Non-Rigid 3D Shape Correspondences:
From Foundations to Open Challenges and Opportunities
Eurographics STAR 2026

A. Zhuravlev1⋆
L. Bastian6,7,8⋆
D. Cao2,3
N. El Amrani2,3
P. Roetzer2,3
V. Ehm7,8
R. Marin7,8
H. Nishizawa4
S. Morishima5
C. Theobalt1
N. Navab7,8
D. Cremers7,8
F. Bernard2,3
Z. Lähner2,3
V. Golyanik1

1MPI for Informatics   2University of Bonn   3Lamarr Institute   4Waseda University   5Waseda Research Institute for Science and Engineering
6Imperial College London   7Technical University of Munich   8Munich Center for Machine Learning   ⋆Equal Contribution


This state-of-the-art report surveys modern approaches to non-rigid 3D shape correspondence, spanning spectral, combinatorial, and deformation-based methods. It is intended as a structured entry point for researchers, practitioners, and students interested in the foundations, recent advances, and open challenges of the field.

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.

BibTeX

@article{zhuravlev2026nonrigid,
    title   = {Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities},
    author  = {Zhuravlev, Aleksei and Bastian, Lennart 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 and Navab, Nassir and Cremers, Daniel and Bernard, Florian and L{\"a}hner, Zorah and Golyanik, Vladislav},
    journal = {Computer Graphics Forum},
    year    = {2026},
    doi     = {10.1111/cgf.70397}
    }