Statistical Shape Research Articles

Femurs in patients with hip dysplasia have fundamental shape differences compared with cam femoroacetabular impingement.

Femoral deformities are common in developmental dysplasia of the hip (DDH), but decisions about how to treat them are not standardized. Of interest are deformities that may be akin to cam femoroacetabular impingement (FAI). We used three-dimensional and two-dimensional measures to clarify the similarities and differences in proximal femur shape variation among female patients with DDH (n = 68) or cam FAI (n = 60). Three-dimensional measures included femoral head asphericity, as well as shape variation using statistical shape modeling and principal component analysis (PCA). Two-dimensional measures included the α-angle, head-neck offset (HNO) and the neck-shaft angle (NSA). Significant shape variations were captured in the first five PCA modes, with the greatest shared variation between groups being the length from the lesser trochanter to the femoral head and greater trochanter height. Variations unique to DDH were irregularities at different areas of the femoral head, but not at the lateral femoral head-neck junction where variation was strong in FAI. The FAI group also had unique variations in greater trochanter shape. DDH femoral heads were less spherical, as indicated by larger sphere-fitting errors (P < 0.001). Radiographically, the DDH group had significantly smaller α-angles (P < 0.001), larger head-neck offsets (P = 0.02) and larger NSAs (P < 0.001). Both the articular and extra-articular regions of the proximal femur have distinct shape features in DDH and cam FAI that can uniquely affect the biomechanics of each disorder. Accordingly, approaches to addressing each disorder should be unique.

Integration of Swin UNETR and statistical shape modeling for a semi-automated segmentation of the knee and biomechanical modeling of articular cartilage

Simulation studies, such as finite element (FE) modeling, provide insight into knee joint mechanics without patient involvement. Generic FE models mimic the biomechanical behavior of the tissue, but overlook variations in geometry, loading, and material properties of a population. Conversely, subject-specific models include these factors, resulting in enhanced predictive precision, but are laborious and time intensive. The present study aimed to enhance subject-specific knee joint FE modeling by incorporating a semi-automated segmentation algorithm using a 3D Swin UNETR for an initial segmentation of the femur and tibia, followed by a statistical shape model (SSM) adjustment to improve surface roughness and continuity. For comparison, a manual FE model was developed through manual segmentation (i.e., the de-facto standard approach). Both FE models were subjected to gait loading and the predicted mechanical response was compared. The semi-automated segmentation achieved a Dice similarity coefficient (DSC) of over 98% for both the femur and tibia. Hausdorff distance (mm) between the semi-automated and manual segmentation was 1.4 mm. The mechanical results (max principal stress and strain, fluid pressure, fibril strain, and contact area) showed no significant differences between the manual and semi-automated FE models, indicating the effectiveness of the proposed semi-automated segmentation in creating accurate knee joint FE models. We have made our semi-automated models publicly accessible to support and facilitate biomechanical modeling and medical image segmentation efforts (https://data.mendeley.com/datasets/k5hdc9cz7w/1).

The role of anatomic shape features in the prognosis of uncomplicated type B aortic dissection initially treated with optimal medical therapy

ObjectiveCurrently, the long-term outcomes of uncomplicated type B aortic dissection (TBAD) patients managed with optimal medical therapy (OMT) remain poor. Aortic expansion is a major factor that determines patient long-term survival. The objective of this study was to investigate the association between anatomic shape features and (i) OMT outcome; (ii) aortic growth rate for TBAD patients initially treated with OMT. Methods108 CT images of TBAD in the acute and chronic phases were collected from 46 patients who were initially treated with OMT. Statistical shape models (SSM) of TBAD were constructed to extract shape features from the earliest initial CT scans of each patient by using principal component analysis (PCA) and partial least square (PLS) regression. Additionally, conventional shape features (e.g., aortic diameter) were quantified from the earliest CT scans as a baseline for comparison. We identified conventional and SSM features that were significant in separating OMT “success” and failure patients. Moreover, the aortic growth rate was predicted by SSM and conventional features using linear and nonlinear regression with cross-validations. ResultsSize-related SSM and conventional features (mean aortic diameter: p=0.0484, centerline length: p=0.0112, PCA score c1: p=0.0192, and PLS scores t1: p=0.0004, t2: p=0.0274) were significantly different between OMT success and failure groups, but these features were incapable of predicting the aortic growth rate. SSM shape features showed superior results in growth rate prediction compared to conventional features. Using multiple linear regression, the conventional, PCA, and PLS shape features resulted in root mean square errors (RMSE) of 1.23, 0.85, and 0.84 mm/year, respectively, in leave-one-out cross-validations. Nonlinear support vector regression (SVR) led to improved RMSE of 0.99, 0.54, and 0.43 mm/year, for the conventional, PCA, and PLS features, respectively. ConclusionSize-related shape features of the earliest scan were correlated with OMT failure but led to large errors in the prediction of the aortic growth rate. SSM features in combination with nonlinear regression could be a promising avenue to predict the aortic growth rate.

