CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes
Published in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2023
Harshil Bhatia, Edith Tretschk, Zorah Lähner, Marcel Seelbach Benkner, Michael Moeller, Christian Theobalt, Vladislav Golyanik
Abstract
Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, NP-hard problem. A perfect matching is necessarily cycle-consistent: Following the pairwise point correspondences along several shapes must end up at the starting vertex of the original shape. Unfortunately, existing quantum shape-matching methods do not support multiple shapes and even less cycle consistency. This paper addresses the open challenges and introduces the first quantum-hybrid approach for 3D shape multi-matching; in addition, it is also cycle-consistent. Its iterative formulation is admissible to modern adiabatic quantum hardware and scales linearly with the total number of input shapes. Both these characteristics are achieved by reducing the N -shape case to a sequence of three-shape matchings, the derivation of which is our main technical contribution. Thanks to quantum annealing, high-quality solutions with low energy are retrieved for the intermediate NP-hard objectives. On benchmark datasets, the proposed approach significantly outperforms extensions to multi-shape matching of a previous quantum-hybrid two-shape matching method and is on-par with classical multi-matching methods.
Resources
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Bibtex
@inproceedings{bhatia2023ccuantumm,
author = {Harshil Bhatia and Edith Tretschk and Zorah L\"ahner and Marcel {Seelbach Benkner} and Michael Moeller and Christian Theobalt and Vladislav Golyanik},
title = { CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes },
booktitle = {IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
year = 2023,
}