Single-Shot X-ray to Multi-View Projections for 3D Pork Shoulder Bone Analysis

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Nicolaï This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6672306/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Dec, 2025 Read the published version in Journal of Nondestructive Evaluation → Version 1 posted 14 You are reading this latest preprint version Abstract Pork is an important meat product for the European Union, which exported over 4.2 million tons in 2023, valued at €8.1 billion. Automating the labor-intensive deboning process is of significant interest, particularly through the development of advanced inline inspection systems capable of analyzing pork shoulder bone structures. While computed tomography (CT) systems provide high-contrast 3D reconstructions, their large size and high-cost present substantial barriers to adoption in industrial meat processing. This study addresses these challenges by introducing a novel approach that uses a single X-ray projection in combination with deep neural networks to predict the 3D segmentation map of pork shoulder bone structures using conventional reconstruction algorithms. To this end, U-Net neural network variants were trained on high-resolution CT scans of 90 pork shoulders. These scans were augmented with synthetic data to simulate different orientations on a conveyor belt, ensuring the model’s robustness. The minimum number of X-ray projections needed for accurate reconstruction was determined based on simulations, and 60 evenly spaced projections between 0° and 180° were found optimal. The Feldkamp-Davis-Kress (FDK) algorithm was chosen for its efficiency and cost-effectiveness in inline processing. The model achieved a Dice score of 0.94 and an SSIM of 0.96 on test data, demonstrating its ability to predict 59 missing projections and reconstruct the 3D bone structure accurately. The method that is proposed in this paper has the potential to advance meat processing by enhancing deboning precision, reducing waste, and streamlining operations. pork shoulder processing X-ray technology 3D segmentation inline inspection multi-angle X-ray prediction neural networks Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1 Introduction Pork is an essential product within the European Union, the largest global exporter, accounting for over 4.2 million tons in 2023, valued at €8.1 billion. Segments of pork processing lines have already been automated, including carcass division and weight estimation using RGB. This enables precise predictions of lean meat and fat ratios in major cuts like tenderloin, sirloin, and striploin [ 1 ], [ 2 ]. However, the deboning process remains highly labor-intensive. Deboning involves repetitive tasks in cold environments, exposing workers to physical strain and potential hazards from sharp tools. Consequently, there is significant interest in enhancing automation to improve efficiency, worker safety, and precision in cutting operations, thereby reducing waste. Inline inspection systems that analyze pork shoulder bone structures offer a promising path for achieving this automation. Such systems could enable automated deboning robots to make precise cuts guided by accurate information about the location of bones. However, the complete automation of the deboning process is still not possible, primarily due to the complexity of accurately capturing the internal bone structures in real time nondestructively. Traditional imaging methods, such as computed tomography (CT), offer high accuracy in reconstructing internal structures. CT scans are, therefore, widely used in medical imaging [ 3 ], materials science [ 4 ], and agricultural research [ 5 ], demonstrating their value in capturing high-resolution 3D data. However, the implementation of CT systems in industrial meat processing is constrained by their size, cost, and time-intensive reconstruction processes, making them impractical for high-throughput environments [ 6 ]. Our study proposes to use neural networks to predict multiple X-ray projections from only one X-ray projection that then can be used for reconstructing a 3D volume of the object of interest, thus avoiding the need for multiple radiographic images. Neural networks have indeed emerged as a promising alternative to traditional methods for Computed Tomography (CT) volume reconstruction [ 7 ]. Convolutional Neural Networks (CNNs), in particular, have demonstrated significant success in learning complex mappings between projection data and the underlying object, enabling high-fidelity image reconstruction [ 8 ]. While neural networks like U-Net are known for their success in segmentation tasks [ 9 ], they are also effective for image-to-image translation and generation [ 10 ]. Here, the application of U-Net type of neural networks for image-to-image translation of projection images for input to X-ray CT for prediction of 3D bone structures in pig shoulders is attempted. The predicted projections that are generated by the trained U-Net models are used to compute a detailed 3D representation of the internal bone structure of pork shoulders by conventional reconstruction algorithms. By applying synthetic data augmentation, the approach ensures robustness to variability in pork shoulder orientation during inline processing. 2 Materials and methods 2.1 Dataset An existing dataset was used that has been explained in more detail in [ 14 ]. The dataset consists of CT scans of 90 pork shoulders, collected from a slaughterhouse in Belgium, with an equal distribution of left and right shoulders. These samples were obtained from DanBred and Large White sows, which were inseminated by Belgian Pietrain boars. The CT scans were performed over a period of three separate days at the University Hospital of Leuven (UZ Leuven), using a Siemens Healthineers Somatom Definition Edge CT scanner with a voxel resolution of 0.83 mm. This setup allowed for a non-destructive scan of the pork shoulders, which provided high-quality 3D imaging of the internal bone structure as well as the surrounding soft tissue. The samples were transported in refrigerated vehicles from the slaughterhouse to the lab where they were stored at 1°C to maintain freshness until the CT scanner became available. Each pork shoulder was placed in a plastic container, with Styrofoam padding along the sides and bottom to help stabilize the sample during scanning. This arrangement made it easier to isolate the pork shoulder from its surroundings in the CT scan, ensuring that the resulting images were focused solely on the meat and bone structure. Following the CT scanning process, the next critical step was the alignment of the scanned volumes to correct for any unwanted variations due to positioning inconsistencies. This alignment process has been described in greater detail in [ 14 ]. To align the scans, we used the software Avizo version 2021.2 (Thermo Scientific) to manually adjust the first scan into the desired orientation, where the X and Y axes represented the width and depth of the volume, respectively, and the Z axis corresponded to the height of the scan. Once the first scan was correctly positioned, the alignment of the other scans was automated using the "imregister" function in Matlab. This function calculates a rigid transformation matrix that optimally adjusts the scans by translating and rotating them into a common coordinate system, thereby ensuring consistency across the dataset. The "imregister" method relies on an intensity-based approach, where the mean squared error (MSE) is used to measure the similarity between corresponding voxels in the CT images. The rigid transformation matrix is iteratively optimized using a gradient descent approach, providing an ideal transformation for all CT scans in the dataset. The alignment process was crucial in ensuring that the variations observed in the dataset were representative of anatomical differences rather than the difference in scan positioning. By aligning the CT scans in this way, we were able to accurately capture the anatomical variations within the pork shoulder dataset, including differences in size, shape, and bone structure. These variations are crucial for understanding the diversity of pork shoulder anatomy, which serves as the basis for training advanced neural network models. 