Validated respiratory drug deposition predictions from 2D and 3D medical images with statistical shape models and convolutional neural networks.

For the one billion sufferers of respiratory disease, managing their disease with inhalers crucially influences their quality of life. Generic treatment plans could be improved with the aid of computational models that account for patient-specific features such as breathing pattern, lung pathology and morphology. Therefore, we aim to develop and validate an automated computational framework for patient-specific deposition modelling. To that end, an image processing approach is proposed that could produce 3D patient respiratory geometries from 2D chest X-rays and 3D CT images. We evaluated the airway and lung morphology produced by our image processing framework, and assessed deposition compared to in vivo data. The 2D-to-3D image processing reproduces airway diameter to 9% median error compared to ground truth segmentations, but is sensitive to outliers of up to 33% due to lung outline noise. Predicted regional deposition gave 5% median error compared to in vivo measurements. The proposed framework is capable of providing patient-specific deposition measurements for varying treatments, to determine which treatment would best satisfy the needs imposed by each patient (such as disease and lung/airway morphology). Integration of patient-specific modelling into clinical practice as an additional decision-making tool could optimise treatment plans and lower the burden of respiratory diseases.

ANALYSIS OF CONFIGURATION OF PILE GROUP ON SUPPORTING CAPACITY AND PILE EFFICIENCY IN TANJUNG BALAI FLAT CONSTRUCTION

In the TanjungBalai Flats creation project, the inspiration used is a mini pile basis with a set pile device. The organization pile device on the inspiration withinside the creation of this flat is deliberate to have a exclusive wide variety of piles, particularly piles, 3 piles, 4 piles. Therefore, on this look at diverse pile configurations might be completed with the aid of using modelling exclusive configurations with the equal wide variety of piles as the development of this flat. Furthermore, the sporting ability and performance values might be as compared that is the first-class value. Calculations on this look at had been the usage of the direct method (Direct One) and the pile performance component for the evaluation of the pile bearing ability. The calculation is accomplished primarily based totally at the soil statistics received withinside the shape of sondir statistics. The significance of the pile performance value (Eg) in a pile organization is encouraged with the aid of using the pile arrangement, the wide variety of rows, the wide variety of piles in a single row, and the pile distance inclusive of the three pile configuration of the project (V3) has an performance value (Eg) = 0,817 and (Qg) = 205.27 whilst the evaluation of the layout pile (V3-1) has an performance value (Eg) = 0.861 and (Qg) = 216.32. From the calculation effects it could be concluded that the affect of organization pile configuration at the pile bearing ability is encouraged with the aid of using the significance of the pile performance (Eg), the more the pile performance, the more the sporting ability.

Gaussian process model based restoration of damaged Buddha statue head

Buddha statues are distributed worldwide, and each piece reflects the aesthetic fashion of a particular region and historical era. Therefore, these sculptures have important cultural, aesthetic, and historical value. Owing to natural or artificial destruction, several Buddha statues have been damaged, with head or facial damage being the most prominent damage type. Because Buddha statue heads exhibit intricate variations in facial expressions and proportions, restoring head or facial damage is the most challenging aspect of damaged sculpture restoration projects. This study provides a new method for the restoration of damaged statues based on a Gaussian process model. The Gaussian process model entails a type of statistical shape modeling that allows it to learn shape distribution properties from a training dataset. During the restoration process, we used the residual parts of the damaged shape for the observations and added them to a Bayesian inference system to obtain the possible restoration result in the form of a posterior distribution. Therefore, the proposed method can be regarded as a quantitative mathematical representation of the subjective deduction process. Compared to those of the traditional manual restoration method, our results were more repeatable and stable, and the restoration process was automatic and rigorous, which reduced the requirements for professional knowledge and experience. Based on the learned model information, the proposed method exhibits strong robustness and anti-noise properties. In contrast to the optimization method, our final restoration result is a probability distribution, applicable to the repair of cultural relics. As our method make the missing shape inference using residual shape information and the regularity learned from training dataset, it is suitable for the restoration of damaged parts with no direct shape evidence. Finally, our model is generative; in other words, we can generate shapes on the posterior distribution and provide the corresponding probability. To demonstrate the effectiveness of our method, a series of experiments were conducted to restore damaged parts under different parameters and damage type settings. Subsequently, a quantitative analysis was performed. Finally, we applied this method to the virtual restoration of a damaged Buddha statue head in Xi 'an Museum.

