A Fast Parallel Algorithm for Convex Hull Problem of Multi-Leveled Images

In this paper, we propose a parallel algorithm to solve the convex hull problem for an (n×n) multi-leveled image using a reconfigurable mesh connected computer of the same size as a computational model. The algorithm determines parallely the convex hull of all the connected components of the multileveled image. It is based on some geometric properties and a top-down strategy. The complexity of the algorithm is O(log n) times. Using some approximations on the component contours, this complexity is reduced to O(log m) times where m is the number of the vertices of the convex hull of the biggest component of the image.This complexity is reached thanks to the polymorphic properties of the mesh where all the components are simultaneously and separately processed.