Shape correspondence based effective combination of linear and quadratic assignment matrices

Mingxuan Zhang; Muhammad Umair Hassan; Dongmei Niu; Na Li; Mingjun Liu; Jin Zhou; Xiuyang Zhao

doi:10.1117/12.2539652

14 August 2019 Shape correspondence based effective combination of linear and quadratic assignment matrices

Mingxuan Zhang, Muhammad Umair Hassan, Dongmei Niu, Na Li, Mingjun Liu, Jin Zhou, Xiuyang Zhao

Proceedings Volume 11179, Eleventh International Conference on Digital Image Processing (ICDIP 2019); 111794E (2019) https://doi.org/10.1117/12.2539652
Event: Eleventh International Conference on Digital Image Processing (ICDIP 2019), 2019, Guangzhou, China

Abstract

This paper describes an automatic dense correspondence approach to match two given isometric or nearly isometric 3D shapes which have non-rigid deformations. Our method is to improve the described ability of the assignment matrix as much as possible and solve the resolution composed of assignment matrices by using a combinatorial optimization algorithm. First, we construct two linear assignment matrices by using the SHOT and HKS descriptor, which can promote similar points into correspondence. Then, we construct a quadratic assignment matrix by using the heat distribution matrix, which can align a set of pairwise descriptors between a pair of points. In the final, we create a new objective function consisting of three assignment matrices which can adequately describe the matching relationship between points on two non-rigid deformed shapes, and the final optimal solution is obtained by solving the objective function using the projected descent optimization procedure. We show that high-quality dense correspondences can be established for a wide variety of model pairs which may have different poses, surface details. The effectiveness of this method is proven by geodesic error distance statistics from two commonly used datasets with ground truth, and we find that our algorithm is better than other state-of-the-art methods.

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Mingxuan Zhang, Muhammad Umair Hassan, Dongmei Niu, Na Li, Mingjun Liu, Jin Zhou, and Xiuyang Zhao "Shape correspondence based effective combination of linear and quadratic assignment matrices", Proc. SPIE 11179, Eleventh International Conference on Digital Image Processing (ICDIP 2019), 111794E (14 August 2019); https://doi.org/10.1117/12.2539652

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KEYWORDS

Matrices

Optimization (mathematics)

Laser range finders

Visualization

Computer programming

Data modeling

Machine learning

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