Polarization super-pixel and feature template for feature extraction from Mueller matrix images

Polarization super-pixel and feature template for feature extraction from Mueller matrix 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 Polarization super-pixel and feature template for feature extraction from Mueller matrix images Jiachen Wan, Haojie Pei, Yue Yao, Hao Li, Wei Cui, Tongyu Huang, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5744002/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Mueller matrix images contain rich microstructural information, comprehensively encoded in the high-dimensional polarization feature space. While Mueller matrix is sensitive to microstructural changes down to subwavelength scale, how to extract the relevant polarization features remains a primary challenge for its applications. In this article, we propose a new approach to obtain characteristic pathological features from polarization pixels. At pixel-level, we divide the density distribution of the polarization pixels into a collection of elementary subsets of similar polarization features, named polarization super-pixels (PSP). These PSPs approximate the distribution in polarization space while containing no image-textural information, enabling polarization feature representation. By assigning specific weight coefficients to PSPs, we construct polarimetry feature templates (PFTs) that represent the polarization characteristics of specific pathological structure of interest. Using spatial labels from pathologists, we calculate PSP contributions and assign weight coefficients to create PFTs for identifying cancerous structures. Additionally, with region-of-interest (ROI)-level labels distinguishing cancerous and benign areas, we isolate PSPs sensitive to cancer and construct PFTs for ROI-level classification, including differentiation of cancer subtypes. Validation on pathological tissue slides demonstrates the stability and completeness property of the derived PSP and PFT. We showcase its clinical applications, such as propagating spatial labels from a limited number of labeled pixels to larger regions, and detecting malignancy or cancer-subtype differentiation at ROI-level, enhancing diagnostic workflows. Biomedical Engineering Mueller matrix imaging polarization imaging polarization super-pixels polarization feature template biophotonics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction While intensity-based imaging systems have been extensively utilized in histology and pathology, Mueller matrix (MM) imaging systems provide a more comprehensive characterization of light-tissue interactions by measuring both intensity and polarization properties 1 – 4 . This additional information enables MM imaging to differentiate microstructural features, such as birefringence and depolarization, which are otherwise indistinguishable with intensity-based imaging methods. Integrating these advantages into histology slide labeling can significantly improve the detection and classification of pathological features, thereby offering a transformative approach to clinical diagnostics. Mueller matrix images contain subwavelength microstructural information in each pixel, but extracting pathological features from high dimension polarization space is not trivial. Since the Mueller matrix elements lack explicit connections to the physical properties of a sample, it is often more convenient to use a set of know polarization basis parameters (PBP) to represent polarization features 5 . With the help of machine learning and supervised methods, previous studies have used PBPs as input, and extracted polarization features of cancerous structures from various types of tissues, such as breast cancer 6 – 9 , lung cancer 10 , 11 , cervical cancer 12 – 17 , and liver cancer 18 , 19 . Despite its ability to reveal hidden correlation between polarization and pathological features, unsupervised learning methods are underused. A recent study 20 explored how unsupervised learning can help extract polarization features from specimens. We use polarization basis parameters to represent the polarization characteristics of different tissues, and apply pixel clustering to show that pathological tissue can be decomposed into a set of basic microstructural components with potential pathological correlation. In the same study, polarization super-pixel was introduced as the method to compress polarimetric data volume while maintaining as much polarization feature information as possible 20 . Microstructural changes in tissues due to pathological variation affect the density distribution of polarization features. In this study, we take the polarization super-pixels approach even further to characterize biological specimen’s density distribution in polarization feature space. We apply unsupervised learning to partition the polarization pixels into many elementary subsets that characterizes polarization features of Mueller matrix images, which are the polarization super-pixels (PSP). The PSP construction process is purely based on polarization features, while no spatial or imagery features are considered. Different pathological features, which are usually characterized by different image features, correspond to different polarization feature. These features can be effectively represented using PSPs with specific weight coefficients, collectively referred to as the Polarization Feature Template (PFT). With a known initial spatial label, we compute the proportion of each PSP that overlaps with the spatial labels of specific pathological features, and thereby assign a weight coefficient to reflect their relative-contribution to the labelled regions. The specific set of PSP and their corresponding weight coefficients form a PFT, which is a disease-specific feature vector representing the distinctive polarization features of the labelled regions. Results demonstrate that we can construct the PFT for cancerous cells in lung adenocarcinoma, and spread the initial pathologist label to the entire field of view. For an alternative approach, we obtain the PFT coefficients using ROI-level labels provided by pathologists, such as “malignant or benign”. PFT would highlight a region in the ROI, the approach optimizes the PFT coefficients to maximize the difference in PFT-highlighted area between malignant and benign ROIs. Cross-validation shows that the PFT for identifying malignant regions achieves an AUROC of 96.14%, effectively distinguishing malignant from benign areas. Similarly, the PFT designed for cancer subtype differentiation can effectively differentiate ICC from HCC regions, achieving an AUROC of 91.08%. PFT essentially functions as the linkage, connecting polarization features to the pathological features of the specimen. Leveraging PSP and PFT the approach provides the capability to identify specific pathological features for assisted diagnosis, effectively reducing labor and time costs for pathologists. Furthermore, the use of Mueller matrix images and unsupervised learning-based analysis opens new avenues for exploring subtle pathological variations that may be overlooked by traditional methods. 2 Methods 2.1 Mueller matrix imaging To acquire the Mueller matrix images, histological slides from biopsy specimens are examined with a Mueller matrix microscope (MMM) that operates at 633nm wavelength and employs a 20x 0.4NA objective lens. With the chosen NA we can obtain a spatial resolution of 1 micron that enables the visualization of subcellular structures, while ensuring optimal precision in the Mueller matrix measurements. As shown in Fig. 1 a, the samples are imaged by the dual-DoFP MMM 21 whose polarization state analyzer consists of two division of focal plane (DoFP) polarimeters (2048 × 2448 pixels, 16-bit, PHX050S-PC, Lucid Vision Labs Inc., Canada). The device demonstrates high accuracy and adequate speed in Mueller matrix imaging, with a root mean square error below 0.01 and an acquisition time under 10 seconds 21 . 2.2 Pathological samples In this study, histological slides of lung adenocarcinoma, liver hepatocellular carcinoma and intrahepatic cholangiocarcinoma are used for Mueller matrix imaging and data analysis. Lung adenocarcinoma is a subtype of non-small cell lung cancer (NSCLC) that originates from glandular cells in the lung tissue. Lung adenocarcinoma is the most common form of lung cancer, accounting for about 40% of all NSCLC cases and more than 30% of all lung cancers 22 . Hepatocellular carcinoma (HCC) and intrahepatic cholangiocarcinoma (ICC) are the two most prevalent forms of primary liver cancer, ranking among the most commonly diagnosed cancers globally. The Mueller matrix images (MMI) are acquired using MM microscope. Figure 1 b shows an example of MMI whose 16 elements are normalized by M11 and diagonal elements are subtracted by 1. The lung cancer samples are obtained from the pathology department of Peking University Shenzhen Hospital, and the study is overseen and approved by the Ethics Committee of Peking University Shenzhen Hospital. The liver cancer Mueller matrix image data are obtained from the public datasets published in prior study 20 , including a total of 188 ROIs, consisting of both HCC and ICC subtypes divided into benign and cancerous regions. 2.3 Polarization super-pixels Unsupervised learning methods can reveal hidden correlations within polarization data, and it has been shown that pixel clustering can decompose the histological slide into a stable set of microstructural subtypes, each corresponds to a pathological structure 20 . Polarization super-pixel (PSP) was proposed as an essential pre-processing step before applying computationally taxing unsupervised algorithms, by clustering the polarization pixels in a single region of interest (ROI) of MMI into 1024 groups as super-pixels. It was proven to be effective for reducing the data volume while preserving polarimetric information of the Mueller matrix images 20 . In this work, we construct a stable and complete set of polarization super-pixels, by processing and clustering the polarization pixels from multiple ROIs from the same types of specimens for super-pixel calculation. We aim to extract the principal polarization features from the samples in the form of super-pixels, to be exploited for polarization feature representation. For a specific specimen, we can divide its polarization feature space into much finer elementary subsets, i.e. the set of PSP. Through approximation, such set of PSP can represent specifically shaped density distribution in polarization space, which means it can be used as a type of basis for polarization feature representation. It could also be interpreted as the polarization equivalent of “codebook” in natural image processing 23 . To construct such a PSP set, we need to cluster the polarization pixels from numerous ROI into roughly 100 ~ 1000 clusters, depending on the the complexity of the biological sample and time constraints. KMeans is one of the few classical unsupervised clustering algorithm that is capable of processing data at such scale 24 . In this work, we create polarization super-pixels with the following steps given the M11-normalized Mueller matrix images. First, we standardize the Mueller matrix elements of individual polarization pixels by subtracting the mean and dividing by the standard deviation. For each pixel in the Mueller matrix image located at \(\:(x,y)\) , the Mueller matrix elements \(\:{\left(M{M}_{\text{1,1}},M{M}_{\text{1,2}},\dots\:,M{M}_{\text{4,4}}\right)}_{x,y}\) are averaged to