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Optimization-Driven Statistical Models of Anatomies using Radial Basis Function Shape Representation

Hong Xu, Shireen Y. Elhabian

TL;DR

This work proposes an adaptation of particle-based shape modeling using a traditional optimization approach that allows more precise control over the desired characteristics of models by leveraging both an eigenshape and a correspondence loss.

Abstract

Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding particles (as pseudo landmarks) on 3D surfaces to allow subsequent shape analysis. A recent deep learning approach leverages implicit radial basis function representations of shapes to better adapt to the underlying complex geometry of anatomies. Here, we propose an adaptation of this method using a traditional optimization approach that allows more precise control over the desired characteristics of models by leveraging both an eigenshape and a correspondence loss. Furthermore, the proposed approach avoids using a black-box model and allows more freedom for particles to navigate the underlying surfaces, yielding more informative statistical models. We demonstrate the efficacy of the proposed approach to state-of-the-art methods on two real datasets and justify our choice of losses empirically.

Optimization-Driven Statistical Models of Anatomies using Radial Basis Function Shape Representation

TL;DR

This work proposes an adaptation of particle-based shape modeling using a traditional optimization approach that allows more precise control over the desired characteristics of models by leveraging both an eigenshape and a correspondence loss.

Abstract

Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding particles (as pseudo landmarks) on 3D surfaces to allow subsequent shape analysis. A recent deep learning approach leverages implicit radial basis function representations of shapes to better adapt to the underlying complex geometry of anatomies. Here, we propose an adaptation of this method using a traditional optimization approach that allows more precise control over the desired characteristics of models by leveraging both an eigenshape and a correspondence loss. Furthermore, the proposed approach avoids using a black-box model and allows more freedom for particles to navigate the underlying surfaces, yielding more informative statistical models. We demonstrate the efficacy of the proposed approach to state-of-the-art methods on two real datasets and justify our choice of losses empirically.

Paper Structure

This paper contains 10 sections, 6 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Radial Basis Function Surface Representation
  4. SSM Optimization
  5. Results
  6. Datasets and Implementation Details
  7. Shape Model Quality
  8. Correspondence and Eigenshape Losses
  9. Conclusion
  10. Compliance with Ethical Standards

Figures (4)

  • Figure 1: A set of control points and their respective dipoles can define an implicit signed distance function within a narrow band that can be efficiently queried for surface representation accuracy at any narrow band point.
  • Figure 2: The two-way surface-to-surface distance between Image2SSM, PSM, and our approach.
  • Figure 3: Shows the compactness (higher is better), specificity (lower is better), and generalization (lower is better) for ten modes on femurs and left atria.
  • Figure 4: By changing $\gamma$ and $\zeta$, we show the results of running our optimization with (a) only correspondence loss, (b) only eigenshape loss, and (c) both. The red circle highlights two control points that are swapped for 6 out of 20 shapes.