ZoomOut: Spectral Upsampling for Efficient Shape Correspondence

TL;DR

ZoomOut introduces a spectral upsampling technique that refines shape correspondences efficiently, improving accuracy and speed across various applications while being robust to noise and scalable to complex shapes.

Contribution

The paper proposes a simple spectral upsampling method for shape correspondence refinement, offering significant speed-ups and robustness over existing techniques.

Findings

Achieves up to two orders of magnitude speed-up in shape matching tasks.

Improves correspondence quality even with noisy or limited spectral data.

Demonstrates robustness and scalability across diverse shape analysis applications.

Abstract

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.