# Reversible Harmonic Maps between Discrete Surfaces

arXiv: https://arxiv.org/abs/1801.02453 · HTML: https://mlsanity.com/paper/1801.02453/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2018.

## Built on by (most cited first, 19 of 19)

- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Denoising Functional Maps: Diffusion Models for Shape Correspondence](https://mlsanity.com/paper/2503.01845/) (2025)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases](https://mlsanity.com/paper/2205.04800/) (2022)
- [Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching](https://mlsanity.com/paper/2310.11420/) (2023)
- [Intuitive Shape Editing in Latent Space](https://mlsanity.com/paper/2111.12488/) (2021)
- [Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2407.08244/) (2024)
- [Mesh Draping: Parametrization-Free Neural Mesh Transfer](https://mlsanity.com/paper/2110.05433/) (2021)
- [Volumetric Parameterization of the Placenta to a Flattened Template](https://mlsanity.com/paper/2111.07900/) (2021)
- [FRIDU: Functional Map Refinement with Guided Image Diffusion](https://mlsanity.com/paper/2506.14322/) (2025)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [Wukong's 72 Transformations: High-fidelity Textured 3D Morphing via Flow Models](https://mlsanity.com/paper/2511.22425/) (2025)
- [Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary](https://mlsanity.com/paper/2202.02568/) (2022)
- [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026)
- [DPC: Unsupervised Deep Point Correspondence via Cross and Self Construction](https://mlsanity.com/paper/2110.08636/) (2021)
- [RealSkin: Spatio-Spectral Partial Neural Adjoint Maps for Image-to-3D Attribute Transfer](https://mlsanity.com/paper/2607.12495/) (2026)
- [MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondence](https://mlsanity.com/paper/2607.15887/) (2026)

## Abstract (arXiv)

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g. point landmarks, a dense map or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state-of-the-art, while succeeding in correctly mapping key features of the input shapes.