Geometrically Consistent Partial Shape Matching

TL;DR

This paper introduces a novel method for partial 3D shape matching that ensures geometric consistency and outperforms existing algorithms in reliability and smoothness by integrating deep features into an optimization framework.

Contribution

It presents a new integer linear programming approach for partial shape matching that guarantees global optimality and incorporates deep shape features for improved accuracy.

Findings

More reliable results on partial shapes compared to existing methods

Matchings are substantially smoother than learning-based approaches

Global optimality achieved on low-resolution shapes

Abstract

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property of matchings is geometric consistency, which means that neighboring triangles in one shape are consistently matched to neighboring triangles in the other shape. Moreover, while in practice one often has only access to partial observations of a 3D shape (e.g. due to occlusion, or scanning artifacts), there do not exist any methods that directly address geometrically consistent partial shape matching. In this work we fill this gap by proposing to integrate state-of-the-art deep shape features into a novel integer linear programming partial shape matching formulation. Our optimization yields a globally optimal solution on low resolution shapes, which we then refine using a coarse-to-fine scheme. We show that our method can find more reliable results on partial shapes in comparison to existing geometrically consistent algorithms (for which one first has to fill missing parts with a dummy geometry). Moreover, our matchings are substantially smoother than learning-based state-of-the-art shape matching methods.