calculate \(\:{\mu\:}_{i,j}\) , and subsequently the standard deviation \(\:{\sigma\:}_{i,j}\) . The mean is then subtracted from each pixel value, and the result is divided by the standard deviation. It makes sure that each Mueller matrix elements are weighted equally for subsequent calculations, and it can be difficult if they are not standardized and with different scales. Then we apply the minibatch KMeans algorithm to all the polarization pixels in the ROI and cluster them into 1024 groups, using the 15 normalized \(\:({M}_{ij}/{M}_{11})\) and standardized Mueller matrix elements \(\:\) as features. We chose the minibatch variant of KMeans algorithm specifically, because it speeds up the KMeans algorithm significantly if the number of data points is large. Lastly, we compute and record the mean and standard deviation of the polarization parameters of choice, for each polarization super-pixel. We also keep track of the coordinates of the pixels that belong to each super-pixel. As the number of ROI increases, the classic KMeans algorithm is no longer capable of processing data with such data volume, because it simply does not fit in the memory for further processing. And in such case the mini-batch approach is considered, by dividing the ROIs into batches and achieve convergence recursively 25 . For the set of PSPs to function as a basis, ideally it should satisfy two criteria: stableness and completeness. A stable set of PSP implies that the centroids should converge to stable values; when new samples are added, these centroids should remain converged. A complete set of PSP implies that any polarization pixels from the same specimen that are obtained from new ROIs should be assigned to a pre-existing PSP. Following the proposed procedure, we should be able to systematically construct a stable set of PSPs, to approximate and represent the polarization characteristic of the given specimen. The stableness of the polarization super-pixels requires large number of ROIs from multiple patients, and how to process such a large amount of polarization pixels is challenging. We use the minibatch techniques from deep learning and big data, and process the pixels in batches. We test for stableness of the PSP by observing the convergence of inertia criteria. The stableness of the centroids can be demonstrated using the average shifts in centroids for the PSPs as the criteria (Fig. 2 a), similar to the within-cluster sum-of-square criteria 25 . The curve shows how the centroids positions change during mini-batch KMeans calculation of the PSPs for a single ROI, and the convergence of the absolute shift-distance to zero indicates that the centroids converged to stable values. We notice that there are irregular jumps in the curve, which are due to the centroid reassignments, which happens when the centroids are not stably converged yet. After about 2000 iterations, the centroid reassignment no longer occurs, which further indicate convergence. On the other hand, completeness means that the established set of PSP can be used to express all polarization features of the specimen, which can be tested by estimating the number of outliers from unseen ROIs. Shown in Fig. 2 b is the spatial distribution of the outliers that cannot be categorized into existing PSPs, which are 3-standard-deviation away from the closest PSP centroids. The estimated number of outliers is 0.734%, comparatively close to the expected statistical margin expressed by the three-sigma rule of thumb. Therefore, the average shifts in centroids and the outlier percentage can potentially be used as evidence to test for PSP stableness and completeness, respectively. Figure 2 c shows another test on the completeness of PSPs using Structural Similarity Index (SSIM) 26 as the indicator. The reconstructed MMI can be created by replacing the original polarization pixel values with their PSP’s centroid values. Then we compare the reconstructed MMI with the original MMI, and calculate their SSIM form comparison. SSIM raises fast with the number of PSPs, reaching almost 0.95 at 512. Essentially, the PSP can be considered as a transformation between the polarization feature space and the spatial feature space. By selecting specific pixel groups in the polarization feature space, it highlights distinct structures in 2D spatial space. This dual representation enables the PSP to map polarization features to spatial characteristics effectively. However, extracting polarization features that correspond to visible imagery features is challenging due to inconsistencies between pixel-level polarization data and human visual perception. To address this, it is necessary to exclude irrelevant polarization features within labeled regions, a process similar to supervised learning methods using PBPs as shown in previous studies. Polarization feature-template (PFT) aims to remove unnecessary polarization features by carefully designing the weights coefficients for PBPs, and the idea it thoroughly explored in the next section. 2.4 Polarization feature-template The set of polarization super-pixel can be used as a basis to represent polarization features of all the pixels in MMIs, but may not encode sufficient information on the spatial distributions of these pixels. We can assign different weights to individual PSPs to differentiate pathological features using MMIs. A set of PSP with weight coefficients constructs polarization feature template (PFT), and we discuss how to construct them using local density information, manual spatial labels, and ROI-level labels provided by pathologists. 2.4.1 Polarization feature-template based on local density The local density in polarization space calculated by dividing number of pixels with the standard deviation of the pixels inside the PSPs, can be used as the weight coefficients to generate a PFT, as shown in Fig. 3 . The color-coded heatmap of the local density for pathological samples, cancerous cells have a relatively higher density comparing to normal and inflammatory cells (shown in Fig. 3 a, Fig. 3 b), colored in yellow and blue respectively. PFTs using density signature in polarization feature space possibly encode information about the pathological structures, but not be sufficient for diagnosis applications. 2.4.2 Polarization feature-template based on spatial label Polarization feature template can be constructed based on an initial spatial label of the interested structure. With an initial label provided by pathologists, we can calculate the relative contribution or contrast ratio for each individual super-pixel to the labelled regions, and use it for PFT construction. For each super-pixel, the “contrast ratio” is calculated as the ratio between the number of pixels inside labelled regions and the super-pixel’s total number of pixels. When the contrast ratios are uses as the weight coefficients for the PSPs and project all the polarization pixels with weights to the image, pixels that shares similar polarization characteristics with the labelled region will be highlighted. Taking into the account that pathologists create labels using imagery feature rather than pixel-level features, we apply 2D mean filtering as smoothing filter, as well as simple thresholding to produce the final segmentation result. The set of super-pixels with their contrast ratios as the weight coefficients approximately represent the polarization density distribution of the labelled features, therefore can be used as the PFT to filter similar polarization features in Mueller matrix images. 2.4.3 Polarization feature-template based on ROI-level weak labels Polarization feature template can also be derived based on pathologists’ classification of the regions of interest (ROIs). By utilizing the pathological classification provided by pathologists for each ROI, the weight coefficients of polarization super-pixels (PSPs) are calculated to highlight specific pathological information within the polarization images. Pathologists provide ROI-level weak labels for each polarization image, such as whether an ROI is benign or cancerous, or the specific subtype of cancer. Based on these labels, PFTs are constructed to identify polarization ROIs with distinct pathological characteristics. To distinguish between cancerous and benign regions of interest (ROIs), pathologists assign classification labels to each ROI. Using these labeled regions, we compute a stable set of polarization super-pixels (PSPs). For each ROI, we calculate the number of polarization pixels associated with each PSP. These values, combined with the coefficients of a polarization feature template (PFT), allow us to map the PFT onto a two-dimensional image and determine its proportional area within the ROI. To maximize the distinction between cancerous and benign regions, we iteratively adjust the PFT coefficients. Each PSP’s coefficient is tested by toggling its value (e.g., from 1 to 0 or 0 to 1) and evaluating whether this change improves the differentiation between the two classes. If the change enhances distinction, it is retained; otherwise, the original value is restored. We use the area under the receiver operating characteristic curve (AUROC) as the metric for measuring differentiation, and the process continues until the coefficients stabilize. This iterative process can be influenced by the initial PFT coefficients and the order in which PSPs are adjusted, potentially affecting the results. To ensure stability, the process is repeated multiple times with randomized initialization, and the final PFT coefficients are averaged across iterations. PSPs that consistently contribute to differentiation will have higher average coefficients, while those with minimal impact will have coefficients near zero. The final PFT, averaged over multiple iterations, provides a robust template for identifying cancerous and benign regions. The approach is straightforward to implement, requiring only the mapping of PSP coefficients and the calculation of mean values across the resulting mapped image. This methodology is not limited to distinguishing cancerous and benign regions; it can also be applied to differentiate other pathological features, such as adenocarcinoma versus squamous cell carcinoma or hepatocellular carcinoma versus intrahepatic cholangiocarcinoma. 