# Point-wise Map Recovery and Refinement from Functional Correspondence

arXiv: https://arxiv.org/abs/1506.05603 · HTML: https://mlsanity.com/paper/1506.05603/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2015.

## Built on by (most cited first, 10 of 10)

- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Surface-Aware Distilled 3D Semantic Features](https://mlsanity.com/paper/2503.18254/) (2025)
- [Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields](https://mlsanity.com/paper/2107.06028/) (2021)
- [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026)
- [Extracting a functional representation from a dictionary for non-rigid shape matching](https://mlsanity.com/paper/2305.10332/) (2023)
- [TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisation](https://mlsanity.com/paper/2609.04202/) (2026)

## Abstract (arXiv)

Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape matching and image segmentation, to exploration of large shape collections. Despite the numerous advantages of such representation, however, the problem of converting a given functional map back to a point-to-point map has received a surprisingly limited interest. In this paper we analyze the general problem of point-wise map recovery from arbitrary functional maps. In doing so, we rule out many of the assumptions required by the currently established approach -- most notably, the limiting requirement of the input shapes being nearly-isometric. We devise an efficient recovery process based on a simple probabilistic model. Experiments confirm that this approach achieves remarkable accuracy improvements in very challenging cases.