2.2 Simulated X-ray projections Medical CT scanners typically output reconstructed 3D volumes, not the raw X-ray projections captured around the object. To have the flexibility to test a wide range of CT systems and parameters, the Astra toolbox (Van Aarle et al., 2016, 2015) was used in this study to generate projections from the 3D CT volumes (Fig. 1 ). 2.3 U-Net neural network for image-to-image translation U-Net and its variants have proven effective in a variety of image-to-image translation tasks as its encoder-decoder architecture is suitable to transform input images into high-quality output representations [ 21 ]. Originally developed for biomedical segmentation tasks [ 22 ], U-Net has since been adapted for applications such as medical imaging [ 23 ], satellite image translation [ 24 ], and industrial defect detection [ 25 ]. Its strength lies in its ability to capture fine-grained details while preserving spatial context, making it an ideal choice for image-to-image tasks involving complex structures [ 26 ]. In the U-Net architecture, the encoder path extracts high-level semantic features by progressively downsampling the input image, while the decoder path upsamples these features to produce the desired output [ 9 ]. Skip connections between corresponding layers of the encoder and decoder allow the network to retain and merge spatial details, a critical capability for accurate image reconstruction and translation [ 27 ]. Variants of U-Net, such as U-Net++ [ 19 ] and V-Net [ 28 ], enhance performance by introducing additional layers, hierarchical architectures, or modifications to skip connections, tailoring the network to specific datasets and challenges. These adaptations are commonly used in domains requiring high precision, such as super-resolution imaging [ 29 ], depth estimation [ 30 ], and X-ray image synthesis [ 31 ]. In this article, the use of U-Net-like architectures is used for bone segmentation of pork shoulders by employing them for the prediction of missing X-ray projections from a single measured projection of a pork shoulder. This involves translating the input X-ray projection into a full set of projections at evenly spaced view angles between 0° and 180°.The reconstructed projections are then utilized with conventional CT reconstruction algorithms to generate a 3D representation of the bone structure. The networks were trained on a dataset comprising 25,920 X-ray projections derived from 72 CT scans of pork shoulders. Each sample was rotated between − 15 and 15 degrees along the x, y, and z axes to simulate realistic orientations. For evaluation, the test and validation datasets each contained 3,240 projections from 9 additional CT scans each, ensuring a standardized protocol for assessing model performance. An 80-10-10 train-test-validation split was consistently applied across all experiments. Early stopping was utilized to prevent overfitting, halting training when no improvement in loss was observed over 100 iterations. The Adam optimizer with a learning rate of 0.001 was used, and the mean squared error (MSE) as loss metric. This loss metric compares the gray values of the predicted X-ray projections with the X-ray projections that were simulated from the rotated ground truth volumes. Two types of neural network architectures were evaluated: standard U-Nets with varying depths and U-Net + + architectures. Additionally, models were trained with both ImageNet-pretrained encoder weights and randomly initialized weights to investigate the impact of pretraining on performance. Each model used a batch size of 4. Once the neural network has predicted the missing X-ray projection, a 3D volume of the object of interest can be reconstructed using a conventional reconstruction algorithm. For this study, the FDK (Feldkamp, Davis, and Kress) reconstruction algorithm was chosen [ 32 ]. After volume reconstruction, the Otsu thresholding method was implemented to segment the bone structure, which is of particular interest for this study [ 33 ]. 2.4 Model performance evaluation The Dice Similarity Coefficient (DSC) is a widely used metric for evaluating the performance of segmentation algorithms, particularly for 3D volume analysis in medical imaging [35]. Unlike the IoU, the DSC is especially relevant when assessing 3D segmentation, such as volumetric bone structures. It is calculated as twice the volume of the intersection between the predicted segmentation and the ground truth, divided by the sum of their individual volumes. The DSC ranges from 0 to 1, with a score of 1 indicating a perfect match between the predicted segmentation and the ground truth. The formula for the DSC is provided in Eq. 1, where \(\:{\varvec{S}}_{\varvec{p}}\:\) represents the predicted segmentation map, and \(\:{\varvec{S}}_{\varvec{g}}\) denotes the ground truth segmentation map. While the DSC is a commonly used metric for volume segmentation evaluation, it is designed to evaluate the overlap between the predicted and ground truth regions. This metric may not fully capture the spatial nuances, especially in cases where the precise localization of structures is vital, such as in medical imaging applications. To address the limitations of DSC, in this article also a voxel-wise distance metric evaluation method was used in addition to the DSC to measure the segmentation performance in millimeters. The equation for this evaluation metric is given as Eq. 2. In this equation j indicates the voxel number in the predicted segmentation map () where the nearest neighbor in the ground truth segmentation map () will be used to calculate the euclidean distance between these 2 voxels. The i variable in this formula indicates the spatial co-ordinates of a voxel. Since only a single class is segmented, the segmentation maps are binarybinary, and the distance is computed between all voxels in the predicted volume and their nearest counterpart in the ground truth. This Euclidian distance is expressed in millimeters, the scans and projections are made with a resolution of 0.83 mm indicated by the variable in the equation. Once this distance metric is calculated over every voxel j , the average, mean, and standard deviation can be calculated for each voxel j to understand the prediction accuracy and variability of each volume. 