Speed-up for AMAT implementation using pyramid reduction

Abstract

After introducing Appearance-Medial Axis Transform (AMAT) back in 2017 by Tsogkas and Dickinson for extending the Medial Axis Transform (MAT) for natural images, we introduce an extension of the algorithm attempting to improve the performances and resolve the set cover problem. The performance improvement will consist of using pyramid image reduction method in order to have simpler and fewer computations, resulting in a divide et impera algorithm. The different approach to the resolution of the set cover problem will follow the old algorithm. The final result will be an AMAT in three dimensions, using the z axis to represent the disks found at different levels of the pyramid. At the lower levels there will be the smallest disks found and on top the biggest ones. In addition, we added a method in the greedy algorithm that will search for suitable disks in the neighborhood of a solution disk found and we attempted to make an implementation that involves the graphic card and an analysis of the possibility to parallelize the algorithm.