3 Results 3.1 Label spreading Pathological variation leads to changes of the density distribution in polarization feature space, and we attempt to use PSP to characterize such distributions, and use PFT to identify correlated polarization features and spatial features. Using lung cancer sample, we cluster the polarization pixels into 512 PSPs with minibatch KMeans algorithm. Each PSP characterizes three basic properties in polarization space: the centroid, standard deviation, and number of pixels contained. The centroid informs the position, or the polarization feature characteristic, of the PSP, while the standard deviation and the number of pixels contained encode information about the local density of the pixels. To find the appropriate PSP weight coefficients that highlight specific structures, we calculate the contrast ratio with initial label, such as labeled cancerous regions by pathologists. The set of PSP is first calculated for all the Mueller pixels in a ROI. Then we select a small region (area 1 in Fig. 4 b) surrounding the initial labelled segments (marked by the green dashed line), and calculate for each PSP the contrast ratio between initial labelled pixels and all the pixels within the selected region. The contrast ratios represent the relative contributions of the PSP to the labelled area and are used as the weights for constructing the PFT as described in section 2.4.2 . With the obtained PFT, PSPs of higher weights highlight all the polarization pixels that shares similar signature with the initial labeled region. Apply smoothing filter and thresholding effectively spread the initial pixel label inside the ROI and segment the highlighted areas for label spreading. The process is supervised by the pathologist, who tunes the key parameters including filter size and threshold value to ensure optimum matches between the new and the initial labelled areas. To improve the quality of PFT, such process can be reiterated with an expanded selected region using the obtained segmentation result as initial label, while constantly under supervision by pathologist. The process is repeated until the selected region covers the entire ROI, under careful supervision by pathologist to ensure segmentation quality. In Fig. 4 a, the contrast ratio is calculated and plotted in decreasing order. The red dashed line shows the threshold, which represents the average contrast of the labelled regions. PSPs above the threshold contribute more to the labelled regions than to the rest of the regions. The PSPs above the threshold can be used as the PFT of the labelled region. When project back onto the H&E image, it generates a pixel level detailed label, rather than patch level label, by highlighting pixels of similar polarization features and higher contributions to the labelled regions. Shown in Fig. 4 b, by gradually extending the target and prelabelled regions, such process effectively spreads the initial label onto the entire field of view. First from the pathologist label (green solid line) to region 1 bounded by the white dashed line, then the results are used as initial label to spread to region 2 bounded by the black solid line, and finally to the entire ROI. The final segmentation result is shown in red. Since pathologists use imagery features for diagnosis, such pixel-level features are converted to image labelling by a smoothing filter and thresholding segmentation. During the process, two key parameters are determined manually under the supervision of experienced pathologists: the cut-off threshold value, and the image filter size. Depending on the sample type, the values need manual adjustment to generate the best match to the labelling by the pathologists. Figure 4 b shows the initial label in green, and the completed label in red. It demonstrates that with a small initial labelled area of the cancerous structures, we can use the PSP-PFT approach to spread labels to the rest of the cancerous regions. It is interesting to note, when exploring the idea of PSP, PFT and label spreading, we were initially under the impression that the PSPs with low density are probably not as important and prominent than denser PSPs, which is quickly proven wrong. In many cases, the low-density PSPs can be more important for detecting cancerous structures. As shown in Fig. 5 , the super-pixels are indexed in decreasing order of local density, which is also indicated in the blue curve. The red line indicates the contrast ratios of the individual PSP, and it can be seen that most PSPs with large density have contrast ratio less than the average contrast ratio, while significantly more low-density PSPs have contrast ratio larger than the average. Despite that some PSPs may contain less pixels, they can be more crucial for cancer detection. 3.2 ROI-level To validate the PFT extraction method based on ROI-level labels, we use pathological samples of lung and liver cancers. For liver cancer samples, PFTs are applied to differentiate between cancerous and benign regions and to distinguish hepatocellular carcinoma (HCC) from intrahepatic cholangiocarcinoma (ICC). For lung cancer samples, PFTs are used to differentiate between adenocarcinoma and squamous cell carcinoma ROIs. Specifically, this method calculates the area proportion of each ROI covered by the PFT, using the PSP coefficients in the PFT. The coefficients are optimized by maximizing the differences in PFT coverage among ROIs with different labels. We first evaluated the proposed method using liver cancer samples. A total of 128 polarization super-pixels (PSPs) were computed from all regions of interest (ROIs) to construct a PFT for identifying cancerous regions. To assess the PFT’s performance, we employed a leave-one-out validation approach. In this process, each ROI was excluded in turn and used as a test set, while the remaining ROIs were used to calculate the PFT. This iterative procedure ensures that every ROI is tested independently, allowing a comprehensive evaluation of the method’s ability to predict new and unseen data. The leave-one-out validation effectively leverages the entire dataset, providing a robust measure of the PFT’s predictive accuracy. Figure 6 a shows the PFT prediction results for each ROI during cross-validation, highlighting its ability to distinguish between cancerous and benign regions. In benign ROIs, the PFT area proportions are mostly below 20%, while in cancerous ROIs, most values exceed 20%. For hepatocellular carcinoma, the PFT achieved an AUROC of 96.14% in distinguishing cancerous from benign regions, demonstrating excellent predictive performance. This represents an improvement over the microstructural segmentation method presented in early study, which achieved an AUROC of 94.84%. The superior performance of the PFT can be attributed to its design. While the microstructural segmentation method is unsupervised and merely categorizes polarization pixels, the PFT explicitly incorporates guidance to maximize the distinction between cancerous and benign regions. Furthermore, microstructural segmentation, although capable of identifying feature subcategories sensitive to pathology, lacks the capacity to generalize predictions to new ROIs. In contrast, the PFT effectively identifies similar features in unseen ROIs, making it more versatile and practical. Therefore, the results demonstrate that the proposed PFT not only captures cancerous features in hepatocellular carcinoma samples but also generalizes effectively for prediction in new ROIs, offering a robust tool for pathological analysis. Next, we applied the same method to distinguish between hepatocellular carcinoma (HCC) and intrahepatic cholangiocarcinoma (ICC) using liver cancer samples. The ROIs were categorized into two groups: HCC and ICC. We followed the same approach as previously described for identifying cancerous regions, with ICC labeled as the positive class (representing cancerous regions) and HCC as the negative class (representing benign regions). Using cross-validation, we evaluated the PFT’s ability to reliably identify features specific to ICC. Figure 6 b presents the PFT prediction results for each test ROI during cross-validation. While a few HCC data points show unusually high PFT area proportions above 50%, the majority of HCC ROIs have a PFT area proportion below 30%. In contrast, most ICC data points have PFT area proportions above 30%. The AUROC for distinguishing ICC from HCC based on PFT area proportions is 91.08%, a notable improvement over the previous method, which achieved an AUROC of 84.94%. These findings highlight the effectiveness of the proposed method in identifying optimal PSP coefficients and constructing a PFT that successfully distinguishes between liver cancer subtypes. 4 Discussion and conclusion In this work, PSP is introduced as a method for representing distributions of polarization pixels in polarization feature space. Different weight coefficients of PSP can highlight different spatial patterns and pathological features. We demonstrate how to carefully design the coefficients by using pathologist’s manual spatial labels or using ROI-level weak labels. The label spreading methodology proposed above is achieved by calculating the PSP with all pixels inside one or many ROIs, incorporating both the pixels inside and outside the labeled regions. However, the process becomes computationally demanding as it necessitates spreading labels across hundreds or thousands of testing ROIs. It means that while the proposed standard labels spreading method can effectively spread the initial label to the entire region, it is hard to apply this method to a large dataset and test for convergence in large scale. Therefore, we explore an alternative PFT construction method which the initial PFT and super-pixels are constructed within the well labeled cancerous regions of large numbers of ROIs, so that the features are specific and focused on cancerous features. Such PFT can speed up the label spreading significantly through a direct comparison of newly acquired polarization pixels against the centroids of existing PSP. Specifically, this means computing the Euclidean distance between the new pixels and the existing PSP centroids within the PFT, followed by a comparison against the standard deviation of the PSP values to determine membership. To explore this idea, we constructed 64 super-pixels based on 10 well labelled ROIs as shown in Fig. 4 b, labeled by the red outline. Then, we assigned the pixels outside the labels to the super-pixels, and used the results to calculate contrast ratio to construct PFT. Based on which, we can assign the pixels from other testing ROIs to the super-pixels, and Fig. 7 shows one of the label-spreading result. Note that it is different from the formally proposed label spreading method in last section. The former can quickly increase the volume of high-quality labelled data by spreading labels from small patches to multiple ROIs under supervision by pathologist, while the latter is much more computationally efficient and suitable for large scale data processing. The polarization feature template can be unstable if insufficient data is used for calculating the contrast ratio and hence the weights of the PSPs. Utilizing the accurate initial label is the key step during PFT construction. In order to have a stable PFT for accurate segmentation of the cancer region, we rely on pathologist’s supervision and intervention at the beginning state of PFT construction. Then, we can improve the labels iteratively, repeatedly using the generated label as the new initial label, and gradually increasing the quality of the initial labels with the help of pathologist. Once enough high-quality labels are accumulated for cancerous regions, the PFT should converge and become stable. To test for convergence, we first find the optimal filter size and threshold parameter combination that matches pathologist’s label, and then, we see if the predicted segmentation of PFT converges when we repeat PFT construction and label predictions on the same group of ROIs. As shown in Fig. 8 a, we identify the best parameter combination that can achieve around 90% intersection over union (IOU). Then, at each iteration, we use the segmentation result from past iteration as the initial label and construct a new PFT, use the PFT to predict the segmentation result, compare the segmentation result with that of the last iteration by calculating the intersection over union (IOU) metric. We use a collection of 10 ROIs to construct PFT and conduct the convergence test, and record the mean IOU metric at each iteration. As shown in Fig. 8 b, the IOU metric quickly converges to around 94%, and always stayed above 90% after a few iterations. Convergence is observed even if for non-ideal parameter combinations. It means that even though the