3 Results and discussion 3.1 Number of projections for bone reconstruction Before training neural networks to predict multiple X-ray projections from a single input, we determined the minimum number of projections required for accurate bone segmentation. Using the Astra toolbox, we reconstructed the pork shoulder for a cone-beam system and the FDK algorithm across 90 pork shoulders, varying the number of projections. Then, for each reconstruction the bones were segmented using Otsu thresholding [ 34 ]. In the Astra toolbox a detector size of 572 by 572 pixels was configured with a source to detector distance of 800 voxels. Figure 2 shows the average loss curves between the ground truth CT scan and those reconstructed from a limited set of simulated projections: the left side plot displays the mean squared error (MSE) for the entire volume, while the right-side plot shows the DSC of the segmented bone structures. Based on these results and visual inspection of the segmented bone structures, it was decided to train a neural network to predict 59 additional projections from a single input, resulting in a total of 60 evenly spaced projections covering 180 degrees around the object. Figures 3 , 4 , and 5 below further demonstrate the accurate segmentation of the bone structure using only 60 X-ray projections. Figure 3 presents a slice from a randomly selected sample in the dataset. The left figure shows a slice from the original CT volume. The middle figure displays the reconstructed slice using only 60 X-ray projections. The right side highlights the absolute difference between the original and reconstructed slice. Figure 4 presents the same three slices as Fig. 3 , but after applying Otsu thresholding to segment the bone structures. Figure 5 provides a 3D visualization of the reconstructed bone volume. These figures collectively underscore that, in this specific case, 60 X-ray projections are sufficient to achieve an accurate 3D representation of the bone volume within a pork shoulder. 3.2 Unet-like neural network architectures for image generation Table 1 provides an overview of different neural network architectures trained to predict multiview X-ray projections from a single X-ray radiograph of pork shoulders. The baseline U-Net model with four layers and no pretraining achieved a 3D DSC of 0.88 ± 0.05. When initialized with ImageNet-pretrained encoder weights, the model's mean DSC increased slightly to 0.90 ± 0.10 but exhibited higher variability, indicating less consistent performance. The U-Net + + architecture with a ResNet-50 encoder emerged as the best-performing model. This configuration achieved a mean DSC of 0.94 ± 0.08, outperforming all other configurations. This architecture utilized residual convolutional blocks and more intricate skip connections between encoder and decoder layers, enabling more effective feature extraction and improving generalization. Notably, the ImageNet-pretrained variant of this model achieved a slightly lower DSC score of 0.91 ± 0.12, reaffirming the observation that pretrained weights optimized for RGB images may not capture the grayscale features required for processing X-ray data effectively. These results demonstrate that the optimal configuration for predicting multiview X-ray projections involves a U-Net + + model with ResNet-50 encoders and no pretrained weights. The capability to accurately predict 59 missing X-ray projections from a single radiograph enables the reconstruction of a 3D segmentation map of the bone structure, providing a robust solution for inline inspection systems in industrial meat processing. This approach offers a significant advancement in real-time automation by enabling precise bone structure analysis with minimal input data. Table 1 3D Dice Similarity Coefficient (DSC) scores for bone segmentation on the test set of pork shoulder samples, using different neural network models to predict X-ray projections for volumetric reconstruction.The table shows the maximum, mean ± standard deviation (σ), and minimum DSC scores for each model configuration, which were used to assess the quality of the reconstructed 3D bone structure from the predicted X-ray projections. DSC of bone segmentation Model Max Mean \(\:\pm\:\sigma\:\) Min Four layer U-Net without pretraining 0.92 0.88 \(\:\pm\:\) 0.05 0.86 Four layer U-Net wit ImageNet weights initialization 0.93 0.90 \(\:\pm\:\) 0.10 0.82 U-Net + + with ResNet-50 encoder without pretraining 0.96 0.94 \(\:\pm\:0.08\) 0.88 U-Net + + with ResNet-50 encoder and ImageNet initialization 0.94 0.91 \(\:\pm\:\) 0.12 0.84 To further demonstrate the performance of the proposed method, the worst-performing sample from the test set of the best-performing model is visualized in the figures below. In Fig. 4 , the ground truth (GT) X-ray projection, rotated 90° from the input X-ray projection provided to the neural network, is shown on the left. The middle figure displays the corresponding predicted projection, while the right figure illustrates the absolute difference between the predicted and ground truth projections. Similarly, in Fig. 5 , the same layout is used to present the predicted projection for a rotation of 2.7° relative to the input projection. These two specific angles were selected from the 59 predicted projections to highlight the neural network’s capability to generate diverse perspectives from a single input projection. Because the dataset used contained different angles, it is also clearly visible that not every projection of the same sample at different angles has the same maximum grayscale value. The maximum value after normalization of the complete dataset is 1. This difference is clearly visible between Fig. 4 and Fig. 5 , where the side view in Fig. 4 generates an X-ray projection with higher values. Figures 6 and 7 illustrate two representative slices (numbers 400 and 44) from the reconstructed volume of the worst-performing test sample, providing a visual overview from the top to the bottom of the shoulder. Despite being the worst-performing sample in our test set, the bone structure within the reconstructed volume remains recognizable and can be effectively segmented. Figure 8 shows the rendering of the bone volumes obtained from the ground truth (GT) CT scan and the reconstructed volume of the worst-performing test sample after applying Otsu thresholding. While some minor discrepancies and small speckles are visible, the overall shape and spatial arrangement of the bone structures are well-predicted by the neural network. This suggests that the model can effectively generate 59 realistic X-ray projections from a single input projection, enabling the reconstruction of a 3D bone structure with reasonable accuracy. The error associated with the reconstructed volume was measured using the euclidean discrete metric. The maximum error observed was 16 mm, indicating that the voxel positions in the reconstructed volume closely correspond to their ground truth counterparts. 4 Conclusions This study presented a novel approach for reconstructing 3D bone structures in pork shoulders using a single measured X-ray projection. By exploiting a deep learning model to predict multiple X-ray projections from various angles, we demonstrate the feasibility of generating accurate 3D bone segmentations using conventional CT reconstruction algorithms. The trained model effectively predicts the missing X-ray projections, achieving high accuracy with an average Dice score of 0.94 on the test set. This approach has the potential to improve industrial meat processing by enabling fast and accurate 3D bone structure analysis from a single X-ray measurement, reducing the need for complex and expensive multi-view imaging systems. However, the current evaluation relies on a limited dataset of synthetic X-ray projections. To fully validate the model's robustness, future work should focus on testing with real X-ray projections from a custom-designed inline X-ray system. Such validation would provide critical insights into the model's performance under practical conditions, including the impact of system noise, diverse pork shoulder orientations, and variability across different pork breeds. Addressing these challenges will be essential to advancing the method toward deployment in industrial environments, ensuring reliability and generalizability across a broad spectrum of use cases. Declarations Acknowledgements The authors gratefully acknowledge the funding received from Flanders Innovation & Entrepreneurship (VLAIO ICON iMeat project HBC.2020.2945) with support of Flanders’ Food. Pieter Verboven and Bart Nicolaï are co-Pis of the KU Leuven XCT Core facility. References N. 