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PICS in Pics: Physics Informed Contour Selection for Rapid Image Segmentation

Vikas Dwivedi, Balaji Srinivasan, Ganapathy Krishnamurthi

TL;DR

PICS tackles the data-label bottleneck in medical image segmentation by merging a traditional active-contour snake with physics-informed principles, leveraging cubic-spline boundaries whose control knots are physically meaningful. It replaces edge-based energy minimization with a region-based Chan-Vese loss and introduces a convexity-preserving shape term and an optimization performance index (OPI) to enable adaptive hyperparameter tuning and improved robustness. The method achieves rapid 2D and 3D segmentation, demonstrated on hydrocephalus CT and the ACDC LV dataset, with an average 3D IoU of 0.88 and the ability to generate usable annotations without labeled masks. While offering speed and interpretability, PICS faces challenges in topology changes and inverse parameter estimation, which the authors address through OPI-guided adaptation and transfer-learning-like 3D propagation, signaling a practical path toward data-efficient medical image segmentation.

Abstract

Effective training of deep image segmentation models is challenging due to the need for abundant, high-quality annotations. Generating annotations is laborious and time-consuming for human experts, especially in medical image segmentation. To facilitate image annotation, we introduce Physics Informed Contour Selection (PICS) - an interpretable, physics-informed algorithm for rapid image segmentation without relying on labeled data. PICS draws inspiration from physics-informed neural networks (PINNs) and an active contour model called snake. It is fast and computationally lightweight because it employs cubic splines instead of a deep neural network as a basis function. Its training parameters are physically interpretable because they directly represent control knots of the segmentation curve. Traditional snakes involve minimization of the edge-based loss functionals by deriving the Euler-Lagrange equation followed by its numerical solution. However, PICS directly minimizes the loss functional, bypassing the Euler Lagrange equations. It is the first snake variant to minimize a region-based loss function instead of traditional edge-based loss functions. PICS uniquely models the three-dimensional (3D) segmentation process with an unsteady partial differential equation (PDE), which allows accelerated segmentation via transfer learning. To demonstrate its effectiveness, we apply PICS for 3D segmentation of the left ventricle on a publicly available cardiac dataset. While doing so, we also introduce a new convexity-preserving loss term that encodes the shape information of the left ventricle to enhance PICS's segmentation quality. Overall, PICS presents several novelties in network architecture, transfer learning, and physics-inspired losses for image segmentation, thereby showing promising outcomes and potential for further refinement.

PICS in Pics: Physics Informed Contour Selection for Rapid Image Segmentation

TL;DR

PICS tackles the data-label bottleneck in medical image segmentation by merging a traditional active-contour snake with physics-informed principles, leveraging cubic-spline boundaries whose control knots are physically meaningful. It replaces edge-based energy minimization with a region-based Chan-Vese loss and introduces a convexity-preserving shape term and an optimization performance index (OPI) to enable adaptive hyperparameter tuning and improved robustness. The method achieves rapid 2D and 3D segmentation, demonstrated on hydrocephalus CT and the ACDC LV dataset, with an average 3D IoU of 0.88 and the ability to generate usable annotations without labeled masks. While offering speed and interpretability, PICS faces challenges in topology changes and inverse parameter estimation, which the authors address through OPI-guided adaptation and transfer-learning-like 3D propagation, signaling a practical path toward data-efficient medical image segmentation.

Abstract

Effective training of deep image segmentation models is challenging due to the need for abundant, high-quality annotations. Generating annotations is laborious and time-consuming for human experts, especially in medical image segmentation. To facilitate image annotation, we introduce Physics Informed Contour Selection (PICS) - an interpretable, physics-informed algorithm for rapid image segmentation without relying on labeled data. PICS draws inspiration from physics-informed neural networks (PINNs) and an active contour model called snake. It is fast and computationally lightweight because it employs cubic splines instead of a deep neural network as a basis function. Its training parameters are physically interpretable because they directly represent control knots of the segmentation curve. Traditional snakes involve minimization of the edge-based loss functionals by deriving the Euler-Lagrange equation followed by its numerical solution. However, PICS directly minimizes the loss functional, bypassing the Euler Lagrange equations. It is the first snake variant to minimize a region-based loss function instead of traditional edge-based loss functions. PICS uniquely models the three-dimensional (3D) segmentation process with an unsteady partial differential equation (PDE), which allows accelerated segmentation via transfer learning. To demonstrate its effectiveness, we apply PICS for 3D segmentation of the left ventricle on a publicly available cardiac dataset. While doing so, we also introduce a new convexity-preserving loss term that encodes the shape information of the left ventricle to enhance PICS's segmentation quality. Overall, PICS presents several novelties in network architecture, transfer learning, and physics-inspired losses for image segmentation, thereby showing promising outcomes and potential for further refinement.
Paper Structure (16 sections, 23 equations, 12 figures, 2 tables)

This paper contains 16 sections, 23 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Brief Review of Snake and PINN
  3. Brief Review of Snake Model
  4. Brief Review of PINNs
  5. Objectives
  6. Methods
  7. PICS Hypothesis
  8. Loss Function and Optimization
  9. Prior Shape-Based Loss Term
  10. Operation Performance Index (OPI)
  11. Results and Discussion
  12. 2D image segmentation without any prior shape information
  13. 2D image segmentation with prior shape information
  14. 3D image segmentation with or without prior shape information
  15. Adaptive hyperparameter tuning with OPI
  16. ...and 1 more sections

Figures (12)

  • Figure 1: Image segmentation with a naive image gradient-based snake. In the cavity case, please note that it gets stuck to a local minima.
  • Figure 2: Distribution of collocation (red triangles) and boundary points (blue rectangles) in the computational domain.
  • Figure 3: Overview of PICS algorithm.
  • Figure 4: Description of the cardiac dataset and sample annotations for the left ventricle.
  • Figure 5: segmentation of enlarged ventricles of a hydrocephalus patient. Left: Initial weights, Right: Optimized weights.
  • ...and 7 more figures