initial segmentation result of the PFT may not match up with the pathologist’s labels perfectly, it will converge nonetheless. The result indicates the convergence of PFT, as well as the predicted segmentation, over iterations. Note that the IOU metric does not come closer to 1.0 because of the intrinsic different between pixel-level segmentation and the image-level segmentation. This study also introduces a method for extracting polarization feature templates (PFTs) using ROI-level weak labels. Pathologists annotate ROIs in polarization images with labels such as “cancerous or benign” or “HCC or ICC”. Validation on liver cancer samples showed that the PFT method achieved 96% AUROC in identifying cancerous regions and 91% AUROC in distinguishing HCC from ICC. These results demonstrate that PSPs effectively capture the polarization features of both liver and lung cancer, enabling the creation of specific PFTs for cancerous regions and subtypes. The classification performance of the PFT can be crucial, as it correlates specific pathological features to polarization characteristics; however, equally important are the PFT coefficients, indicating which polarization features play the key role in identifying pathological features. By applying hierarchical clustering to the 128 PSPs, we can group them into categories and visualize their relationships in a tree structure. Figure 9 shows the dendrogram of the PSPs, with the y-axis indicating inter-cluster distances and the x-axis representing individual PSPs. Below them, we can visualize the PFT coefficients for malignant detection and cancer-subtype differentiation. In these visualizations, the color intensity of each PSP corresponds to its coefficient in the PFT, with red and blue indicating higher coefficients in their respective templates. The results show that specific PSP coefficients can highlight distinct pathological features. By combining these coefficients with the clustering results, we can define sub-PFTs that correspond to specific pathological structures, such as cell nuclei or collagen fibers. This approach enhances the understanding of the structural components captured by the PFT and provides a clearer view of their relationship to pathology. In conclusion, we propose a novel framework for analyzing the optical and microstructural properties of biological samples using polarization super-pixels (PSPs) and polarization feature templates (PFTs) in Mueller matrix imaging. This approach partitions the polarization feature space into elementary subsets, or PSPs, which are shown to be stable and complete, making them effective for feature representation. By assigning specific weight coefficients to PSPs, we construct PFTs that encapsulate the polarization characteristics of targeted pathological structures. The method enables label-spreading and ROI-level classification of polarization images, providing insights into the correlation between polarization and pathological features. This framework holds significant potential for advancing polarization-based biophotonics applications. Declarations Disclosures The authors declare no conflicts of interest. Code, Data, and Materials Availability Data are available from the authors upon request. References He C et al (2022) Revealing complex optical phenomena through vectorial metrics. Adv Photonics 4(2):026001 Singh MD, Ghosh N, Vitkin IA (2022) Mueller matrix polarimetry in biomedicine: Enabling technology, biomedical applications, and future prospects. Polarized light in biomedical imaging and sensing: Clinical and preclinical applications. Springer, pp 61–103 Qi J, Elson DS (2017) Mueller polarimetric imaging for surgical and diagnostic applications: A review. 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Seminars Ultrasound CT MRI 40(3):255–264 Fei-Fei L, Perona P (2005) A bayesian hierarchical model for learning natural scene categories, IEEE computer society conference on computer vision and pattern recognition (CVPR'05) 524–531 (2005) Arthur D, Vassilvitskii S (2007) K-means + + the advantages of careful seeding, Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms 1027–1035 Sculley D (2010) Web-scale k-means clustering, in Proceedings of the 19th international conference on World wide web , pp. 1177–1178, Association for Computing Machinery, Raleigh, North Carolina, USA Zhou W et al (2004) Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612 Additional Declarations The authors declare no competing interests. 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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-5744002","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":396294646,"identity":"d15ee6f8-1b15-43d3-8678-bae16b823756","order_by":0,"name":"Jiachen Wan","email":"","orcid":"https://orcid.org/0009-0004-8904-5113","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Jiachen","middleName":"","lastName":"Wan","suffix":""},{"id":396294647,"identity":"b7377ba2-db62-43a6-a34a-83636e042de4","order_by":1,"name":"Haojie Pei","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Haojie","middleName":"","lastName":"Pei","suffix":""},{"id":396294648,"identity":"8ac05542-3188-4e93-a665-c8dfe7e4004e","order_by":2,"name":"Yue Yao","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Yue","middleName":"","lastName":"Yao","suffix":""},{"id":396294649,"identity":"89393138-90f5-4848-9da1-c7ae1d5bcf52","order_by":3,"name":"Hao Li","email":"","orcid":"","institution":"Department of Pathology, Peking University Shenzhen Hospital, Shenzhen 518034, China","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Li","suffix":""},{"id":396294650,"identity":"34bdf0e7-b59d-49c3-8005-271e1d94e1c8","order_by":4,"name":"Wei Cui","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Cui","suffix":""},{"id":396294651,"identity":"039e3332-c18d-4141-8503-5ddb4f8200e2","order_by":5,"name":"Tongyu Huang","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Tongyu","middleName":"","lastName":"Huang","suffix":""},{"id":396294652,"identity":"365ce8cd-626e-45bc-ae8b-4bd64d903ca2","order_by":6,"name":"Xue Jin","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Xue","middleName":"","lastName":"Jin","suffix":""},{"id":396294653,"identity":"7dc51b48-6f1c-4087-b491-767d2c5746a0","order_by":7,"name":"Dakai Wang","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Dakai","middleName":"","lastName":"Wang","suffix":""},{"id":396294654,"identity":"ef2210f0-4269-475f-aca0-97b32dfccb71","order_by":8,"name":"Ran Liao","email":"","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":false,"prefix":"","firstName":"Ran","middleName":"","lastName":"Liao","suffix":""},{"id":396294655,"identity":"b2244697-ac19-44ed-9882-71ca5e0e30d5","order_by":9,"name":"Lili Tao","email":"","orcid":"","institution":"Department of Pathology, Peking University Shenzhen Hospital, Shenzhen 518034, China","correspondingAuthor":false,"prefix":"","firstName":"Lili","middleName":"","lastName":"Tao","suffix":""},{"id":396294656,"identity":"4c0dbade-4a71-4223-9e0b-16ac166e75de","order_by":10,"name":"Hui Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYFACHgaGhAoGBjYwAoEDRGk5Y0CqFsY2AxCLSC267WePSTyc98eeT7r92mOeGgY5vhsJjJ8L8GgxO5OXJpG4zSCxTeZMuTHPMQZjyRsJzNIz8Gk5kGMG0pLAJpGTJs3DxpC44UYCGzMPPi3n3wC1zDGwh2j5x1BPWMsNkC0NBoxtEunHpHnbGBIMCGt5Y2yRcMw4sU0ih01ybp+E4cwzD5ul8Tssx/Dmjxo5e/kZ6c8k3nyzkec7nnzwMz4tSIAHFDkSQMzYQJwGBgb2B8SqHAWjYBSMghEGAEuyRj2m+8ndAAAAAElFTkSuQmCC","orcid":"","institution":"Guangdong Engineering Center of Polarization Imaging and Sensing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","correspondingAuthor":true,"prefix":"","firstName":"Hui","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2024-12-31 23:21:30","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5744002/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5744002/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":72909701,"identity":"aa030e66-b6ee-4986-b6eb-30a6d64756be","added_by":"auto","created_at":"2025-01-03 14:32:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":708743,"visible":true,"origin":"","legend":"\u003cp\u003eThe Mueller matrix microscope and Mueller matrix images. a. shows the diagram and photo of the dual-DoFP Mueller matrix microscope prototype, and b shows the sample Mueller matrix image of lung adenocarcinoma sample. The unit matrix is subtracted from the Mueller matrix for display.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/70addfdc28a7258880bf1f99.png"},{"id":72910696,"identity":"d3815490-29aa-456a-af0f-4c1af135e0de","added_by":"auto","created_at":"2025-01-03 14:40:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":822194,"visible":true,"origin":"","legend":"\u003cp\u003eTesting polarization super-pixels’ stableness and completeness. a. shows the plot depicting the relationship between centroids shift distance and number of iterations, where the x-axis shows the iteration number and the y-axis shows the inertia values. b. shows the outliers in a unsee ROI, which are pixels that cannot be assigned to an existing polarization super-pixel. The outliers are labeled with blue, surrounded by red circle. c. shows how a small number of PSPs leads to satisfactory structure similarity (SSIM) in the texture of Mueller matrix image.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/fd77c81baa237d85ccf07dbe.png"},{"id":72909703,"identity":"6d9df028-6a12-436d-bf61-51990bf95176","added_by":"auto","created_at":"2025-01-03 14:32:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":3830089,"visible":true,"origin":"","legend":"\u003cp\u003eDiagram for the local density in polarization feature space of biological samples. a shows the color-coded heatmap of local density in logscale, and b is the corresponding H\u0026amp;E-stained image.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/373adf96b3ae94e452565172.png"},{"id":72909715,"identity":"0086e3c6-0f1a-44c9-a95c-e7bad6778388","added_by":"auto","created_at":"2025-01-03 14:32:29","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":830410,"visible":true,"origin":"","legend":"\u003cp\u003eContrast ratio and label spreading demonstration. a. shows the contrast ratio calculated for each PSP, and sorted in descending order. The red line indicates the cut-off threshold, determined under pathologist supervision for best label spreading result. b. displays the label spreading results, created by first spreading the pathologist label (in green) to region 1 bounded by white dashed line, and then the result is used to spread to region 2 bounded by the black solid line, and then to the entire ROI. The red regions are the pathologist initial label region, and the blue region are the completed label created through label spreading. The histogram plot under the image corresponds to the PSPs, where the height indicates the local density and the colors indicates the coefficient weights (blue means coefficient 1, and white means coefficient 0).\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/1c3c5018f2c186cfa4f39c51.png"},{"id":72909720,"identity":"f677634c-bc27-457e-9b61-6b9a7686d4b2","added_by":"auto","created_at":"2025-01-03 14:32:30","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":218980,"visible":true,"origin":"","legend":"\u003cp\u003eContrast ratio of polarization super-pixels (indicated in blue) and their relative contrast ratios (indicated in red). Many small size PSP have high values of contrast ratios, indicating a higher contribution to the labelled cancerous region. The x-axis shows the Polarization super-pixel number, and the y-axis indicates the normalized density or contrast ratio, normalized by their maximum value.