NON-LINEAR APPLICATIONS OF STATISTICAL SHAPE ANALYSIS IN ORTHOPAEDIC RESEARCH

Non-linear methods in statistical shape analysis have become increasingly important in orthopedic research as they allow for more accurate and robust analysis of complex shape data such as articulated joints, bony defects and cartilage loss. These methods involve the use of non-linear transformations to describe shapes, rather than the traditional linear approaches, and have been shown to improve the precision and sensitivity of shape analysis in a variety of applications. In orthopedic research, non-linear methods have been used to study a range of topics, including the analysis of bone shape and structure in relation to osteoarthritis, the assessment of joint deformities and their impact on joint function, and the prediction of patient outcomes following surgical interventions. Overall, the use of non-linear methods in statistical shape analysis has the potential to advance our understanding of the relationship between shape and function in the musculoskeletal system and improve the diagnosis and treatment of orthopedic conditions.

THORACOLUMBAR SPINE PATIENT-SPECIFIC FINITE ELEMENT MODEL REPOSITORY WITH ONLINE USER-INTERFACE PLATFORM

Adult Spine Deformity (ASD) is a degenerative condition of the adult spine leading to altered spine curvatures and mechanical balance. Computational approaches, like Finite Element (FE) Models have been proposed to explore the etiology or the treatment of ASD, through biomechanical simulations. However, while the personalization of the models is a cornerstone, personalized FE models are cumbersome to generate. To cover this need, we share a virtual cohort of 16807 thoracolumbar spine FE models with different spine morphologies, presented in an online user-interface platform (SpineView). To generate these models, EOS images are used, and 3D surface spine models are reconstructed. Then, a Statistical Shape Model (SSM), is built, to further adapt a FE structured mesh template for both the bone and the soft tissues of the spine, through mesh morphing. Eventually, the SSM deformation fields allow the personalization of the mean structured FE model, leading to generate FE meshes of thoracolumbar spines with different morphologies. Models can be selectively viewed and downloaded through SpineView, according to personalized user requests of specific morphologies characterized by the geometrical parameters: Pelvic Incidence; Pelvic Tilt; Sacral Slope; Lumbar Lordosis; Global Tilt; Cobb Angle; and GAP score. Data quality is assessed using visual aids, correlation analyses, heatmaps, network graphs, Anova and t-tests, and kernel density plots to compare spinopelvic parameter distributions and identify similarities and differences. Mesh quality and ranges of motion have been assessed to evaluate the quality of the FE models. This functional repository is unique to generate virtual patient cohorts in ASD.Acknowledgements: European Commission (MSCA-TN-ETN-2020-Disc4All-955735, ERC-2021-CoG-O-Health-101044828)

On preserving anatomical detail in statistical shape analysis for clustering: focus on left atrial appendage morphology.

Statistical shape analysis (SSA) with clustering is often used to objectively define and categorise anatomical shape variations. However, studies until now have often focused on simplified anatomical reconstructions, despite the complexity of studied anatomies. This work aims to provide insights on the anatomical detail preservation required for SSA of highly diverse and complex anatomies, with particular focus on the left atrial appendage (LAA). This anatomical region is clinically relevant as the location of almost all left atrial thrombi forming during atrial fibrillation (AF). Moreover, its highly patient-specific complex architecture makes its clinical classification especially subjective. Preliminary LAA meshes were automatically detected after robust image selection and wider left atrial segmentation. Following registration, four additional LAA mesh datasets were created as reductions of the preliminary dataset, with surface reconstruction based on reduced sample point densities. Utilising SSA model parameters determined to optimally represent the preliminary dataset, SSA model performance for the four simplified datasets was calculated. A representative simplified dataset was selected, and clustering analysis and performance were evaluated (compared to clinical labels) between the original trabeculated LAA anatomy and the representative simplification. As expected, simplified anatomies have better SSA evaluation scores (compactness, specificity and generalisation), corresponding to simpler LAA shape representation. However, oversimplification of shapes may noticeably affect 3D model output due to differences in geometric correspondence. Furthermore, even minor simplification may affect LAA shape clustering, where the adjusted mutual information (AMI) score of the clustered trabeculated dataset was 0.67, in comparison to 0.12 for the simplified dataset. This study suggests that greater anatomical preservation for complex and diverse LAA morphologies, currently neglected, may be more useful for shape categorisation via clustering analyses.

