# Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases

arXiv: https://arxiv.org/abs/2205.04800 · HTML: https://mlsanity.com/paper/2205.04800/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 79 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 12 of 12)

- [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018)
- [ZoomOut: Spectral Upsampling for Efficient Shape Correspondence](https://mlsanity.com/paper/1904.07865/) (2019)
- [FARM: Functional Automatic Registration Method for 3D Human Bodies](https://mlsanity.com/paper/1807.10517/) (2018)
- [Reversible Harmonic Maps between Discrete Surfaces](https://mlsanity.com/paper/1801.02453/) (2018)
- [On the optimality of shape and data representation in the spectral domain](https://mlsanity.com/paper/1409.4349/) (2014)
- [MADMM: a generic algorithm for non-smooth optimization on manifolds](https://mlsanity.com/paper/1505.07676/) (2015)
- [Localized Manifold Harmonics for Spectral Shape Analysis](https://mlsanity.com/paper/1707.02596/) (2017)
- [Spectral Generalized Multi-Dimensional Scaling](https://mlsanity.com/paper/1311.2187/) (2013)
- [Hamiltonian operator for spectral shape analysis](https://mlsanity.com/paper/1611.01990/) (2016)
- [Robust Structure-based Shape Correspondence](https://mlsanity.com/paper/1710.05592/) (2017)
- [A Dual Iterative Refinement Method for Non-rigid Shape Matching](https://mlsanity.com/paper/2007.13049/) (2020)
- [Laplacian Spectral Basis Functions](https://mlsanity.com/paper/1906.03856/) (2019)

## Built on by (most cited first, 8 of 8)

- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithms](https://mlsanity.com/paper/2411.03511/) (2024)
- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)
- [Neural Isometries: Taming Transformations for Equivariant ML](https://mlsanity.com/paper/2405.19296/) (2024)
- [SIGMA: Scale-Invariant Global Sparse Shape Matching](https://mlsanity.com/paper/2308.08393/) (2023)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [Extracting a functional representation from a dictionary for non-rigid shape matching](https://mlsanity.com/paper/2305.10332/) (2023)
- [Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes](https://mlsanity.com/paper/2607.24954/) (2026)

## Abstract (arXiv)

We propose a principled approach for non-isometric landmark-preserving non-rigid shape matching. Our method is based on the functional maps framework, but rather than promoting isometries we focus instead on near-conformal maps that preserve landmarks exactly. We achieve this, first, by introducing a novel landmark-adapted basis using an intrinsic Dirichlet-Steklov eigenproblem. Second, we establish the functional decomposition of conformal maps expressed in this basis. Finally, we formulate a conformally-invariant energy that promotes high-quality landmark-preserving maps, and show how it can be solved via a variant of the recently proposed ZoomOut method that we extend to our setting. Our method is descriptor-free, efficient and robust to significant mesh variability. We evaluate our approach on a range of benchmark datasets and demonstrate state-of-the-art performance on non-isometric benchmarks and near state-of-the-art performance on isometric ones.