# Continuous and Orientation-preserving Correspondences via Functional Maps

arXiv: https://arxiv.org/abs/1806.04455 · HTML: https://mlsanity.com/paper/1806.04455/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2018.

## Built on by (most cited first, 30 of 77)

- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022)
- [Zero-Shot 3D Shape Correspondence](https://mlsanity.com/paper/2306.03253/) (2023)
- [Spatially and Spectrally Consistent Deep Functional Maps](https://mlsanity.com/paper/2308.08871/) (2023)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (2023)
- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2204.12805/) (2022)
- [SE-ORNet: Self-Ensembling Orientation-aware Network for Unsupervised Point Cloud Shape Correspondence](https://mlsanity.com/paper/2304.05395/) (2023)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [Complex Functional Maps : a Conformal Link Between Tangent Bundles](https://mlsanity.com/paper/2112.09546/) (2021)
- [Partial-to-Partial Shape Matching with Geometric Consistency](https://mlsanity.com/paper/2404.12209/) (2024)
- [Memory-Scalable and Simplified Functional Map Learning](https://mlsanity.com/paper/2404.00330/) (2024)
- [Denoising Functional Maps: Diffusion Models for Shape Correspondence](https://mlsanity.com/paper/2503.01845/) (2025)
- [Hierarchical Neural Semantic Representation for 3D Semantic Correspondence](https://mlsanity.com/paper/2509.17431/) (2025)
- [Implicit field supervision for robust non-rigid shape matching](https://mlsanity.com/paper/2203.07694/) (2022)
- [SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence](https://mlsanity.com/paper/2209.07806/) (2022)
- [Neural Semantic Surface Maps](https://mlsanity.com/paper/2309.04836/) (2023)
- [Geometrically Consistent Partial Shape Matching](https://mlsanity.com/paper/2309.05013/) (2023)
- [Non-Rigid Shape Registration via Deep Functional Maps Prior](https://mlsanity.com/paper/2311.04494/) (2023)
- [Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning](https://mlsanity.com/paper/2403.01781/) (2024)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)

## Abstract (arXiv)

We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated directly in the functional (spectral) domain without using landmark or region correspondences and without relying on external symmetry information. This allows us to obtain functional maps that promote orientation preservation, even when using descriptors, that are invariant to orientation changes. We then show how higher quality, approximately continuous and bijective pointwise correspondences can be obtained from initial functional maps by introducing a novel refinement technique that aims to simultaneously improve the maps both in the spectral and spatial domains. This leads to a general pipeline for computing correspondences between shapes that results in high-quality maps, while admitting an efficient optimization scheme. We show through extensive evaluation that our approach improves upon state-of-the-art results on challenging isometric and non-isometric correspondence benchmarks according to both measures of continuity and coverage as well as producing semantically meaningful correspondences as measured by the distance to ground truth maps.