SCorP: Statistics-Informed Dense Correspondence Prediction Directly from Unsegmented Medical Images.

Statistical shape modeling (SSM) is a powerful computational framework for quantifying and analyzing the geometric variability of anatomical structures, facilitating advancements in medical research, diagnostics, and treatment planning. Traditional methods for shape modeling from imaging data demand significant manual and computational resources. Additionally, these methods necessitate repeating the entire modeling pipeline to derive shape descriptors (e.g., surface-based point correspondences) for new data. While deep learning approaches have shown promise in streamlining the construction of SSMs on new data, they still rely on traditional techniques to supervise the training of the deep networks. Moreover, the predominant linearity assumption of traditional approaches restricts their efficacy, a limitation also inherited by deep learning models trained using optimized/established correspondences. Consequently, representing complex anatomies becomes challenging. To address these limitations, we introduce SCorP, a novel framework capable of predicting surface-based correspondences directly from unsegmented images. By leveraging the shape prior learned directly from surface meshes in an unsupervised manner, the proposed model eliminates the need for an optimized shape model for training supervision. The strong shape prior acts as a teacher and regularizes the feature learning of the student network to guide it in learning image-based features that are predictive of surface correspondences. The proposed model streamlines the training and inference phases by removing the supervision for the correspondence prediction task while alleviating the linearity assumption. Experiments on the LGE MRI left atrium dataset and Abdomen CT-1K liver datasets demonstrate that the proposed technique enhances the accuracy and robustness of image-driven SSM, providing a compelling alternative to current fully supervised methods.

Simultaneous Hip Implant Segmentation and Gruen Landmarks Detection.

The assessment of implant status and complications of Total Hip Replacement (THR) relies mainly on the clinical evaluation of the X-ray images to analyse the implant and the surrounding rigid structures. Current clinical practise depends on the manual identification of important landmarks to define the implant boundary and to analyse many features in arthroplasty X-ray images, which is time-consuming and could be prone to human error. Semantic segmentation based on the Convolutional Neural Network (CNN) has demonstrated successful results in many medical segmentation tasks. However, these networks cannot define explicit properties that lead to inaccurate segmentation, especially with the limited size of image datasets. Our work integrates clinical knowledge with CNN to segment the implant and detect important features simultaneously. This is instrumental in the diagnosis of complications of arthroplasty, particularly for loose implant and implant-closed bone fractures, where the location of the fracture in relation to the implant must be accurately determined. In this work, we define the points of interest using Gruen zones that represent the interface of the implant with the surrounding bone to build a Statistical Shape Model (SSM). We propose a multitask CNN that combines regression of pose and shape parameters constructed from the SSM and semantic segmentation of the implant. This integrated approach has improved the estimation of implant shape, from 74% to 80% dice score, making segmentation realistic and allowing automatic detection of Gruen zones. To train and evaluate our method, we generated a dataset of annotated hip arthroplasty X-ray images that will be made available.

ShapeMed-Knee: A Dataset and Neural Shape Model Benchmark for Modeling 3D Femurs.

Analyzing anatomic shapes of tissues and organs is pivotal for accurate disease diagnostics and clinical decision-making. One prominent disease that depends on anatomic shape analysis is osteoarthritis, which affects 30 million Americans. To advance osteoarthritis diagnostics and prognostics, we introduce ShapeMed-Knee, a 3D shape dataset with 9,376 high-resolution, medical-imaging-based 3D shapes of both femur bone and cartilage. Besides data, ShapeMed-Knee includes two benchmarks for assessing reconstruction accuracy and five clinical prediction tasks that assess the utility of learned shape representations. Leveraging ShapeMed-Knee, we develop and evaluate a novel hybrid explicit-implicit neural shape model which achieves up to 40% better reconstruction accuracy than a statistical shape model and implicit neural shape model. Our hybrid models achieve state-of-the-art performance for preserving cartilage biomarkers; they're also the first models to successfully predict localized structural features of osteoarthritis, outperforming shape models and convolutional neural networks applied to raw magnetic resonance images and segmentations. The ShapeMed-Knee dataset provides medical evaluations to reconstruct multiple anatomic surfaces and embed meaningful disease-specific information. ShapeMed-Knee reduces barriers to applying 3D modeling in medicine, and our benchmarks highlight that advancements in 3D modeling can enhance the diagnosis and risk stratification for complex diseases. The dataset, code, and benchmarks will be made freely accessible.

