Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities
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Date
2026
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
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.
Description
@article{10.1111:cgf.70397,
journal = {Computer Graphics Forum},
title = {{Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities}},
author = {Zhuravlev, Aleksei and Bastian, Lennart and Navab, Nassir and Cremers, Daniel and Bernard, Florian and Lähner, Zorah and Golyanik, Vladislav and Cao, Dongliang and El Amrani, Nafie and Roetzer, Paul and Ehm, Viktoria and Marin, Riccardo and Nishizawa, Hiroki and Morishima, Shigeo and Theobalt, Christian},
year = {2026},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.70397}
}