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Cite Share Download PDF Status: Published Journal Publication published 01 Dec, 2025 Read the published version in Journal of Nondestructive Evaluation → Version 1 posted Editorial decision: Revision requested 04 Sep, 2025 Reviews received at journal 04 Sep, 2025 Reviews received at journal 03 Sep, 2025 Reviewers agreed at journal 02 Sep, 2025 Reviewers agreed at journal 31 Aug, 2025 Reviewers agreed at journal 31 Aug, 2025 Reviewers agreed at journal 31 Aug, 2025 Reviewers agreed at journal 31 Aug, 2025 Reviews received at journal 02 Jun, 2025 Reviewers agreed at journal 20 May, 2025 Reviewers invited by journal 19 May, 2025 Editor assigned by journal 19 May, 2025 Submission checks completed at journal 15 May, 2025 First submitted to journal 15 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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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-6672306","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":459054019,"identity":"3806158f-e7a4-4a90-bfbf-d7ea4bb8a751","order_by":0,"name":"Michiel Pieters","email":"","orcid":"","institution":"BIOSYST-MeBioS","correspondingAuthor":false,"prefix":"","firstName":"Michiel","middleName":"","lastName":"Pieters","suffix":""},{"id":459054020,"identity":"0fa8d3de-bbbc-44cf-87d1-68ea17c96dc3","order_by":1,"name":"Pieter Verboven","email":"data:image/png;base64,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","orcid":"","institution":"BIOSYST-MeBioS","correspondingAuthor":true,"prefix":"","firstName":"Pieter","middleName":"","lastName":"Verboven","suffix":""},{"id":459054023,"identity":"cca96e46-3fdc-434d-a523-a70f7e44be7b","order_by":2,"name":"Bart M. Nicolaï","email":"","orcid":"","institution":"BIOSYST-MeBioS","correspondingAuthor":false,"prefix":"","firstName":"Bart","middleName":"M.","lastName":"Nicolaï","suffix":""}],"badges":[],"createdAt":"2025-05-15 11:53:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6672306/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6672306/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10921-025-01301-x","type":"published","date":"2025-12-01T15:56:57+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83298988,"identity":"1fb4e8f4-b4fe-4d8e-a7ad-91c694fa7589","added_by":"auto","created_at":"2025-05-22 14:37:38","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":244103,"visible":true,"origin":"","legend":"\u003cp\u003eA CT scan rendering of a pork shoulder (left side) and the corresponding X-ray projection simulated with the Astra toolbox (right side) for a cone beam scanner geometry.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/6d15826c09589f2f1c58b864.png"},{"id":83299906,"identity":"41b9ba4d-276e-43ae-acf4-8ebe946173de","added_by":"auto","created_at":"2025-05-22 14:45:38","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":131843,"visible":true,"origin":"","legend":"\u003cp\u003eReconstruction accuracy loss curves as a function of the number of projections. The left side figure illustrates the mean squared error (MSE) for the entire volume, while the right side figure depicts the Dice score (DSC) of segmented bone structures after Otsu thresholding. Both curves represent the average performance across 90 pork shoulders in the dataset.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/a596f0224fcdcac201d3e0e4.png"},{"id":83299910,"identity":"71c6482b-4afa-4246-97fd-382ea0895f44","added_by":"auto","created_at":"2025-05-22 14:45:38","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":704441,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of a CT slice (Slice 460) (left), reconstructed slice using 60 X-ray projections (middle), and their absolute difference (right).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/0f7002232b91b0e5bf36698f.png"},{"id":83298987,"identity":"37615ff8-0a28-4120-a75c-cf7de2c452a4","added_by":"auto","created_at":"2025-05-22 14:37:38","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":87437,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eSegmentation of the same CT slice (Slice 460) (left), showing the bone structure extracted using 60 X-ray projections (middle) and difference image (right).\u003c/em\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/1f10fe6aee7d44aecfd89243.png"},{"id":83299907,"identity":"c9dd8bc8-df1e-456d-80f8-77ea42e3e730","added_by":"auto","created_at":"2025-05-22 14:45:38","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":254814,"visible":true,"origin":"","legend":"\u003cp\u003e3D visualization of the reconstructed bone volume. The left panel shows the bone volume extracted from the original CT scan, while the right panel displays the bone volume reconstructed using the FDK algorithm with only 60 X-ray projections.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/bd05bd7b6c4af86963989e92.png"},{"id":83300648,"identity":"9b6a5709-eacc-4942-8b0c-1794da3819cf","added_by":"auto","created_at":"2025-05-22 14:53:38","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":175831,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 4. Ground truth X-ray projection (left), the corresponding predicted projection (middle), and the absolute difference (right) for the worst-performing test sample. The ground truth projection is rotated 90° from the input projection.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/7ba45a29e0b4e2206300d635.png"},{"id":83300651,"identity":"51bc7c76-b6cd-45ac-bc70-585bad404e85","added_by":"auto","created_at":"2025-05-22 14:53:38","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":230715,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 5. Ground truth X-ray projection (left), the corresponding predicted projection (middle), and the absolute difference (right) for the worst-performing test sample. The ground truth projection is rotated 2.7° from the input projection.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/437f365948c2b09b5e44659a.png"},{"id":83299915,"identity":"851f800e-d482-462a-b97e-aa17d3cf14b4","added_by":"auto","created_at":"2025-05-22 14:45:38","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":651553,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 6. Slice from the reconstructed volume of the worst-performing test sample, providing a visual overview from the top of the shoulder. The figure shows the ground truth slice (left), the predicted slice (middle), and the absolute difference between the two slices (right).\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/be7cdca37c49ecbac56150f8.png"},{"id":83298998,"identity":"289eda6a-31e7-443b-8220-7d5cde425da0","added_by":"auto","created_at":"2025-05-22 14:37:38","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":644008,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 7. Representative slice from the reconstructed volume of the worst-performing test sample, providing a visual overview from the bottom of the shoulder.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/73a4fb6613cd51419881b0ce.png"},{"id":83300666,"identity":"c03ec14c-c744-42bd-bcae-0514805361b9","added_by":"auto","created_at":"2025-05-22 14:53:39","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":437099,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 8. Rendering of the bone volume obtained from the ground truth (GT) CT scan (left) and the reconstructed volume (right) of the worst-performing test sample after applying Otsu thresholding.