\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/7387f0325ced4b3414e4571d.png"},{"id":72910699,"identity":"77041f10-84b2-44b0-8807-dbd4b41cba44","added_by":"auto","created_at":"2025-01-03 14:40:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":104194,"visible":true,"origin":"","legend":"\u003cp\u003eBox plot of PFT predictions for malignat detection and cancer subtype differentiation. X-axis shows the class labels, and the Y-axis shows the area ratio of the PFT for the ROIs. During cross-validation, the PFT prediction values for each test ROI were recorded and plotted as box plots.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/caf4da8c512a597a1a9b40d3.png"},{"id":72909713,"identity":"bd0d0538-c1dd-4dda-ba6e-d19c48689bd7","added_by":"auto","created_at":"2025-01-03 14:32:29","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":125052,"visible":true,"origin":"","legend":"\u003cp\u003eLabel spreading result on testing ROI using distance-based PFT (polarization feature template) calculated from the labeled region as shown Fig.4b.\u003c/p\u003e","description":"","filename":"Figure7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/675fced4fadd4f534880cfca.jpg"},{"id":72909716,"identity":"d081aecf-e34b-4170-ba30-3693cc172aa9","added_by":"auto","created_at":"2025-01-03 14:32:29","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":192888,"visible":true,"origin":"","legend":"\u003cp\u003eTest for convergence over iterations. a. shows the IOU metric for various parameter combinations, which is used to find the optimal filter size and threshold value. For b., at each iteration, the segmentation result of the last iteration is used as the initial label for PFT construction, and then the PFT is used to predict a new segmentation region, which is to be compared with the old segmentation result for IOU calculation. The stabilization and convergence of the IOU metric over iterations indicates convergence of PFT, even for non-optimal parameter combinations.\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/bd7c911911cdc56e7f554a13.png"},{"id":72909730,"identity":"95240eaf-8810-438d-baaf-594677e15885","added_by":"auto","created_at":"2025-01-03 14:32:30","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":253388,"visible":true,"origin":"","legend":"\u003cp\u003eHierarchical clustering dendrogram of polarization super-pixels (PSPs) and polarization feature templates (PFTs) visualization. Higer colors intensity in the ‘barcode’ indicate higher PFT coefficients. The red PFT identifies cancerous regions, while the blue PFT distinguishes liver cancer subtypes.\u003c/p\u003e","description":"","filename":"Figure9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/162e8b81299c898ff7398f52.jpg"},{"id":72912351,"identity":"4c63e6ce-82fb-47c1-9e4b-9f7bce7fb560","added_by":"auto","created_at":"2025-01-03 15:04:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9143136,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5744002/v1/c65d8829-5d38-45fc-acf9-5239bca55441.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePolarization super-pixel and feature template for feature extraction from Mueller matrix images\u003c/p\u003e","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWhile intensity-based imaging systems have been extensively utilized in histology and pathology, Mueller matrix (MM) imaging systems provide a more comprehensive characterization of light-tissue interactions by measuring both intensity and polarization properties\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. This additional information enables MM imaging to differentiate microstructural features, such as birefringence and depolarization, which are otherwise indistinguishable with intensity-based imaging methods. Integrating these advantages into histology slide labeling can significantly improve the detection and classification of pathological features, thereby offering a transformative approach to clinical diagnostics.\u003c/p\u003e \u003cp\u003eMueller matrix images contain subwavelength microstructural information in each pixel, but extracting pathological features from high dimension polarization space is not trivial. Since the Mueller matrix elements lack explicit connections to the physical properties of a sample, it is often more convenient to use a set of know polarization basis parameters (PBP) to represent polarization features \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. With the help of machine learning and supervised methods, previous studies have used PBPs as input, and extracted polarization features of cancerous structures from various types of tissues, such as breast cancer \u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, lung cancer \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, cervical cancer \u003csup\u003e\u003cspan additionalcitationids=\"CR13 CR14 CR15 CR16\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, and liver cancer \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDespite its ability to reveal hidden correlation between polarization and pathological features, unsupervised learning methods are underused. A recent study \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e explored how unsupervised learning can help extract polarization features from specimens. We use polarization basis parameters to represent the polarization characteristics of different tissues, and apply pixel clustering to show that pathological tissue can be decomposed into a set of basic microstructural components with potential pathological correlation. In the same study, polarization super-pixel was introduced as the method to compress polarimetric data volume while maintaining as much polarization feature information as possible \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eMicrostructural changes in tissues due to pathological variation affect the density distribution of polarization features. In this study, we take the polarization super-pixels approach even further to characterize biological specimen\u0026rsquo;s density distribution in polarization feature space. We apply unsupervised learning to partition the polarization pixels into many elementary subsets that characterizes polarization features of Mueller matrix images, which are the polarization super-pixels (PSP). The PSP construction process is purely based on polarization features, while no spatial or imagery features are considered. Different pathological features, which are usually characterized by different image features, correspond to different polarization feature. These features can be effectively represented using PSPs with specific weight coefficients, collectively referred to as the Polarization Feature Template (PFT).\u003c/p\u003e \u003cp\u003eWith a known initial spatial label, we compute the proportion of each PSP that overlaps with the spatial labels of specific pathological features, and thereby assign a weight coefficient to reflect their relative-contribution to the labelled regions. The specific set of PSP and their corresponding weight coefficients form a PFT, which is a disease-specific feature vector representing the distinctive polarization features of the labelled regions. Results demonstrate that we can construct the PFT for cancerous cells in lung adenocarcinoma, and spread the initial pathologist label to the entire field of view.\u003c/p\u003e \u003cp\u003eFor an alternative approach, we obtain the PFT coefficients using ROI-level labels provided by pathologists, such as \u0026ldquo;malignant or benign\u0026rdquo;. PFT would highlight a region in the ROI, the approach optimizes the PFT coefficients to maximize the difference in PFT-highlighted area between malignant and benign ROIs. Cross-validation shows that the PFT for identifying malignant regions achieves an AUROC of 96.14%, effectively distinguishing malignant from benign areas. Similarly, the PFT designed for cancer subtype differentiation can effectively differentiate ICC from HCC regions, achieving an AUROC of 91.08%.\u003c/p\u003e \u003cp\u003ePFT essentially functions as the linkage, connecting polarization features to the pathological features of the specimen. Leveraging PSP and PFT the approach provides the capability to identify specific pathological features for assisted diagnosis, effectively reducing labor and time costs for pathologists. Furthermore, the use of Mueller matrix images and unsupervised learning-based analysis opens new avenues for exploring subtle pathological variations that may be overlooked by traditional methods.\u003c/p\u003e"},{"header":"2 Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Mueller matrix imaging\u003c/h2\u003e \u003cp\u003eTo acquire the Mueller matrix images, histological slides from biopsy specimens are examined with a Mueller matrix microscope (MMM) that operates at 633nm wavelength and employs a 20x 0.4NA objective lens. With the chosen NA we can obtain a spatial resolution of 1 micron that enables the visualization of subcellular structures, while ensuring optimal precision in the Mueller matrix measurements. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, the samples are imaged by the dual-DoFP MMM \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e whose polarization state analyzer consists of two division of focal plane (DoFP) polarimeters (2048 \u0026times; 2448 pixels, 16-bit, PHX050S-PC, Lucid Vision Labs Inc., Canada). The device demonstrates high accuracy and adequate speed in Mueller matrix imaging, with a root mean square error below 0.01 and an acquisition time under 10 seconds \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Pathological samples\u003c/h2\u003e \u003cp\u003eIn this study, histological slides of lung adenocarcinoma, liver hepatocellular carcinoma and intrahepatic cholangiocarcinoma are used for Mueller matrix imaging and data analysis. Lung adenocarcinoma is a subtype of non-small cell lung cancer (NSCLC) that originates from glandular cells in the lung tissue. Lung adenocarcinoma is the most common form of lung cancer, accounting for about 40% of all NSCLC cases and more than 30% of all lung cancers \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Hepatocellular carcinoma (HCC) and intrahepatic cholangiocarcinoma (ICC) are the two most prevalent forms of primary liver cancer, ranking among the most commonly diagnosed cancers globally. The Mueller matrix images (MMI) are acquired using MM microscope. