  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.
