Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis
This addresses the need for efficient and accurate registration of shape graphs, which is critical for statistical shape analysis in fields like medical imaging or computer vision, representing a novel method for a known bottleneck.
The paper tackles the registration problem for statistical shape analysis of shape graphs by proposing a novel neural-network architecture with an unsupervised loss function, achieving state-of-the-art matching performance and an order of magnitude reduction in computational cost compared to baseline approaches.
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.