Non‐Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities
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.
Authors
- А. Ф. Журавлев (ORCID: https://orcid.org/0000-0003-4282-3702)
- Lennart Bastian (ORCID: https://orcid.org/0000-0001-8088-3920)
- Christian Theobalt (ORCID: https://orcid.org/0000-0001-6104-6625)
- Zorah Lähner (ORCID: https://orcid.org/0000-0003-0599-094X)
- Nassir Navab (ORCID: https://orcid.org/0000-0002-6032-5611)
- Riccardo Marin (ORCID: https://orcid.org/0000-0003-2392-4612)
- Shigeo Morishima (ORCID: https://orcid.org/0000-0001-8859-6539)
- Paul Roetzer (ORCID: https://orcid.org/0009-0005-6698-6663)
- Daniel Cremers (ORCID: https://orcid.org/0000-0002-3079-7984)
- Florian Bernard (ORCID: https://orcid.org/0009-0008-1137-0003)
- V. Golyanik
- V. Ehm (ORCID: https://orcid.org/0009-0009-0142-5442)
- N. El Amrani (ORCID: https://orcid.org/0009-0004-9961-2855)
- H. Nishizawa (ORCID: https://orcid.org/0009-0009-0802-9047)
- D. Cao (ORCID: https://orcid.org/0000-0002-6505-6465)
Institutions
- University of Bonn (DE)
- Waseda University (JP)
- Lamarr Institute for Machine Learning and Artificial Intelligence
- Munich Center for Machine Learning
- Imperial College London (GB)
- Technical University of Munich (DE)
Publication Details
- Journal
- Computer Graphics Forum
- Published
- 2026-04-15
- DOI
- https://doi.org/10.1111/cgf.70397
- Primary Topic
- 3D Shape Modeling and Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- California Department of Fish and Game
- Deutsche Forschungsgemeinschaft
- Bundesministerium für Bildung und Forschung
- Japan Society for the Promotion of Science
- H2020 European Research Council