Simplicial Complex based Point Correspondence between Images warped onto Manifolds

TL;DR

This paper introduces a novel simplicial complex-based method for point correspondence in images warped onto manifolds, effectively addressing distortions caused by projection and outperforming existing spherical matching techniques.

Contribution

It formulates the matching problem as a constrained quadratic assignment on simplicial complexes, enabling higher-order, distortion-robust correspondences on manifold-warped images.

Findings

Outperforms existing spherical matching methods on multiple datasets

Demonstrates robustness on synthetic and real-world warped images

Achieves higher accuracy in point correspondence tasks

Abstract

Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved higher-order matching algorithms on warped images due to projection. Although currently, several existing methods "flatten" such 3D images to use planar graph / hypergraph matching methods, they still suffer from severe distortions and other undesired artifacts, which result in inaccurate matching. Alternatively, current planar methods cannot be trivially extended to effectively match points on images warped onto manifolds. Hence, matching on these warped images persists as a formidable challenge. In this paper, we pose the assignment problem as finding a bijective map between two graph induced simplicial complexes, which are higher-order analogues of graphs. We propose a constrained quadratic assignment problem (QAP) that matches each p-skeleton of the simplicial complexes, iterating from the highest to the lowest dimension. The accuracy and robustness of our approach are illustrated on both synthetic and real-world spherical / warped (projected) images with known ground-truth correspondences. We significantly outperform existing state-of-the-art spherical matching methods on a diverse set of datasets.