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb shows an example of MMI whose 16 elements are normalized by M11 and diagonal elements are subtracted by 1. The lung cancer samples are obtained from the pathology department of Peking University Shenzhen Hospital, and the study is overseen and approved by the Ethics Committee of Peking University Shenzhen Hospital. The liver cancer Mueller matrix image data are obtained from the public datasets published in prior study \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, including a total of 188 ROIs, consisting of both HCC and ICC subtypes divided into benign and cancerous regions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Polarization super-pixels\u003c/h2\u003e \u003cp\u003eUnsupervised learning methods can reveal hidden correlations within polarization data, and it has been shown that pixel clustering can decompose the histological slide into a stable set of microstructural subtypes, each corresponds to a pathological structure \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Polarization super-pixel (PSP) was proposed as an essential pre-processing step before applying computationally taxing unsupervised algorithms, by clustering the polarization pixels in a single region of interest (ROI) of MMI into 1024 groups as super-pixels. It was proven to be effective for reducing the data volume while preserving polarimetric information of the Mueller matrix images \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. In this work, we construct a stable and complete set of polarization super-pixels, by processing and clustering the polarization pixels from multiple ROIs from the same types of specimens for super-pixel calculation. We aim to extract the principal polarization features from the samples in the form of super-pixels, to be exploited for polarization feature representation. For a specific specimen, we can divide its polarization feature space into much finer elementary subsets, i.e. the set of PSP. Through approximation, such set of PSP can represent specifically shaped density distribution in polarization space, which means it can be used as a type of basis for polarization feature representation. It could also be interpreted as the polarization equivalent of \u0026ldquo;codebook\u0026rdquo; in natural image processing \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo construct such a PSP set, we need to cluster the polarization pixels from numerous ROI into roughly 100\u0026thinsp;~\u0026thinsp;1000 clusters, depending on the the complexity of the biological sample and time constraints. KMeans is one of the few classical unsupervised clustering algorithm that is capable of processing data at such scale\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. In this work, we create polarization super-pixels with the following steps given the M11-normalized Mueller matrix images. First, we standardize the Mueller matrix elements of individual polarization pixels by subtracting the mean and dividing by the standard deviation. For each pixel in the Mueller matrix image located at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(x,y)\\)\u003c/span\u003e\u003c/span\u003e, the Mueller matrix elements \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\left(M{M}_{\\text{1,1}},M{M}_{\\text{1,2}},\\dots\\:,M{M}_{\\text{4,4}}\\right)}_{x,y}\\)\u003c/span\u003e\u003c/span\u003e are averaged to calculate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{i,j}\\)\u003c/span\u003e\u003c/span\u003e, and subsequently the standard deviation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{i,j}\\)\u003c/span\u003e\u003c/span\u003e. The mean is then subtracted from each pixel value, and the result is divided by the standard deviation. It makes sure that each Mueller matrix elements are weighted equally for subsequent calculations, and it can be difficult if they are not standardized and with different scales. Then we apply the minibatch KMeans algorithm to all the polarization pixels in the ROI and cluster them into 1024 groups, using the 15 normalized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:({M}_{ij}/{M}_{11})\\)\u003c/span\u003e\u003c/span\u003e and standardized Mueller matrix elements\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\)\u003c/span\u003e\u003c/span\u003e as features. We chose the minibatch variant of KMeans algorithm specifically, because it speeds up the KMeans algorithm significantly if the number of data points is large. Lastly, we compute and record the mean and standard deviation of the polarization parameters of choice, for each polarization super-pixel. We also keep track of the coordinates of the pixels that belong to each super-pixel. As the number of ROI increases, the classic KMeans algorithm is no longer capable of processing data with such data volume, because it simply does not fit in the memory for further processing. And in such case the mini-batch approach is considered, by dividing the ROIs into batches and achieve convergence recursively \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor the set of PSPs to function as a basis, ideally it should satisfy two criteria: stableness and completeness. A stable set of PSP implies that the centroids should converge to stable values; when new samples are added, these centroids should remain converged. A complete set of PSP implies that any polarization pixels from the same specimen that are obtained from new ROIs should be assigned to a pre-existing PSP. Following the proposed procedure, we should be able to systematically construct a stable set of PSPs, to approximate and represent the polarization characteristic of the given specimen.\u003c/p\u003e \u003cp\u003eThe stableness of the polarization super-pixels requires large number of ROIs from multiple patients, and how to process such a large amount of polarization pixels is challenging. We use the minibatch techniques from deep learning and big data, and process the pixels in batches. We test for stableness of the PSP by observing the convergence of inertia criteria. The stableness of the centroids can be demonstrated using the average shifts in centroids for the PSPs as the criteria (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea), similar to the within-cluster sum-of-square criteria \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. The curve shows how the centroids positions change during mini-batch KMeans calculation of the PSPs for a single ROI, and the convergence of the absolute shift-distance to zero indicates that the centroids converged to stable values. We notice that there are irregular jumps in the curve, which are due to the centroid reassignments, which happens when the centroids are not stably converged yet. After about 2000 iterations, the centroid reassignment no longer occurs, which further indicate convergence. On the other hand, completeness means that the established set of PSP can be used to express all polarization features of the specimen, which can be tested by estimating the number of outliers from unseen ROIs. Shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb is the spatial distribution of the outliers that cannot be categorized into existing PSPs, which are 3-standard-deviation away from the closest PSP centroids. The estimated number of outliers is 0.734%, comparatively close to the expected statistical margin expressed by the three-sigma rule of thumb. Therefore, the average shifts in centroids and the outlier percentage can potentially be used as evidence to test for PSP stableness and completeness, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec shows another test on the completeness of PSPs using Structural Similarity Index (SSIM) \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e as the indicator. The reconstructed MMI can be created by replacing the original polarization pixel values with their PSP\u0026rsquo;s centroid values. Then we compare the reconstructed MMI with the original MMI, and calculate their SSIM form comparison. SSIM raises fast with the number of PSPs, reaching almost 0.95 at 512.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eEssentially, the PSP can be considered as a transformation between the polarization feature space and the spatial feature space. By selecting specific pixel groups in the polarization feature space, it highlights distinct structures in 2D spatial space. This dual representation enables the PSP to map polarization features to spatial characteristics effectively.\u003c/p\u003e \u003cp\u003eHowever, extracting polarization features that correspond to visible imagery features is challenging due to inconsistencies between pixel-level polarization data and human visual perception. To address this, it is necessary to exclude irrelevant polarization features within labeled regions, a process similar to supervised learning methods using PBPs as shown in previous studies. Polarization feature-template (PFT) aims to remove unnecessary polarization features by carefully designing the weights coefficients for PBPs, and the idea it thoroughly explored in the next section.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Polarization feature-template\u003c/h2\u003e \u003cp\u003eThe set of polarization super-pixel can be used as a basis to represent polarization features of all the pixels in MMIs, but may not encode sufficient information on the spatial distributions of these pixels. We can assign different weights to individual PSPs to differentiate pathological features using MMIs. A set of PSP with weight coefficients constructs polarization feature template (PFT), and we discuss how to construct them using local density information, manual spatial labels, and ROI-level labels provided by pathologists.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1 Polarization feature-template based on local density\u003c/h2\u003e \u003cp\u003eThe local density in polarization space calculated by dividing number of pixels with the standard deviation of the pixels inside the PSPs, can be used as the weight coefficients to generate a PFT, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The color-coded heatmap of the local density for pathological samples, cancerous cells have a relatively higher density comparing to normal and inflammatory cells (shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), colored in yellow and blue respectively. PFTs using density signature in polarization feature space possibly encode information about the pathological structures, but not be sufficient for diagnosis applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2 Polarization feature-template based on spatial label\u003c/h2\u003e \u003cp\u003ePolarization feature template can be constructed based on an initial spatial label of the interested structure. With an initial label provided by pathologists, we can calculate the relative contribution or contrast ratio for each individual super-pixel to the labelled regions, and use it for PFT construction. For each super-pixel, the \u0026ldquo;contrast ratio\u0026rdquo; is calculated as the ratio between the number of pixels inside labelled regions and the super-pixel\u0026rsquo;s total number of pixels. When the contrast ratios are uses as the weight coefficients for the PSPs and project all the polarization pixels with weights to the image, pixels that shares similar polarization characteristics with the labelled region will be highlighted. Taking into the account that pathologists create labels using imagery feature rather than pixel-level features, we apply 2D mean filtering as smoothing filter, as well as simple thresholding to produce the final segmentation result. The set of super-pixels with their contrast ratios as the weight coefficients approximately represent the polarization density distribution of the labelled features, therefore can be used as the PFT to filter similar polarization features in Mueller matrix images.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.4.3 Polarization feature-template based on ROI-level weak labels\u003c/h2\u003e \u003cp\u003ePolarization feature template can also be derived based on pathologists\u0026rsquo; classification of the regions of interest (ROIs). By utilizing the pathological classification provided by pathologists for each ROI, the weight coefficients of polarization super-pixels (PSPs) are calculated to highlight specific pathological information within the polarization images. Pathologists provide ROI-level weak labels for each polarization image, such as whether an ROI is benign or cancerous, or the specific subtype of cancer. Based on these labels, PFTs are constructed to identify polarization ROIs with distinct pathological characteristics.