0026oacute;s-Gradua\u0026ccedil;\u0026atilde;o em Planejamento Urbano e Regional. Universidade Federal do Rio Grande do Sul.\u003c/li\u003e\n\u003cli\u003eLeao, S., \u0026amp; Leao, D. (2011). Targeting Housing Problems through Urban Texture Analysis. In: \u003cem\u003eProceedings of the 12th International Conference on Computers in Urban Planning and Urban Management\u003c/em\u003e, Lake Louise, AB, Canada, 5\u0026ndash;8 July.\u003c/li\u003e\n\u003cli\u003eMandelbrot, B. (1995). \u003cem\u003eMeasures of fractal lacunarity:\u003c/em\u003e Minkowski content and alternatives. Progress in Probability, 37, 15\u0026ndash;42.\u003c/li\u003e\n\u003cli\u003eMandelbrot, B. B. (1982). \u003cem\u003eThe fractal geometry of nature\u003c/em\u003e (Freeman, New York).\u003c/li\u003e\n\u003cli\u003eMahabir, R., Croitru, A., Crooks, A., Agouris, P., \u0026amp; Stefanidis, A. (2017). A Critical Review of High andVery High-Resolution Remote Sensing Approaches for Detecting and Mapping Slums: Trends, Challenges And Emerging Opportunities. \u003cem\u003eUrban Scienc\u003c/em\u003ee 2(1), 1\u0026ndash;38.\u003c/li\u003e\n\u003cli\u003eMurueta-Goyena, A., Barrenechea, M., Erramuzpe, A., Teijeira-Portas, S., Pengo, M., Ayala, U., Romero-Bascones, D., Acera, M., Del Pino, R., G\u0026oacute;mez-Esteban, JC., \u0026amp; Gabilondo, I. (2021). Foveal Remodeling of Retinal Microvasculature in Parkinson\u0026rsquo;s Disease. Front. \u003cem\u003eNeurosci. \u003c/em\u003e15:708700. doi: 10.3389/fnins.2021.708700\u003c/li\u003e\n\u003cli\u003eMyint, S., \u0026amp; Lam, N. (2005). A study of lacunarity-based texture analysis approaches to improve urban image classification, \u003cem\u003eComputer, Environment and Urban Systems\u003c/em\u003e 21, 501-523.\u003c/li\u003e\n\u003cli\u003eOwen, K. K., \u0026amp; Wong, D. W. (2013). An approach to differentiate informal settlements using spectral, texture, geomorphology and road accessibility metrics. \u003cem\u003eApplied Geography\u003c/em\u003e, 38, 107\u0026ndash;118.\u003c/li\u003e\n\u003cli\u003ePereira, E. T., Barros Filho, M. N. M., Sim\u0026otilde;es, M. B.; \u0026amp; Bezerra Neto, J. A. (2022). Automatic detection of deprived urban areas using Google EarthTM images of cities from the Brazilian semi-arid region. city.\u003cem\u003e Revista Brasileira de Gest\u0026atilde;o Urbana (URBE)\u003c/em\u003e, 14, e20210209.\u003c/li\u003e\n\u003cli\u003ePlotnick, R., Gardner, R., Hasgrove, W., \u0026amp; Prestegaard, K. (1996). Lacunarity analysis: a general technique for the analysis of spatial patterns, \u003cem\u003ePhysical Review\u003c/em\u003e 55(5), 5461-68.\u003c/li\u003e\n\u003cli\u003eReu\u0026szlig;, F. (2017). \u003cem\u003eDetection of favelas in Brazil using texture parameters and machine learning\u003c/em\u003e.\u003c/li\u003e\n\u003cli\u003eRosenberg, M. S., \u0026amp; Anderson, C. D. (2011). PASSaGE: Pattern Analysis, Spatial Statistics and Geographic Exegesis. Version 2. \u003cem\u003eMethods in Ecology and Evolution\u003c/em\u003e, 2: 229-232. https://doi.org/10.1111/j.2041-210X.2010.00081.x\u003c/li\u003e\n\u003cli\u003eRoy, A., \u0026amp; Sivaji, L. (2022). Quantifying Connectivity of Fracture Networks: A Lacunarity Approach. \u003cem\u003e3rd International Discrete Fracture Network Engineering Conference\u003c/em\u003e, Santa Fe, New Mexico, USA. doi: https://doi.org/10.56952/ARMA-DFNE-22-0049\u003c/li\u003e\n\u003cli\u003eSampurno, J., Apriansyah, A., Adriat, R., \u0026amp; Srigutomo, W. (2018). Fractal analysis of land surface temperature for geothermal and non-geothermal sites characterization. \u003cem\u003eJournal of Physics: \u003c/em\u003eConference Series. 1028. 012198. 10.1088/1742-6596/1028/1/012198.