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Image2SSM: Reimagining Statistical Shape Models from Images with Radial Basis Functions

Hong Xu, Shireen Y. Elhabian

TL;DR

This work tackles the bottleneck in statistical shape modeling by removing the need for explicit segmentation and dense correspondence construction during inference. It introduces Image2SSM, a deep-learning approach that learns an RBF-based implicit surface from image-segmentation pairs, yielding a compact, continuous representation with control points and normals. Training leverages four losses (surface, normals, correspondence, sampling) to ensure accurate surface adherence, correct normals, stable correspondences, and geometry-aware point distribution, while weights are learned end-to-end with a detached linear solver. Empirical results on femur CT and left atrium MRI data show competitive modes of variation, compactness, and generalization compared to ShapeWorks PSM and DeepSSM, with improved surface detail and favorable inference speed on unseen data, signaling a scalable path for end-to-end SSM from imagery.

Abstract

Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using lower-dimensional shape features, on which statistical analysis can be performed. Various methods for constructing compact shape representations have been proposed, but they involve laborious and costly steps. We propose Image2SSM, a novel deep-learning-based approach for SSM that leverages image-segmentation pairs to learn a radial-basis-function (RBF)-based representation of shapes directly from images. This RBF-based shape representation offers a rich self-supervised signal for the network to estimate a continuous, yet compact representation of the underlying surface that can adapt to complex geometries in a data-driven manner. Image2SSM can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes while requiring minimal parameter tuning and no user assistance. Once trained, Image2SSM can be used to infer low-dimensional shape representations from new unsegmented images, paving the way toward scalable approaches for SSM, especially when dealing with large cohorts. Experiments on synthetic and real datasets show the efficacy of the proposed method compared to the state-of-art correspondence-based method for SSM.

Image2SSM: Reimagining Statistical Shape Models from Images with Radial Basis Functions

TL;DR

This work tackles the bottleneck in statistical shape modeling by removing the need for explicit segmentation and dense correspondence construction during inference. It introduces Image2SSM, a deep-learning approach that learns an RBF-based implicit surface from image-segmentation pairs, yielding a compact, continuous representation with control points and normals. Training leverages four losses (surface, normals, correspondence, sampling) to ensure accurate surface adherence, correct normals, stable correspondences, and geometry-aware point distribution, while weights are learned end-to-end with a detached linear solver. Empirical results on femur CT and left atrium MRI data show competitive modes of variation, compactness, and generalization compared to ShapeWorks PSM and DeepSSM, with improved surface detail and favorable inference speed on unseen data, signaling a scalable path for end-to-end SSM from imagery.

Abstract

Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using lower-dimensional shape features, on which statistical analysis can be performed. Various methods for constructing compact shape representations have been proposed, but they involve laborious and costly steps. We propose Image2SSM, a novel deep-learning-based approach for SSM that leverages image-segmentation pairs to learn a radial-basis-function (RBF)-based representation of shapes directly from images. This RBF-based shape representation offers a rich self-supervised signal for the network to estimate a continuous, yet compact representation of the underlying surface that can adapt to complex geometries in a data-driven manner. Image2SSM can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes while requiring minimal parameter tuning and no user assistance. Once trained, Image2SSM can be used to infer low-dimensional shape representations from new unsegmented images, paving the way toward scalable approaches for SSM, especially when dealing with large cohorts. Experiments on synthetic and real datasets show the efficacy of the proposed method compared to the state-of-art correspondence-based method for SSM.
Paper Structure (7 sections, 6 equations, 7 figures)

This paper contains 7 sections, 6 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Representing shapes using RBFs
  4. Loss Functions
  5. Results
  6. Datasets
  7. Conclusion

Figures (7)

  • Figure 1: (a) Concept of populating a surface using control points and the iso-surfaces using positive and negative pole points. (b) Same concept applied to an output three-dimensional reconstructed femur. (c) Normals can be used to describe very distinct features of the greater trochanter.
  • Figure 2: The Image2SSM architecture. A 3D image is fed to the convolutional backbone, which produces a flattened output for the feature extractor to produce control points and their respective normals. These are then used to compute the losses of the network.
  • Figure 3: (a) First and second modes of variation obtained from Image2SSM training data and PSM. (b) Surface-to-surface distance on a best, median, and worst training femur mesh. (c) The left image shows the surface-to-surface distance comparison on all the data used to train Image2SSM; the right shows it without outliers.
  • Figure 4: (a) Surface-to-surface distance on a reconstructed femur mesh from particles of a few test samples. (b) Surface-to-surface distance plot between DeepSSM and Image2SSM, and the same plot without the outlier femur. (c) Illustrates Image2SSM 's capacity to capture detail on an unseen test image. (d) Shows the compactness (higher is better), specificity (lower is better) and generalization (lower is better) graphs against the number of modes of variation.
  • Figure 5: We also demonstrate our results on a dataset of 1018 aligned left atrium MRI image-segmentation pairs. This dataset is very challenging due to the high variability in the manual labeling of the pulmonary arteries and the presence of various atrial fibrillation phenotypes (Persistent, paroxysmal, AFL, nonAF, other arrhythmia) As before, we build the model with 128 particles. We show the first three modes of variation of Image2SSM compared to PSM. The results are comparable and match expectations. We observe that both models capture the shape variability of the atrium itself well, less so with the pulmonary arteries.
  • ...and 2 more figures