Adaptive Block Coordinate Descent for Distortion Minimization

Naitsat, Alexander; Zeevi,  Yehoshua Y.

Adaptive Block Coordinate Descent for Distortion Minimization

Files

003-004.pdf (1.99 MB)

Date

2019

Authors

Naitsat, Alexander
Zeevi, Yehoshua Y.

Publisher

The Eurographics Association

Abstract

We present a new unified algorithm for optimizing geometric energies and computing positively oriented simplicial mappings. Its major improvements over the state-of-the-art are: adaptive partition of vertices into coordinate blocks with the blended local-global strategy, introduction of new distortion energies for repairing inverted and degenerated simplices, modification of standard rotation-invariant measures, introduction of displacement norm for improving convergence criteria and for controlling the proposed local-global blending. Together these improvements form the basis for Adaptive Block Coordinate Descent (ABCD) algorithm aimed at robust geometric optimization. Our algorithm achieves state-of-the-art results in distortion minimization, even with highly distorted invalid initializations that contain thousands of inverted and degenerated elements. We show over a wide range of 2D and 3D problems that ABCD is more robust than existing techniques in locally injective mappings.

        @inproceedings{10.2312:sgp.20191214
,
booktitle = {Symposium on Geometry Processing 2019- Posters
},
editor = {Bommes, David and Huang, Hui
},
title = {{Adaptive Block Coordinate Descent for Distortion Minimization
}},
author = {Naitsat, Alexander and 
Zeevi,  Yehoshua Y.
},
year = {2019
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {978-3-03868-094-9
},
DOI = {10.2312/sgp.20191214
}
}