\u003c/li\u003e\n\u003cli\u003eSchneider, C. A., Rasband, W. S., \u0026amp; Eliceiri, K. W. (2012). NIH Image to ImageJ: 25 years of image analysis. \u003cem\u003eNature Methods\u003c/em\u003e, \u003cem\u003e9 \u003c/em\u003e(7), 671\u0026ndash;675. doi:10.1038/nmeth.2089\u003c/li\u003e\n\u003cli\u003eSim\u0026otilde;es, M. B., \u0026amp; Barros Filho, M. N. M. (2022). Da textura orbital \u0026agrave; superf\u0026iacute;cie social: investigando padr\u0026otilde;es socioespaciais atrav\u0026eacute;s da lacunaridade e habitabilidade. \u003cem\u003eRevista De Morfologia Urbana\u003c/em\u003e, \u003cem\u003e10\u003c/em\u003e(2). https://doi.org/10.47235/rmu.v10i2.241\u003c/li\u003e\n\u003cli\u003eSim\u0026otilde;es, M. B., Anjos, K. L. dos., \u0026amp; Barros Filho, M. N. M. (2024). Investigando a fragmenta\u0026ccedil;\u0026atilde;o socioespacial a partir de assentamentos prec\u0026aacute;rios designados como Zonas Especiais de Interesse Social. \u003cem\u003eRevista De Morfologia Urbana\u003c/em\u003e, \u003cem\u003e12\u003c/em\u003e(2). https://doi.org/10.47235/rmu.v12i2.403\u003c/li\u003e\n\u003cli\u003eSim\u0026otilde;es, M. B., Anjos, K. L. dos., \u0026amp; Barros Filho, M. N. M. (2024). Quais os limites da segrega\u0026ccedil;\u0026atilde;o socioespacial? Contribui\u0026ccedil;\u0026otilde;es metodol\u0026oacute;gicas para classifica\u0026ccedil;\u0026atilde;o de Zonas Especiais de Interesse Social (ZEIS). \u003cem\u003eCaderno de Geografia.\u003c/em\u003e 34(78). https://doi.org/10.5752/p.2318-2962.2024v3,4n78p846\u003c/li\u003e\n\u003cli\u003eSu, H., \u0026amp; Krummel, J. Lacunarity as a Texture Measure for a Tropical Forest Landscape. (1996). \u003cem\u003eEnvironment Assessment Division\u003c/em\u003e, ERDAS Users Group Meeting, January 25.\u003c/li\u003e\n\u003cli\u003eScott, R., Kadum, H., Salmaso, G., Calaf, M., \u0026amp; Cal, R. B. (2022). A lacunarity-based index for spatial heterogeneity. \u003cem\u003eEarth and Space Science\u003c/em\u003e, 9, e2021EA002180. https://doi.org/10.1029/2021EA002180\u003c/li\u003e\n\u003cli\u003eSmith, T. G., Jr, Lange, G. D., \u0026amp; Marks, W. B. (1996). Fractal methods and results in cellular morphology--dimensions, lacunarity and multifractals. \u003cem\u003eJournal of neuroscience methods\u003c/em\u003e, \u003cem\u003e69\u003c/em\u003e(2), 123\u0026ndash;136. https://doi.org/10.1016/S0165-0270(96)00080-5\u003c/li\u003e\n\u003cli\u003eVeiga, M. E. B. da, Sim\u0026otilde;es, M. B., Barros Filho, M. N. M., \u0026amp; Galv\u0026atilde;o, C. de O. (2024). A suscetibilidade \u0026agrave;s inunda\u0026ccedil;\u0026otilde;es em extremos clim\u0026aacute;ticos: o papel da morfologia urbana revelado por an\u0026aacute;lise multicriterial. \u003cem\u003eParano\u0026aacute;\u003c/em\u003e, \u003cem\u003e17\u003c/em\u003e, e47439. https://doi.org/10.18830/1679-09442024v17e47439\u003c/li\u003e\n\u003cli\u003eWang, J., Kuffer, M., \u0026amp; Pfeffer, K. (2018). The role of spatial heterogeneity in detecting urban slums. \u003cem\u003eComputers, Environment and Urban Systems\u003c/em\u003e, v. 73, pp. 95-107. https://doi.org/10.1016/j.compenvurbsys.2018.08.007\u003c/li\u003e\n\u003cli\u003eYadav N., Mohanty A. V. A., \u0026amp; Tiwari V. (2024). Fractal dimension and lacunarity measures of glioma subcomponents are discriminative of the grade of gliomas and IDH status. \u003cem\u003eNMR in Biomedicine\u003c/em\u003e. 37(12):e5272. doi:10.1002/nbm.5272\u003c/li\u003e\n\u003cli\u003eYasar, F., \u0026amp; Akg\u0026uuml;nl\u0026uuml;, F. (2005). Fractal dimension and lacunarity analysis of dental radiographs. \u003cem\u003eDento maxillo facial radiology\u003c/em\u003e, \u003cem\u003e34\u003c/em\u003e(5), 261\u0026ndash;267. https://doi.org/10.1259/dmfr/85149245\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e FRACLAC for ImageJ, version 2.5. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://imagej.net/ij/plugins/fraclac/FLHelp/Introduction.htm\u003c/span\u003e\u003cspan address=\"https://imagej.net/ij/plugins/fraclac/FLHelp/Introduction.htm\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. Accessed on: Feb. 10, 2024.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Citations to FRACLAC. Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://imagej.net/ij/plugins/fraclac/FLHelp/FLCitations.htm\u003c/span\u003e\u003cspan address=\"https://imagej.net/ij/plugins/fraclac/FLHelp/FLCitations.htm\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. Accessed on: Feb. 10, 2024.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In this paper, we will use the term sample or image for the image under study, and cell for each unit of the partitioning of this image, a process that was carried out in the LACUNAE software.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e When the Overlap is 0%, it implies that the cells will be analyzed in a juxtaposed manner, with no overlap between them.