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/0820e827ae2649daa75b9f04.png"},{"id":97723752,"identity":"1a791816-d817-486b-aefc-4b5953a4ed19","added_by":"auto","created_at":"2025-12-08 16:02:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5568302,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6672306/v1/f1820b68-3100-4179-96ee-9c4cb129d4dc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Single-Shot X-ray to Multi-View Projections for 3D Pork Shoulder Bone Analysis","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003ePork is an essential product within the European Union, the largest global exporter, accounting for over 4.2\u0026nbsp;million tons in 2023, valued at \u0026euro;8.1\u0026nbsp;billion. Segments of pork processing lines have already been automated, including carcass division and weight estimation using RGB. This enables precise predictions of lean meat and fat ratios in major cuts like tenderloin, sirloin, and striploin [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. However, the deboning process remains highly labor-intensive. Deboning involves repetitive tasks in cold environments, exposing workers to physical strain and potential hazards from sharp tools. Consequently, there is significant interest in enhancing automation to improve efficiency, worker safety, and precision in cutting operations, thereby reducing waste. Inline inspection systems that analyze pork shoulder bone structures offer a promising path for achieving this automation. Such systems could enable automated deboning robots to make precise cuts guided by accurate information about the location of bones. However, the complete automation of the deboning process is still not possible, primarily due to the complexity of accurately capturing the internal bone structures in real time nondestructively.\u003c/p\u003e \u003cp\u003eTraditional imaging methods, such as computed tomography (CT), offer high accuracy in reconstructing internal structures. CT scans are, therefore, widely used in medical imaging [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], materials science [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and agricultural research [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], demonstrating their value in capturing high-resolution 3D data. However, the implementation of CT systems in industrial meat processing is constrained by their size, cost, and time-intensive reconstruction processes, making them impractical for high-throughput environments [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Our study proposes to use neural networks to predict multiple X-ray projections from only one X-ray projection that then can be used for reconstructing a 3D volume of the object of interest, thus avoiding the need for multiple radiographic images. Neural networks have indeed emerged as a promising alternative to traditional methods for Computed Tomography (CT) volume reconstruction [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Convolutional Neural Networks (CNNs), in particular, have demonstrated significant success in learning complex mappings between projection data and the underlying object, enabling high-fidelity image reconstruction [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. While neural networks like U-Net are known for their success in segmentation tasks [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], they are also effective for image-to-image translation and generation [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Here, the application of U-Net type of neural networks for image-to-image translation of projection images for input to X-ray CT for prediction of 3D bone structures in pig shoulders is attempted.\u003c/p\u003e \u003cp\u003eThe predicted projections that are generated by the trained U-Net models are used to compute a detailed 3D representation of the internal bone structure of pork shoulders by conventional reconstruction algorithms. By applying synthetic data augmentation, the approach ensures robustness to variability in pork shoulder orientation during inline processing.\u003c/p\u003e"},{"header":"2 Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Dataset\u003c/h2\u003e\n \u003cp\u003eAn existing dataset was used that has been explained in more detail in [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e]. The dataset consists of CT scans of 90 pork shoulders, collected from a slaughterhouse in Belgium, with an equal distribution of left and right shoulders. These samples were obtained from DanBred and Large White sows, which were inseminated by Belgian Pietrain boars. The CT scans were performed over a period of three separate days at the University Hospital of Leuven (UZ Leuven), using a Siemens Healthineers Somatom Definition Edge CT scanner with a voxel resolution of 0.83 mm. This setup allowed for a non-destructive scan of the pork shoulders, which provided high-quality 3D imaging of the internal bone structure as well as the surrounding soft tissue. The samples were transported in refrigerated vehicles from the slaughterhouse to the lab where they were stored at 1\u0026deg;C to maintain freshness until the CT scanner became available. Each pork shoulder was placed in a plastic container, with Styrofoam padding along the sides and bottom to help stabilize the sample during scanning. This arrangement made it easier to isolate the pork shoulder from its surroundings in the CT scan, ensuring that the resulting images were focused solely on the meat and bone structure.\u003c/p\u003e\n \u003cp\u003eFollowing the CT scanning process, the next critical step was the alignment of the scanned volumes to correct for any unwanted variations due to positioning inconsistencies. This alignment process has been described in greater detail in [\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e]. To align the scans, we used the software Avizo version 2021.2 (Thermo Scientific) to manually adjust the first scan into the desired orientation, where the X and Y axes represented the width and depth of the volume, respectively, and the Z axis corresponded to the height of the scan. Once the first scan was correctly positioned, the alignment of the other scans was automated using the \u0026quot;imregister\u0026quot; function in Matlab. This function calculates a rigid transformation matrix that optimally adjusts the scans by translating and rotating them into a common coordinate system, thereby ensuring consistency across the dataset. The \u0026quot;imregister\u0026quot; method relies on an intensity-based approach, where the mean squared error (MSE) is used to measure the similarity between corresponding voxels in the CT images. The rigid transformation matrix is iteratively optimized using a gradient descent approach, providing an ideal transformation for all CT scans in the dataset. The alignment process was crucial in ensuring that the variations observed in the dataset were representative of anatomical differences rather than the difference in scan positioning. By aligning the CT scans in this way, we were able to accurately capture the anatomical variations within the pork shoulder dataset, including differences in size, shape, and bone structure. These variations are crucial for understanding the diversity of pork shoulder anatomy, which serves as the basis for training advanced neural network models.