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

Krithika Iyer, Jadie Adams, Shireen Y. Elhabian

TL;DR

SCorP tackles the bottleneck of statistical shape modeling from medical images by predicting dense surface correspondences directly from unsegmented volumes. It achieves this with a teacher-student framework where a surface-based prior (learned via a surface autoencoder and an implicit field decoder) guides an image encoder to produce correspondences $\mathcal{C}_j^{I}$ without relying on an optimised ground-truth PDM. The training proceeds in three phases—surface-prior learning, embedding alignment, and prediction refinement—using losses such as $\mathcal{L}_S$, $\mathcal{L}_{EA}$, and $\mathcal{L}_{PR}$, and a final inference that yields correspondences from images alone. Results on LA and AbdomenCT-1K liver datasets show SCorP outperforms baselines on key metrics like Chamfer distance, with strong robustness across dataset sizes and flexibility across surface representations, thereby enabling more scalable and non-linear shape analysis in clinical settings.

Abstract

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.

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

TL;DR

SCorP tackles the bottleneck of statistical shape modeling from medical images by predicting dense surface correspondences directly from unsegmented volumes. It achieves this with a teacher-student framework where a surface-based prior (learned via a surface autoencoder and an implicit field decoder) guides an image encoder to produce correspondences without relying on an optimised ground-truth PDM. The training proceeds in three phases—surface-prior learning, embedding alignment, and prediction refinement—using losses such as , , and , and a final inference that yields correspondences from images alone. Results on LA and AbdomenCT-1K liver datasets show SCorP outperforms baselines on key metrics like Chamfer distance, with strong robustness across dataset sizes and flexibility across surface representations, thereby enabling more scalable and non-linear shape analysis in clinical settings.

Abstract

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.
Paper Structure (24 sections, 3 equations, 7 figures, 2 tables)

This paper contains 24 sections, 3 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Surface Autoencoder and Implicit Field Decoder
  5. Image Encoder
  6. Embedding alignment phase
  7. Prediction refinement phase
  8. Training Strategy
  9. Datasets and Evaluation
  10. Datasets
  11. Models for Comparison
  12. Metrics
  13. Experimental Setup
  14. Results
  15. Ablation Experiments
  16. ...and 9 more sections

Figures (7)

  • Figure 1: Comparison of requirements and training pipelines
  • Figure 2: Architecture of SCorP: Training involves three phases: (1) Surface branch training focuses on shape prior development using the teacher network consisting of the surface autoencoder and IM-NET decoder; (2) Image branch embedding alignment trains the student i.e., image encoder to predict image feature that aligns with the shape prior; (3) Image branch prediction refinement improves predicted correspondences from images.
  • Figure 3: Performance metrics Boxplots illustrating the distribution of performance metrics, with mean values displayed above each plot, for the held-out test samples from the LA and liver datasets. Compactness plots illustrate the cumulative population variation captured by PCA modes, where a larger area under the curve indicates a more compact model. The best metrics are highlighted in the figure. Comp = Compactness, Spec = Specificity, Gen = Generalization.
  • Figure 4: PCA modes of variations: The first four modes of variations of the LA dataset identified by SCorP, DeepSSM, and TL-DeepSSM bhalodia2018deepssmbhalodia2024deepssm. The color map and arrows show the signed distance and direction from the mean shape. SCorP shows detailed and smoother variations as compared to the other methods, which are highlighted with boxes.
  • Figure 5: PCA modes of variations: The first four modes of variations of the liver dataset identified by SCorP, DeepSSM, and TL-DeepSSM bhalodia2018deepssmbhalodia2024deepssm. The color map and arrows show the signed distance and direction from the mean shape. SCorP shows detailed and smoother variations as compared to the other methods, which are highlighted with boxes.
  • ...and 2 more figures