Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities

TL;DR

This paper reviews recent advances in non-rigid 3D shape correspondence, categorizing methods into spectral, combinatorial, and deformation-based approaches, and discusses emerging challenges and future research directions.

Contribution

It provides a comprehensive survey of current methods, highlights recent developments, and identifies open challenges in non-rigid 3D shape correspondence.

Findings

Spectral methods based on functional maps are effective for smooth shape matching.

Deformation-based methods directly recover global alignments for complex shapes.

Emerging challenges include matching partial shapes and leveraging vision foundation models.

Abstract

Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many methods have thus been proposed to tackle this challenging problem from varying perspectives, depending on the downstream application. This state-of-the-art report is geared towards researchers, practitioners, and students seeking to understand recent trends and advances in the field. We categorise developments into three paradigms: spectral methods based on functional maps, combinatorial formulations that impose discrete constraints, and deformation-based methods that directly recover a global alignment. Each school of thought offers different advantages and disadvantages, which we discuss throughout the report. Meanwhile, we highlight the latest developments in each area and suggest new potential research directions. Finally, we provide an overview of emerging challenges and opportunities in this growing field, including the recent use of vision foundation models for zero-shot correspondence and the particularly challenging task of matching partial shapes.