# Smooth Shells: Multi-Scale Shape Registration with Functional Maps

## TL;DR

This paper introduces a multi-scale shape registration method using smooth shells and functional maps, achieving state-of-the-art accuracy and robustness in 3D shape correspondence, especially under noisy real-world conditions.

## Contribution

The paper presents a novel multi-scale shape registration approach combining smooth shells with functional maps and symmetry disambiguation, improving robustness and accuracy over existing methods.

## Key findings

- Achieves state-of-the-art quantitative results on multiple datasets.
- Produces smoother, more realistic shape correspondences in real-world applications.
- Effectively handles noise, non-isometry, and incompatible meshing in 3D scans.

## Abstract

We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main idea is to first align rough approximations of the geometry and then add more and more details to refine the correspondence. We fuse classical shape registration with Functional Maps by embedding the input shapes into an intrinsic-extrinsic product space. Moreover, we disambiguate intrinsic symmetries by applying a surrogate based Markov chain Monte Carlo initialization. Our method naturally handles various types of noise that commonly occur in real scans, like non-isometry or incompatible meshing. Finally, we demonstrate state-of-the-art quantitative results on several datasets and show that our pipeline produces smoother, more realistic results than other automatic matching methods in real world applications.