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Simulated X-ray projections\u003c/h2\u003e\n \u003cp\u003eMedical CT scanners typically output reconstructed 3D volumes, not the raw X-ray projections captured around the object. To have the flexibility to test a wide range of CT systems and parameters, the Astra toolbox (Van Aarle et al., 2016, 2015) was used in this study to generate projections from the 3D CT volumes (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 U-Net neural network for image-to-image translation\u003c/h2\u003e\n \u003cp\u003eU-Net and its variants have proven effective in a variety of image-to-image translation tasks as its encoder-decoder architecture is suitable to transform input images into high-quality output representations [\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e]. Originally developed for biomedical segmentation tasks [\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e], U-Net has since been adapted for applications such as medical imaging [\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e], satellite image translation [\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e], and industrial defect detection [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. Its strength lies in its ability to capture fine-grained details while preserving spatial context, making it an ideal choice for image-to-image tasks involving complex structures [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e]. In the U-Net architecture, the encoder path extracts high-level semantic features by progressively downsampling the input image, while the decoder path upsamples these features to produce the desired output [\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e]. Skip connections between corresponding layers of the encoder and decoder allow the network to retain and merge spatial details, a critical capability for accurate image reconstruction and translation [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e]. Variants of U-Net, such as U-Net++ [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e] and V-Net [\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e], enhance performance by introducing additional layers, hierarchical architectures, or modifications to skip connections, tailoring the network to specific datasets and challenges. These adaptations are commonly used in domains requiring high precision, such as super-resolution imaging [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e], depth estimation [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e], and X-ray image synthesis [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eIn this article, the use of U-Net-like architectures is used for bone segmentation of pork shoulders by employing them for the prediction of missing X-ray projections from a single measured projection of a pork shoulder. This involves translating the input X-ray projection into a full set of projections at evenly spaced view angles between 0\u0026deg; and 180\u0026deg;.The reconstructed projections are then utilized with conventional CT reconstruction algorithms to generate a 3D representation of the bone structure. The networks were trained on a dataset comprising 25,920 X-ray projections derived from 72 CT scans of pork shoulders. Each sample was rotated between \u0026minus;\u0026thinsp;15 and 15 degrees along the x, y, and z axes to simulate realistic orientations. For evaluation, the test and validation datasets each contained 3,240 projections from 9 additional CT scans each, ensuring a standardized protocol for assessing model performance. An 80-10-10 train-test-validation split was consistently applied across all experiments. Early stopping was utilized to prevent overfitting, halting training when no improvement in loss was observed over 100 iterations. The Adam optimizer with a learning rate of 0.001 was used, and the mean squared error (MSE) as loss metric. This loss metric compares the gray values of the predicted X-ray projections with the X-ray projections that were simulated from the rotated ground truth volumes. Two types of neural network architectures were evaluated: standard U-Nets with varying depths and U-Net\u0026thinsp;+\u0026thinsp;+\u0026thinsp;architectures. Additionally, models were trained with both ImageNet-pretrained encoder weights and randomly initialized weights to investigate the impact of pretraining on performance. Each model used a batch size of 4.\u003c/p\u003e\n \u003cp\u003eOnce the neural network has predicted the missing X-ray projection, a 3D volume of the object of interest can be reconstructed using a conventional reconstruction algorithm. For this study, the FDK (Feldkamp, Davis, and Kress) reconstruction algorithm was chosen [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e]. After volume reconstruction, the Otsu thresholding method was implemented to segment the bone structure, which is of particular interest for this study [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4 Model performance evaluation\u003c/h2\u003e\n \u003cp\u003eThe Dice Similarity Coefficient (DSC) is a widely used metric for evaluating the performance of segmentation algorithms, particularly for 3D volume analysis in medical imaging [35]. Unlike the IoU, the DSC is especially relevant when assessing 3D segmentation, such as volumetric bone structures. It is calculated as twice the volume of the intersection between the predicted segmentation and the ground truth, divided by the sum of their individual volumes. The DSC ranges from 0 to 1, with a score of 1 indicating a perfect match between the predicted segmentation and the ground truth. The formula for the DSC is provided in Eq. 1, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{S}}_{\\varvec{p}}\\:\\)\u003c/span\u003e\u003c/span\u003erepresents the predicted segmentation map, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{S}}_{\\varvec{g}}\\)\u003c/span\u003e\u003c/span\u003e denotes the ground truth segmentation map.\u003c/p\u003e\n \u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n \u003cp\u003eWhile the DSC is a commonly used metric for volume segmentation evaluation, it is designed to evaluate the overlap between the predicted and ground truth regions. This metric may not fully capture the spatial nuances, especially in cases where the precise localization of structures is vital, such as in medical imaging applications. To address the limitations of DSC, in this article also a voxel-wise distance metric evaluation method was used in addition to the DSC to measure the segmentation performance in millimeters. The equation for this evaluation metric is given as Eq. 2. In this equation j indicates the voxel number in the predicted segmentation map () where the nearest neighbor in the ground truth segmentation map () will be used to calculate the euclidean distance between these 2 voxels. The i variable in this formula indicates the spatial co-ordinates of a voxel. Since only a single class is segmented, the segmentation maps are binarybinary, and the distance is computed between all voxels in the predicted volume and their nearest counterpart in the ground truth. This Euclidian distance is expressed in millimeters, the scans and projections are made with a resolution of 0.83 mm indicated by the variable in the equation. Once this distance metric is calculated over every voxel \u003cem\u003ej\u003c/em\u003e, the average, mean, and standard deviation can be calculated for each voxel \u003cem\u003ej\u003c/em\u003e to understand the prediction accuracy and variability of each volume.\u003c/p\u003e\n \u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Number of projections for bone reconstruction\u003c/h2\u003e \u003cp\u003eBefore training neural networks to predict multiple X-ray projections from a single input, we determined the minimum number of projections required for accurate bone segmentation. Using the Astra toolbox, we reconstructed the pork shoulder for a cone-beam system and the FDK algorithm across 90 pork shoulders, varying the number of projections. Then, for each reconstruction the bones were segmented using Otsu thresholding [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. In the Astra toolbox a detector size of 572 by 572 pixels was configured with a source to detector distance of 800 voxels. