Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis

Shenyuan Liang, Anuj Srivastava, Maurício Pamplona Segundo, Sudeep Sarkar, Sathyanarayanan N. Aakur

Abstract: This paper focuses on the registration problem of shape graphs, where a shape graph is a set of nodes connected by articulated curves with arbitrary shapes. This registration requires optimization over the permutation group, made challenging by differences in nodes (in terms of numbers, locations) and edges (in terms of shapes, placements, and sizes) across graphs. We tackle this registration problem using a neuralnetwork architecture with an unsupervised loss function based on the elastic shape metric for curves. This architecture results in (1) state-of-the-art matching performance and (2) an order of magnitude reduction in the computational cost relative to baseline approaches. We demonstrate the effectiveness of the proposed approach using both simulated data and real-world 2D retinal blood vessels and 3D microglia graphs.