# MapTree: Recovering Multiple Solutions in the Space of Maps

arXiv: https://arxiv.org/abs/2006.02532 · HTML: https://mlsanity.com/paper/2006.02532/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [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)
- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [Complex Functional Maps : a Conformal Link Between Tangent Bundles](https://mlsanity.com/paper/2112.09546/) (2021)
- [Discovering Relationships between Object Categories via Universal Canonical Maps](https://mlsanity.com/paper/2106.09758/) (2021)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstruction](https://mlsanity.com/paper/2403.06804/) (2024)
- [Robust Extrinsic Symmetry Estimation in 3D Point Clouds](https://mlsanity.com/paper/2109.09927/) (2021)
- [Learning Canonical Embedding for Non-rigid Shape Matching](https://mlsanity.com/paper/2110.02994/) (2021)
- [Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud](https://mlsanity.com/paper/2112.02713/) (2021)
- [Extracting a functional representation from a dictionary for non-rigid shape matching](https://mlsanity.com/paper/2305.10332/) (2023)

## Abstract (arXiv)

In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This allows us to analyze the full space of maps and extract multiple diverse and accurate solutions, rather than optimizing for a single optimal correspondence as done in most previous approaches. To achieve this, we propose a compact tree structure based on the spectral map representation for encoding and enumerating possible rough initializations, and a novel efficient approach for refining them to dense pointwise maps. This leads to a new method capable of both producing multiple high-quality correspondences across shapes and revealing the symmetry structure of a shape without a priori information. In addition, we demonstrate through extensive experiments that our method is robust and results in more accurate correspondences than state-of-the-art for shape matching and symmetry detection.