Adaptive Block Coordinate Descent for Distortion Minimization

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.