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the average loss curves between the ground truth CT scan and those reconstructed from a limited set of simulated projections: the left side plot displays the mean squared error (MSE) for the entire volume, while the right-side plot shows the DSC of the segmented bone structures. Based on these results and visual inspection of the segmented bone structures, it was decided to train a neural network to predict 59 additional projections from a single input, resulting in a total of 60 evenly spaced projections covering 180 degrees around the object.\u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e below further demonstrate the accurate segmentation of the bone structure using only 60 X-ray projections. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents a slice from a randomly selected sample in the dataset. The left figure shows a slice from the original CT volume. The middle figure displays the reconstructed slice using only 60 X-ray projections. The right side highlights the absolute difference between the original and reconstructed slice. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the same three slices as Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, but after applying Otsu thresholding to segment the bone structures. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e provides a 3D visualization of the reconstructed bone volume. These figures collectively underscore that, in this specific case, 60 X-ray projections are sufficient to achieve an accurate 3D representation of the bone volume within a pork shoulder.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Unet-like neural network architectures for image generation\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e provides an overview of different neural network architectures trained to predict multiview X-ray projections from a single X-ray radiograph of pork shoulders. The baseline U-Net model with four layers and no pretraining achieved a 3D DSC of 0.88\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05. When initialized with ImageNet-pretrained encoder weights, the model's mean DSC increased slightly to 0.90\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10 but exhibited higher variability, indicating less consistent performance. The U-Net\u0026thinsp;+\u0026thinsp;+\u0026thinsp;architecture with a ResNet-50 encoder emerged as the best-performing model. This configuration achieved a mean DSC of 0.94\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08, outperforming all other configurations. This architecture utilized residual convolutional blocks and more intricate skip connections between encoder and decoder layers, enabling more effective feature extraction and improving generalization. Notably, the ImageNet-pretrained variant of this model achieved a slightly lower DSC score of 0.91\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12, reaffirming the observation that pretrained weights optimized for RGB images may not capture the grayscale features required for processing X-ray data effectively.\u003c/p\u003e \u003cp\u003eThese results demonstrate that the optimal configuration for predicting multiview X-ray projections involves a U-Net\u0026thinsp;+\u0026thinsp;+\u0026thinsp;model with ResNet-50 encoders and no pretrained weights. The capability to accurately predict 59 missing X-ray projections from a single radiograph enables the reconstruction of a 3D segmentation map of the bone structure, providing a robust solution for inline inspection systems in industrial meat processing. This approach offers a significant advancement in real-time automation by enabling precise bone structure analysis with minimal input data.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e3D Dice Similarity Coefficient (DSC) scores for bone segmentation on the test set of pork shoulder samples, using different neural network models to predict X-ray projections for volumetric reconstruction.The table shows the maximum, mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation (σ), and minimum DSC scores for each model configuration, which were used to assess the quality of the reconstructed 3D bone structure from the predicted X-ray projections.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eDSC of bone segmentation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMax\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\pm\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMin\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFour layer U-Net without pretraining\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.88\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\pm\\:\\)\u003c/span\u003e\u003c/span\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFour layer U-Net wit ImageNet weights initialization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.90\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\pm\\:\\)\u003c/span\u003e\u003c/span\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eU-Net\u0026thinsp;+\u0026thinsp;+\u0026thinsp;with ResNet-50 encoder without pretraining\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.94\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\pm\\:0.08\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eU-Net\u0026thinsp;+\u0026thinsp;+\u0026thinsp;with ResNet-50 encoder and ImageNet initialization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.91\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\pm\\:\\)\u003c/span\u003e\u003c/span\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo further demonstrate the performance of the proposed method, the worst-performing sample from the test set of the best-performing model is visualized in the figures below. In Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the ground truth (GT) X-ray projection, rotated 90\u0026deg; from the input X-ray projection provided to the neural network, is shown on the left. The middle figure displays the corresponding predicted projection, while the right figure illustrates the absolute difference between the predicted and ground truth projections. Similarly, in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the same layout is used to present the predicted projection for a rotation of 2.7\u0026deg; relative to the input projection. These two specific angles were selected from the 59 predicted projections to highlight the neural network\u0026rsquo;s capability to generate diverse perspectives from a single input projection. Because the dataset used contained different angles, it is also clearly visible that not every projection of the same sample at different angles has the same maximum grayscale value. The maximum value after normalization of the complete dataset is 1. This difference is clearly visible between Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e5\u003c/span\u003e, where the side view in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e generates an X-ray projection with higher values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrate two representative slices (numbers 400 and 44) from the reconstructed volume of the worst-performing test sample, providing a visual overview from the top to the bottom of the shoulder. Despite being the worst-performing sample in our test set, the bone structure within the reconstructed volume remains recognizable and can be effectively segmented.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the rendering of the bone volumes obtained from the ground truth (GT) CT scan and the reconstructed volume of the worst-performing test sample after applying Otsu thresholding. While some minor discrepancies and small speckles are visible, the overall shape and spatial arrangement of the bone structures are well-predicted by the neural network. This suggests that the model can effectively generate 59 realistic X-ray projections from a single input projection, enabling the reconstruction of a 3D bone structure with reasonable accuracy. The error associated with the reconstructed volume was measured using the euclidean discrete metric. The maximum error observed was 16 mm, indicating that the voxel positions in the reconstructed volume closely correspond to their ground truth counterparts.