Towards Semantically-Consistent Deformable 2D-3D Registration for 3D Craniofacial Structure Estimation from A Single-View Lateral Cephalometric Radiograph.

The deep neural networks combined with the statistical shape model have enabled efficient deformable 2D-3D registration and recovery of 3D anatomical structures from a single radiograph. However, the recovered volumetric image tends to lack the volumetric fidelity of fine-grained anatomical structures and explicit consideration of cross-dimensional semantic correspondence. In this paper, we introduce a simple but effective solution for semantically-consistent deformable 2D-3D registration and detailed volumetric image recovery by inferring a voxel-wise registration field between the cone-beam computed tomography and a single lateral cephalometric radiograph (LC). The key idea is to refine the initial statistical model-based registration field with craniofacial structural details and semantic consistency from the LC. Specifically, our framework employs a self-supervised scheme to learn a voxel-level refiner of registration fields to provide fine-grained craniofacial structural details and volumetric fidelity. We also present a weakly supervised semantic consistency measure for semantic correspondence, relieving the requirements of volumetric image collections and annotations. Experiments showcase that our method achieves deformable 2D-3D registration with performance gains over state-of-the-art registration and radiograph-based volumetric reconstruction methods. The source code is available at https://github.com/Jyk-122/SC-DREG.

Generating novel tennis racket shape concepts using a theoretical morphospace.

Statistical shape analysis, or morphometrics, is a technique commonly used in evolutionary biology to summarise a population of samples. Theoretical morphometrics extends the current population of samples into a theoretical space. Using the lawn tennis racket as an example, this paper showcases the potential of morphometrics as a tool for inspiring design concepts for novel sporting goods. It showcases how morphometrics can be applied to summarise the shape of a sample of rackets and applies theoretical morphometrics to systematically present new candidate designs that fall outside of the inputted existing, racket population. The input population was 514 tennis rackets dating back to the origins of the game. The shape analysis was performed on "front-on" silhouette images of the rackets using the R Package Momocs. The outline shape of each racket was reconstructed using the elliptical Fourier transform curve fitting technique. A principal component analysis performed on the reconstructed outlines showed that >90% of the variance in the shape of the rackets was captured by the first two principal components. An evenly spaced grid of theoretical racket shape outlines was then created in a principal component 2 vs. principal component 1 "morphospace". The limits of this space were then expanded to give a theoretical morphospace that extended beyond the range of the first two principal components for the 514 samples. We propose that the shapes located within such a theoretical morphospace could inspire designers and help them to systematically identify candidates for novel products. Specifically, we suggest that experimenting with wide-angled throats and heads with angled sides might be an interesting starting point for exploring future tennis racket design concepts. The novel technique presented here could be used by a sporting goods brand during the ideation phase of product development to schematically summarise current designs and identify candidates for new ones.

A novel mean shape based post-processing method for enhancing deep learning lower-limb muscle segmentation accuracy.

This study aims at improving the lower-limb muscle segmentation accuracy of deep learning approaches based on Magnetic Resonance Imaging (MRI) scans, crucial for the diagnostic and therapeutic processes in musculoskeletal diseases. In general, segmentation methods such as U-Net deep learning neural networks can achieve good Dice Similarity Coefficient (DSC) values, e.g. around 0.83 to 0.91 on various cohorts. Some generic post-processing strategies have been studied to incorporate connectivity constraints into the resulting masks for the purpose of further improving the segmentation accuracy. In this paper, a novel mean shape (MS) based post-processing method is proposed, utilizing Statistical Shape Modelling (SSM) to fine-tune the segmentation output, taking into consideration the muscle anatomical shape. The methodology was compared to existing post-processing techniques and a commercial semi-automatic tool on MRI scans from two cohorts of post-menopausal women (10 Training, 8 Testing, voxel size 1.0x1.0x1.0 mm3). The MS based method obtained a mean DSC of 0.83 across the different analysed muscles and the best performance for the Hausdorff Distance (HD, 20.6 mm) and the Average Symmetric Surface Distance (ASSD, 2.1 mm). These findings highlight the feasibility and potential of using anatomical mean shape in post-processing of human lower-limb muscle segmentation task and indicate that the proposed method can be popularized to other biological organ segmentation mission.

