MapTree: Recovering Multiple Solutions in the Space of Maps

TL;DR

MapTree introduces a fully automatic method for discovering multiple high-quality dense correspondences between 3D shapes, capturing shape symmetries and diversity without relying on landmarks or descriptors.

Contribution

The paper presents a novel tree-based spectral map representation and an efficient refinement approach to recover multiple diverse solutions in shape correspondence tasks.

Findings

Outperforms state-of-the-art in shape matching accuracy

Effectively reveals shape symmetry structures

Robust across various shape datasets

Abstract

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.