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

TL;DR

This paper introduces SGM-net, a neural network architecture for registering shape graphs, achieving state-of-the-art accuracy and significantly reduced computational cost in statistical shape analysis.

Contribution

The paper presents a novel neural network approach with an unsupervised elastic shape metric loss for shape graph registration, improving performance and efficiency.

Findings

Achieves state-of-the-art matching accuracy

Reduces computational cost by an order of magnitude

Effective on both simulated and real-world data

Abstract

This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to nodes, edges to edges) across objects. This, in turn, 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 objects. This paper tackles this registration problem using a novel neural-network architecture and involves an unsupervised loss function developed using 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 and 3D shape graphs. Code and data will be made publicly available after review to foster research.