ZoomOut: Spectral Upsampling for Efficient Shape Correspondence

04/16/2019
by   Simone Melzi, et al.
0

We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.

READ FULL TEXT

page 3

page 5

page 6

page 8

page 9

06/01/2020

MapTree: Recovering Multiple Solutions in the Space of Maps

In this paper we propose an approach for computing multiple high-quality...
09/30/2020

Structured Regularization of Functional Map Computations

We consider the problem of non-rigid shape matching using the functional...
06/12/2018

Continuous and Orientation-preserving Correspondences via Functional Maps

We propose a method for efficiently computing orientation-preserving and...
10/19/2021

DPFM: Deep Partial Functional Maps

We consider the problem of computing dense correspondences between non-r...
12/10/2018

Unsupervised Deep Learning for Structured Shape Matching

We present a novel method for computing correspondences across shapes us...
12/05/2021

Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud

Despite the success of deep functional maps in non-rigid 3D shape matchi...
05/10/2022

Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases

We propose a principled approach for non-isometric landmark-preserving n...