Fast and Simple Statistical Shape Analysis of Pregnant Women Using Radial Deformation of a Cylindrical Template.

Non-rigid deformation of a template to fit 3D scans of human subjects is widely used to develop statistical models of 3D human shapes and poses. Complex optimization problems must be solved to use these models to parameterize scans of pregnant women, thus limiting their use in antenatal point-of-care tools in low-resource settings. Moreover, these models were developed using datasets that did not contain any 3D scans of pregnant women. In this study, we developed a statistical shape model of the torso of pregnant women at greater than 36 weeks of gestation using fast and simple vertex-based deformation of a cylindrical template constrained along the radial direction. The 3D scans were pre-processed to remove noisy outlier points and segment the torso based on anatomical landmarks. A cylindrical template mesh was then fitted onto the segmented scan of the torso by moving each vertex of in the direction of the radial vector. This process is computationally inexpensive taking only 14.80 seconds to deform a template with 9090 vertices. Principal component analysis (PCA) was performed on the deformed vertex co-ordinates to find the directions of maximum variance. The first 10 principal vectors of our model explained 79.03% of the total variance and reconstructed unseen scans with a mean error of 2.43 cm. We also used the PCA weights of the first 10 principal vectors to accurately predict anthropometric measurements of the pregnant women.

The spatial orientation of crista ampullaris: implications for BPPV diagnosis and treatment.

This study aimed to provide a comprehensive understanding of the spatial orientation of the crista ampullaris within the inner ear and its implications for the diagnosis and management of benign paroxysmal positional vertigo (BPPV). Using high-resolution MRI scans of 55 normal inner ears, 3D models of the semicircular canals were segmented. These were complemented by detailed membrane labyrinth models from micro-CT scans of human temporal bones, accessed via the Comparative Ear Bank (www.earbank.org). A statistical shape model of inner ears and eyeballs was established, and a standardized 3D spatial coordinate system was created. The horizontal plane was defined using the top of the common crus and the bottom of the eyeballs. This calibrated reference system allowed for precise quantification of crista ampullaris orientations by calculating angles between the defined crista planes and coordinate planes. The plane of the ampulla and the corresponding semicircular canal plane are nearly perpendicular to each other. In the upright position, the posterior semicircular canal crista ampullaris formed an angle of 48.9° with the horizontal plane. The relative orientations of the crista ampullaris of the lateral and superior canals were also defined. Furthermore, we identified "zero-point planes" representing crista orientations perpendicular to gravity, which resulted in minimal ampullary stimulation. A 6.2° tilt to the left in the supine position resulted in the plane of the left lateral semicircular canal crista ampullaris being parallel to the direction of gravity. This study elucidates the precise spatial orientation of the crista ampullaris, thereby providing an anatomical basis for understanding BPPV pathophysiology and improving the accuracy of diagnostic and therapeutic maneuvers. The findings have the potential to significantly enhance the management of BPPV and other inner ear disorders.

A statistical shape modelling method for predicting the human head from the face

A statistical shape modelling method for predicting the human head from the face

Statistical Analysis of Complex Shape Graphs.

This paper provides developments in statistical shape analysis of shape graphs, and demonstrates them using such complex objects as Retinal Blood Vessel (RBV) networks and neurons. The shape graphs are represented by sets of nodes and edges (articulated curves) connecting some nodes. The goals are to utilize nodes (locations, connectivity) and edges (edge weights and shapes) to: (1) characterize shapes, (2) quantify shape differences, and (3) model statistical variability. We develop a mathematical representation, elastic Riemannian metrics, and associated tools for shape graphs. Specifically, we derive tools for shape graph registration, geodesics, statistical summaries, shape modeling, and shape synthesis. Geodesics are convenient for visualizing optimal deformations, and PCA helps in dimension reduction and statistical modeling. One key challenge in comparing shape graphs with vastly different complexities (in number of nodes and edges). This paper introduces a novel multi-scale representation to handle this challenge. Using the notions of (1) "effective resistance" to cluster nodes and (2) elastic shape averaging of edge curves, it reduces graph complexity while retaining overall structures. This allows shape comparisons by bringing graphs to similar complexities. We demonstrate these ideas on 2D RBV networks from the STARE and DRIVE databases and 3D neurons from the NeuroMorpho database.

Leveraging Statistical Shape Priors in GAN-Based ECG Synthesis

Leveraging Statistical Shape Priors in GAN-Based ECG Synthesis