\u003c/p\u003e \u003cp\u003eTo distinguish between cancerous and benign regions of interest (ROIs), pathologists assign classification labels to each ROI. Using these labeled regions, we compute a stable set of polarization super-pixels (PSPs). For each ROI, we calculate the number of polarization pixels associated with each PSP. These values, combined with the coefficients of a polarization feature template (PFT), allow us to map the PFT onto a two-dimensional image and determine its proportional area within the ROI.\u003c/p\u003e \u003cp\u003eTo maximize the distinction between cancerous and benign regions, we iteratively adjust the PFT coefficients. Each PSP\u0026rsquo;s coefficient is tested by toggling its value (e.g., from 1 to 0 or 0 to 1) and evaluating whether this change improves the differentiation between the two classes. If the change enhances distinction, it is retained; otherwise, the original value is restored. We use the area under the receiver operating characteristic curve (AUROC) as the metric for measuring differentiation, and the process continues until the coefficients stabilize. This iterative process can be influenced by the initial PFT coefficients and the order in which PSPs are adjusted, potentially affecting the results. To ensure stability, the process is repeated multiple times with randomized initialization, and the final PFT coefficients are averaged across iterations. PSPs that consistently contribute to differentiation will have higher average coefficients, while those with minimal impact will have coefficients near zero. The final PFT, averaged over multiple iterations, provides a robust template for identifying cancerous and benign regions. The approach is straightforward to implement, requiring only the mapping of PSP coefficients and the calculation of mean values across the resulting mapped image.\u003c/p\u003e \u003cp\u003eThis methodology is not limited to distinguishing cancerous and benign regions; it can also be applied to differentiate other pathological features, such as adenocarcinoma versus squamous cell carcinoma or hepatocellular carcinoma versus intrahepatic cholangiocarcinoma.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Label spreading\u003c/h2\u003e \u003cp\u003ePathological variation leads to changes of the density distribution in polarization feature space, and we attempt to use PSP to characterize such distributions, and use PFT to identify correlated polarization features and spatial features. Using lung cancer sample, we cluster the polarization pixels into 512 PSPs with minibatch KMeans algorithm. Each PSP characterizes three basic properties in polarization space: the centroid, standard deviation, and number of pixels contained. The centroid informs the position, or the polarization feature characteristic, of the PSP, while the standard deviation and the number of pixels contained encode information about the local density of the pixels.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo find the appropriate PSP weight coefficients that highlight specific structures, we calculate the contrast ratio with initial label, such as labeled cancerous regions by pathologists. The set of PSP is first calculated for all the Mueller pixels in a ROI. Then we select a small region (area 1 in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb) surrounding the initial labelled segments (marked by the green dashed line), and calculate for each PSP the contrast ratio between initial labelled pixels and all the pixels within the selected region. The contrast ratios represent the relative contributions of the PSP to the labelled area and are used as the weights for constructing the PFT as described in section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e2.4.2\u003c/span\u003e. With the obtained PFT, PSPs of higher weights highlight all the polarization pixels that shares similar signature with the initial labeled region. Apply smoothing filter and thresholding effectively spread the initial pixel label inside the ROI and segment the highlighted areas for label spreading. The process is supervised by the pathologist, who tunes the key parameters including filter size and threshold value to ensure optimum matches between the new and the initial labelled areas. To improve the quality of PFT, such process can be reiterated with an expanded selected region using the obtained segmentation result as initial label, while constantly under supervision by pathologist. The process is repeated until the selected region covers the entire ROI, under careful supervision by pathologist to ensure segmentation quality. In Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, the contrast ratio is calculated and plotted in decreasing order. The red dashed line shows the threshold, which represents the average contrast of the labelled regions. PSPs above the threshold contribute more to the labelled regions than to the rest of the regions. The PSPs above the threshold can be used as the PFT of the labelled region. When project back onto the H\u0026amp;E image, it generates a pixel level detailed label, rather than patch level label, by highlighting pixels of similar polarization features and higher contributions to the labelled regions. Shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb, by gradually extending the target and prelabelled regions, such process effectively spreads the initial label onto the entire field of view. First from the pathologist label (green solid line) to region 1 bounded by the white dashed line, then the results are used as initial label to spread to region 2 bounded by the black solid line, and finally to the entire ROI. The final segmentation result is shown in red. Since pathologists use imagery features for diagnosis, such pixel-level features are converted to image labelling by a smoothing filter and thresholding segmentation. During the process, two key parameters are determined manually under the supervision of experienced pathologists: the cut-off threshold value, and the image filter size. Depending on the sample type, the values need manual adjustment to generate the best match to the labelling by the pathologists. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb shows the initial label in green, and the completed label in red. It demonstrates that with a small initial labelled area of the cancerous structures, we can use the PSP-PFT approach to spread labels to the rest of the cancerous regions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is interesting to note, when exploring the idea of PSP, PFT and label spreading, we were initially under the impression that the PSPs with low density are probably not as important and prominent than denser PSPs, which is quickly proven wrong. In many cases, the low-density PSPs can be more important for detecting cancerous structures. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the super-pixels are indexed in decreasing order of local density, which is also indicated in the blue curve. The red line indicates the contrast ratios of the individual PSP, and it can be seen that most PSPs with large density have contrast ratio less than the average contrast ratio, while significantly more low-density PSPs have contrast ratio larger than the average. Despite that some PSPs may contain less pixels, they can be more crucial for cancer detection.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.2 ROI-level\u003c/h2\u003e \u003cp\u003eTo validate the PFT extraction method based on ROI-level labels, we use pathological samples of lung and liver cancers. For liver cancer samples, PFTs are applied to differentiate between cancerous and benign regions and to distinguish hepatocellular carcinoma (HCC) from intrahepatic cholangiocarcinoma (ICC). For lung cancer samples, PFTs are used to differentiate between adenocarcinoma and squamous cell carcinoma ROIs. Specifically, this method calculates the area proportion of each ROI covered by the PFT, using the PSP coefficients in the PFT. The coefficients are optimized by maximizing the differences in PFT coverage among ROIs with different labels.\u003c/p\u003e \u003cp\u003eWe first evaluated the proposed method using liver cancer samples. A total of 128 polarization super-pixels (PSPs) were computed from all regions of interest (ROIs) to construct a PFT for identifying cancerous regions. To assess the PFT\u0026rsquo;s performance, we employed a leave-one-out validation approach. In this process, each ROI was excluded in turn and used as a test set, while the remaining ROIs were used to calculate the PFT. This iterative procedure ensures that every ROI is tested independently, allowing a comprehensive evaluation of the method\u0026rsquo;s ability to predict new and unseen data. The leave-one-out validation effectively leverages the entire dataset, providing a robust measure of the PFT\u0026rsquo;s predictive accuracy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea shows the PFT prediction results for each ROI during cross-validation, highlighting its ability to distinguish between cancerous and benign regions. In benign ROIs, the PFT area proportions are mostly below 20%, while in cancerous ROIs, most values exceed 20%. For hepatocellular carcinoma, the PFT achieved an AUROC of 96.14% in distinguishing cancerous from benign regions, demonstrating excellent predictive performance. This represents an improvement over the microstructural segmentation method presented in early study, which achieved an AUROC of 94.84%.\u003c/p\u003e \u003cp\u003eThe superior performance of the PFT can be attributed to its design. While the microstructural segmentation method is unsupervised and merely categorizes polarization pixels, the PFT explicitly incorporates guidance to maximize the distinction between cancerous and benign regions. Furthermore, microstructural segmentation, although capable of identifying feature subcategories sensitive to pathology, lacks the capacity to generalize predictions to new ROIs. In contrast, the PFT effectively identifies similar features in unseen ROIs, making it more versatile and practical. Therefore, the results demonstrate that the proposed PFT not only captures cancerous features in hepatocellular carcinoma samples but also generalizes effectively for prediction in new ROIs, offering a robust tool for pathological analysis.\u003c/p\u003e \u003cp\u003eNext, we applied the same method to distinguish between hepatocellular carcinoma (HCC) and intrahepatic cholangiocarcinoma (ICC) using liver cancer samples. The ROIs were categorized into two groups: HCC and ICC. We followed the same approach as previously described for identifying cancerous regions, with ICC labeled as the positive class (representing cancerous regions) and HCC as the negative class (representing benign regions). Using cross-validation, we evaluated the PFT\u0026rsquo;s ability to reliably identify features specific to ICC.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb presents the PFT prediction results for each test ROI during cross-validation. While a few HCC data points show unusually high PFT area proportions above 50%, the majority of HCC ROIs have a PFT area proportion below 30%. In contrast, most ICC data points have PFT area proportions above 30%. The AUROC for distinguishing ICC from HCC based on PFT area proportions is 91.08%, a notable improvement over the previous method, which achieved an AUROC of 84.94%. These findings highlight the effectiveness of the proposed method in identifying optimal PSP coefficients and constructing a PFT that successfully distinguishes between liver cancer subtypes.