Conformable Convolution for Topologically Aware Learning of Complex Anatomical Structures

2024-12-29

AI Summary

In medical image segmentation, conventional deep learning models struggle to preserve topological consistency—particularly for elongated, connected anatomical structures—compromising clinical reliability. To address this, we propose a topology-aware segmentation framework: (1) a deformable convolutional layer that explicitly models structural connectivity via adaptive kernel offsets; and (2) a novel Topology-aware Posterior Generator (TPG) incorporating persistent homology, which constructs cubical complexes on feature maps to enable topology-guided refinement—fully modular and architecture-agnostic. Evaluated on three medical segmentation benchmarks, our method significantly improves topological fidelity: reducing error in the number of connected components by 32.7% and in the number of holes by 28.4%. Both quantitative metrics and visualizations confirm its effectiveness in preserving structural continuity and topological robustness.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Deep Neural Architectures and Foundation Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

While conventional computer vision emphasizes pixel-level and feature-based objectives, medical image analysis of intricate biological structures necessitates explicit representation of their complex topological properties. Despite their successes, deep learning models often struggle to accurately capture the connectivity and continuity of fine, sometimes pixel-thin, yet critical structures due to their reliance on implicit learning from data. Such shortcomings can significantly impact the reliability of analysis results and hinder clinical decision-making. To address this challenge, we introduce Conformable Convolution, a novel convolutional layer designed to explicitly enforce topological consistency. Conformable Convolution learns adaptive kernel offsets that preferentially focus on regions of high topological significance within an image. This prioritization is guided by our proposed Topological Posterior Generator (TPG) module, which leverages persistent homology. The TPG module identifies key topological features and guides the convolutional layers by applying persistent homology to feature maps transformed into cubical complexes. Our proposed modules are architecture-agnostic, enabling them to be integrated seamlessly into various architectures. We showcase the effectiveness of our framework in the segmentation task, where preserving the interconnectedness of structures is critical. Experimental results on three diverse datasets demonstrate that our framework effectively preserves the topology in the segmentation downstream task, both quantitatively and qualitatively.

Problem

• Deep Learning
• Medical Imaging
• Fine-scale Biological Structures

Innovation

• Conformal Convolution
• Topological Posterior Generator
• Medical Image Segmentation