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eThis study presented a novel approach for reconstructing 3D bone structures in pork shoulders using a single measured X-ray projection. By exploiting a deep learning model to predict multiple X-ray projections from various angles, we demonstrate the feasibility of generating accurate 3D bone segmentations using conventional CT reconstruction algorithms. The trained model effectively predicts the missing X-ray projections, achieving high accuracy with an average Dice score of 0.94 on the test set. This approach has the potential to improve industrial meat processing by enabling fast and accurate 3D bone structure analysis from a single X-ray measurement, reducing the need for complex and expensive multi-view imaging systems.\u003c/p\u003e \u003cp\u003eHowever, the current evaluation relies on a limited dataset of synthetic X-ray projections. To fully validate the model's robustness, future work should focus on testing with real X-ray projections from a custom-designed inline X-ray system. Such validation would provide critical insights into the model's performance under practical conditions, including the impact of system noise, diverse pork shoulder orientations, and variability across different pork breeds. Addressing these challenges will be essential to advancing the method toward deployment in industrial environments, ensuring reliability and generalizability across a broad spectrum of use cases.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThe authors gratefully acknowledge the funding received from Flanders Innovation \u0026amp; Entrepreneurship (VLAIO ICON iMeat project HBC.2020.2945) with support of Flanders\u0026rsquo; Food. Pieter Verboven and Bart Nicola\u0026iuml; are co-Pis of the KU Leuven XCT Core facility.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eN. Makange, \u0026ldquo;On-line weight estimation of broiler carcass and cuts by a computer vision system,\u0026rdquo; \u003cem\u003ePoult Sci\u003c/em\u003e, Jan. 2021, Accessed: Dec. 16, 2024. [Online]. 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Otsu, \u0026ldquo;A Threshold Selection Method from Gray-Level Histograms,\u0026rdquo; \u003cem\u003eIEEE Trans Syst Man Cybern\u003c/em\u003e, vol. 9, no. 1, pp. 62\u0026ndash;66, Jan. 1979, doi: 10.1109/TSMC.1979.4310076.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-nondestructive-evaluation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jone","sideBox":"Learn more about [Journal of Nondestructive Evaluation](http://link.springer.com/journal/10921)","snPcode":"10921","submissionUrl":"https://submission.nature.com/new-submission/10921/3","title":"Journal of Nondestructive Evaluation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"pork shoulder processing, X-ray technology, 3D segmentation, inline inspection, multi-angle X-ray prediction, neural networks","lastPublishedDoi":"10.21203/rs.3.rs-6672306/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6672306/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePork is an important meat product for the European Union, which exported over 4.2\u0026nbsp;million tons in 2023, valued at \u0026euro;8.1\u0026nbsp;billion. Automating the labor-intensive deboning process is of significant interest, particularly through the development of advanced inline inspection systems capable of analyzing pork shoulder bone structures. While computed tomography (CT) systems provide high-contrast 3D reconstructions, their large size and high-cost present substantial barriers to adoption in industrial meat processing. This study addresses these challenges by introducing a novel approach that uses a single X-ray projection in combination with deep neural networks to predict the 3D segmentation map of pork shoulder bone structures using conventional reconstruction algorithms. To this end, U-Net neural network variants were trained on high-resolution CT scans of 90 pork shoulders. These scans were augmented with synthetic data to simulate different orientations on a conveyor belt, ensuring the model\u0026rsquo;s robustness. The minimum number of X-ray projections needed for accurate reconstruction was determined based on simulations, and 60 evenly spaced projections between 0\u0026deg; and 180\u0026deg; were found optimal. The Feldkamp-Davis-Kress (FDK) algorithm was chosen for its efficiency and cost-effectiveness in inline processing. The model achieved a Dice score of 0.94 and an SSIM of 0.96 on test data, demonstrating its ability to predict 59 missing projections and reconstruct the 3D bone structure accurately. The method that is proposed in this paper has the potential to advance meat processing by enhancing deboning precision, reducing waste, and streamlining operations.\u003c/p\u003e","manuscriptTitle":"Single-Shot X-ray to Multi-View Projections for 3D Pork Shoulder Bone Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-22 14:37:33","doi":"10.21203/rs.3.rs-6672306/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-04T13:29:14+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-04T13:18:39+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-03T15:54:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"229342373783391802291804316717460126130","date":"2025-09-03T00:03:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"143196181736775889127877565102982295847","date":"2025-09-01T02:32:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"126275746234375542571414683641050248201","date":"2025-09-01T01:24:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"56820264957424628059334224755899980193","date":"2025-08-31T17:34:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"237404668046149566786953655337047362878","date":"2025-08-31T16:47:39+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-02T04:55:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"122479856644773829664033221279547302708","date":"2025-05-20T04:05:47+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-19T15:34:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-19T15:29:46+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-15T12:11:58+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Nondestructive Evaluation","date":"2025-05-15T11:37:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-nondestructive-evaluation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jone","sideBox":"Learn more about [Journal of Nondestructive Evaluation](http://link.springer.com/journal/10921)","snPcode":"10921","submissionUrl":"https://submission.nature.com/new-submission/10921/3","title":"Journal of Nondestructive Evaluation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"fc9f1384-419c-43cf-9acd-fabd47bf2442","owner":[],"postedDate":"May 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-08T15:58:56+00:00","versionOfRecord":{"articleIdentity":"rs-6672306","link":"https://doi.org/10.1007/s10921-025-01301-x","journal":{"identity":"journal-of-nondestructive-evaluation","isVorOnly":false,"title":"Journal of Nondestructive Evaluation"},"publishedOn":"2025-12-01 15:56:57","publishedOnDateReadable":"December 1st, 2025"},"versionCreatedAt":"2025-05-22 14:37:33","video":"","vorDoi":"10.1007/s10921-025-01301-x","vorDoiUrl":"https://doi.org/10.1007/s10921-025-01301-x","workflowStages":[]},"version":"v1","identity":"rs-6672306","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6672306","identity":"rs-6672306","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}