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Discussion and conclusion","content":"\u003cp\u003eIn this work, PSP is introduced as a method for representing distributions of polarization pixels in polarization feature space. Different weight coefficients of PSP can highlight different spatial patterns and pathological features. We demonstrate how to carefully design the coefficients by using pathologist\u0026rsquo;s manual spatial labels or using ROI-level weak labels.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe label spreading methodology proposed above is achieved by calculating the PSP with all pixels inside one or many ROIs, incorporating both the pixels inside and outside the labeled regions. However, the process becomes computationally demanding as it necessitates spreading labels across hundreds or thousands of testing ROIs. It means that while the proposed standard labels spreading method can effectively spread the initial label to the entire region, it is hard to apply this method to a large dataset and test for convergence in large scale. Therefore, we explore an alternative PFT construction method which the initial PFT and super-pixels are constructed within the well labeled cancerous regions of large numbers of ROIs, so that the features are specific and focused on cancerous features. Such PFT can speed up the label spreading significantly through a direct comparison of newly acquired polarization pixels against the centroids of existing PSP. Specifically, this means computing the Euclidean distance between the new pixels and the existing PSP centroids within the PFT, followed by a comparison against the standard deviation of the PSP values to determine membership. To explore this idea, we constructed 64 super-pixels based on 10 well labelled ROIs as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb, labeled by the red outline. Then, we assigned the pixels outside the labels to the super-pixels, and used the results to calculate contrast ratio to construct PFT. Based on which, we can assign the pixels from other testing ROIs to the super-pixels, and Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows one of the label-spreading result. Note that it is different from the formally proposed label spreading method in last section. The former can quickly increase the volume of high-quality labelled data by spreading labels from small patches to multiple ROIs under supervision by pathologist, while the latter is much more computationally efficient and suitable for large scale data processing.\u003c/p\u003e \u003cp\u003eThe polarization feature template can be unstable if insufficient data is used for calculating the contrast ratio and hence the weights of the PSPs. Utilizing the accurate initial label is the key step during PFT construction. In order to have a stable PFT for accurate segmentation of the cancer region, we rely on pathologist\u0026rsquo;s supervision and intervention at the beginning state of PFT construction. Then, we can improve the labels iteratively, repeatedly using the generated label as the new initial label, and gradually increasing the quality of the initial labels with the help of pathologist. Once enough high-quality labels are accumulated for cancerous regions, the PFT should converge and become stable. To test for convergence, we first find the optimal filter size and threshold parameter combination that matches pathologist\u0026rsquo;s label, and then, we see if the predicted segmentation of PFT converges when we repeat PFT construction and label predictions on the same group of ROIs. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea, we identify the best parameter combination that can achieve around 90% intersection over union (IOU). Then, at each iteration, we use the segmentation result from past iteration as the initial label and construct a new PFT, use the PFT to predict the segmentation result, compare the segmentation result with that of the last iteration by calculating the intersection over union (IOU) metric. We use a collection of 10 ROIs to construct PFT and conduct the convergence test, and record the mean IOU metric at each iteration. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb, the IOU metric quickly converges to around 94%, and always stayed above 90% after a few iterations. Convergence is observed even if for non-ideal parameter combinations. It means that even though the initial segmentation result of the PFT may not match up with the pathologist\u0026rsquo;s labels perfectly, it will converge nonetheless. The result indicates the convergence of PFT, as well as the predicted segmentation, over iterations. Note that the IOU metric does not come closer to 1.0 because of the intrinsic different between pixel-level segmentation and the image-level segmentation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis study also introduces a method for extracting polarization feature templates (PFTs) using ROI-level weak labels. Pathologists annotate ROIs in polarization images with labels such as \u0026ldquo;cancerous or benign\u0026rdquo; or \u0026ldquo;HCC or ICC\u0026rdquo;. Validation on liver cancer samples showed that the PFT method achieved 96% AUROC in identifying cancerous regions and 91% AUROC in distinguishing HCC from ICC. These results demonstrate that PSPs effectively capture the polarization features of both liver and lung cancer, enabling the creation of specific PFTs for cancerous regions and subtypes.\u003c/p\u003e \u003cp\u003eThe classification performance of the PFT can be crucial, as it correlates specific pathological features to polarization characteristics; however, equally important are the PFT coefficients, indicating which polarization features play the key role in identifying pathological features. By applying hierarchical clustering to the 128 PSPs, we can group them into categories and visualize their relationships in a tree structure. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the dendrogram of the PSPs, with the y-axis indicating inter-cluster distances and the x-axis representing individual PSPs. Below them, we can visualize the PFT coefficients for malignant detection and cancer-subtype differentiation. In these visualizations, the color intensity of each PSP corresponds to its coefficient in the PFT, with red and blue indicating higher coefficients in their respective templates. The results show that specific PSP coefficients can highlight distinct pathological features. By combining these coefficients with the clustering results, we can define sub-PFTs that correspond to specific pathological structures, such as cell nuclei or collagen fibers. This approach enhances the understanding of the structural components captured by the PFT and provides a clearer view of their relationship to pathology.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn conclusion, we propose a novel framework for analyzing the optical and microstructural properties of biological samples using polarization super-pixels (PSPs) and polarization feature templates (PFTs) in Mueller matrix imaging. This approach partitions the polarization feature space into elementary subsets, or PSPs, which are shown to be stable and complete, making them effective for feature representation. By assigning specific weight coefficients to PSPs, we construct PFTs that encapsulate the polarization characteristics of targeted pathological structures. The method enables label-spreading and ROI-level classification of polarization images, providing insights into the correlation between polarization and pathological features. This framework holds significant potential for advancing polarization-based biophotonics applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003e\u003cem\u003eDisclosures\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eCode, Data, and Materials Availability\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eData are available from the authors upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHe C et al (2022) Revealing complex optical phenomena through vectorial metrics. Adv Photonics 4(2):026001\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSingh MD, Ghosh N, Vitkin IA (2022) Mueller matrix polarimetry in biomedicine: Enabling technology, biomedical applications, and future prospects. Polarized light in biomedical imaging and sensing: Clinical and preclinical applications. 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IEEE Trans Image Process 13(4):600\u0026ndash;612\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Tsinghua University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Mueller matrix imaging, polarization imaging, polarization super-pixels, polarization feature template, biophotonics","lastPublishedDoi":"10.21203/rs.3.rs-5744002/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5744002/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMueller matrix images contain rich microstructural information, comprehensively encoded in the high-dimensional polarization feature space. While Mueller matrix is sensitive to microstructural changes down to subwavelength scale, how to extract the relevant polarization features remains a primary challenge for its applications. In this article, we propose a new approach to obtain characteristic pathological features from polarization pixels. At pixel-level, we divide the density distribution of the polarization pixels into a collection of elementary subsets of similar polarization features, named polarization super-pixels (PSP). These PSPs approximate the distribution in polarization space while containing no image-textural information, enabling polarization feature representation. By assigning specific weight coefficients to PSPs, we construct polarimetry feature templates (PFTs) that represent the polarization characteristics of specific pathological structure of interest. Using spatial labels from pathologists, we calculate PSP contributions and assign weight coefficients to create PFTs for identifying cancerous structures. Additionally, with region-of-interest (ROI)-level labels distinguishing cancerous and benign areas, we isolate PSPs sensitive to cancer and construct PFTs for ROI-level classification, including differentiation of cancer subtypes. Validation on pathological tissue slides demonstrates the stability and completeness property of the derived PSP and PFT. We showcase its clinical applications, such as propagating spatial labels from a limited number of labeled pixels to larger regions, and detecting malignancy or cancer-subtype differentiation at ROI-level, enhancing diagnostic workflows.\u003c/p\u003e","manuscriptTitle":"Polarization super-pixel and feature template for feature extraction from Mueller matrix images","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-03 14:32:24","doi":"10.21203/rs.3.rs-5744002/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a5282413-ae2c-4ab5-9606-5356f7211d5d","owner":[],"postedDate":"January 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":42221061,"name":"Biomedical Engineering"}],"tags":[],"updatedAt":"2025-01-03T14:32:24+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-03 14:32:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5744002","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5744002","identity":"rs-5744002","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}