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e These cells were processed using the Gliding Box algorithm (Dong, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2000\u003c/span\u003e), considering in the case of the 150m x 150m (250 x 250 pixels) cells, 6 box sizes with the following pixel sizes: 2, 4, 8, 16, 32 and 64. And in the case of 75m x 75m (125 x 125 pixels) cells, 5 box sizes with the following pixel sizes: 2, 4, 8, 16, 32. The reduction by one box is justified in order to preserve sliding. Subsequently, the average lacunarity was calculated for all the box sizes, and this value was taken into account in the discriminant analysis.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e It was decided not to run the scenario with 75m x 75m cells in the case of the Planet Sensor, since it is not possible to clearly distinguish morphological aspects of slums and non-slums areas in so few pixels.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"urban-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Urban Informatics](https://link.springer.com/journal/44212)","snPcode":"4212","submissionUrl":"https://submission.springernature.com/new-submission/44212/3","title":"Urban Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"lacunarity, software, images, urban areas","lastPublishedDoi":"10.21203/rs.3.rs-6812524/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6812524/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper aims to present the main features and functionalities of LACUNAE, a software for analyzing lacunarity of digital images, which represents an advance in the application of Fractal Geometry by implementing innovations in relation to other software of this nature already used by the scientific community. A satellite image sample, characterized by the presence of formal and informal areas in the city of Recife, Brazil, was used to validate LACUNAE, using Discriminant Analysis to investigate the software's ability to distinguish spatial patterns between formal and informal urban areas. The lacunarity results obtained showed consistently different canonical means for groups of cells with different urban forms, with the advantage of performing the calculation on a batch of images. This type of development has the potential to subsidize spatial analyses that consider lacunarity as the main texture metric, and its implementation logic can be replicated for other indicators useful in distinguishing urban morphological patterns in digital images.\u003c/p\u003e","manuscriptTitle":"Lacunae: A Software for Lacunarity Analysis of Digital Images","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-17 09:22:34","doi":"10.21203/rs.3.rs-6812524/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-02T08:11:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-02T06:48:23+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-14T08:41:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"258794330362514337914501102104005423832","date":"2025-06-13T03:21:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"264474121450281698756645806748584780404","date":"2025-06-12T16:48:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-12T15:25:05+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-11T07:26:57+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-11T07:24:23+00:00","index":"","fulltext":""},{"type":"submitted","content":"Urban Informatics","date":"2025-06-03T14:38:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"urban-informatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Urban Informatics](https://link.springer.com/journal/44212)","snPcode":"4212","submissionUrl":"https://submission.springernature.com/new-submission/44212/3","title":"Urban Informatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"90edd276-e5fb-4866-938b-69011d549253","owner":[],"postedDate":"June 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-08-27T03:53:28+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-17 09:22:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6812524","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6812524","identity":"rs-6812524","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}