Simplicial Complex based Point Correspondence between Images warped onto Manifolds

by   Charu Sharma, et al.

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.



There are no comments yet.


page 8

page 10

page 13


Solving Partial Assignment Problems using Random Clique Complexes

We present an alternate formulation of the partial assignment problem as...

Higher-order Projected Power Iterations for Scalable Multi-Matching

The matching of multiple objects (e.g. shapes or images) is a fundamenta...

A Flexible Tensor Block Coordinate Ascent Scheme for Hypergraph Matching

The estimation of correspondences between two images resp. point sets is...

Geometric Polynomial Constraints in Higher-Order Graph Matching

Correspondence is a ubiquitous problem in computer vision and graph matc...

A constrained clustering based approach for matching a collection of feature sets

In this paper, we consider the problem of finding the feature correspond...

Alternating Direction Graph Matching

In this paper, we introduce a graph matching method that can account for...

An Exact Hypergraph Matching Algorithm for Nuclear Identification in Embryonic Caenorhabditis elegans

Finding an optimal correspondence between point sets is a common task in...

Code Repositories

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.