Topology-Calibrated Correspondence Transfer across Non-Isometric Object Families

Abstract

Establishing meaningful point-to-point correspondences between distinct three-dimensional objects represents a foundational challenge in computer graphics, vision, and geometry processing. Traditional techniques have predominantly focused on isometric shapes, wherein intrinsic geodesic distances between points remain largely invariant despite extensive articulated deformations. However, real-world object families exhibit profound non-isometric variations characterized by differing topologies, structural additions, absent components, and significant scaling discrepancies. Such structural divergences severely disrupt conventional spectral and spatial alignment algorithms. This paper introduces a comprehensive framework for topology-calibrated correspondence transfer designed explicitly to bridge the semantic and geometric gap across highly non-isometric object families. By abstracting complex three-dimensional meshes into resilient topological skeletal graphs, the proposed methodology captures the essential structural hierarchy of an object independent of its localized geometric fluctuations. Through a meticulously designed alignment protocol, these skeletal abstractions serve as a robust scaffolding to guide the transfer of dense surface correspondences. The proposed framework integrates multi-scale geometric descriptors with global topological constraints, effectively mitigating the ambiguities that plague standard functional mapping techniques. Extensive evaluations conducted on challenging non-isometric datasets demonstrate that the proposed topology-calibrated approach significantly reduces alignment errors while preserving the structural integrity of the transferred maps. The findings underscore the critical importance of embedding global topological awareness into localized geometric matching processes, paving the way for more resilient structural analysis across diverse object categories.