Parallelization Strategy for Elementary Morphological Operators on Graphs

Abstract

International audienceThis article focuses on the graph-based mathematical morphology operators presented in [J. Cousty et al, Morphological ltering on graphs, CVIU 2013]. These operators depend on a size parameter that species the number of iterations of elementary dilations/erosions. Thus, the associated running times increase with the size parameter. In this article, we present distance maps that allow us to recover (by thresh-olding) all considered dilations and erosions. The algorithms based on distance maps allow the operators to be computed with a single linear-time iteration, without any dependence to the size parameter. Then, we investigate a parallelization strategy to compute these distance maps. The idea is to build iteratively the successive level-sets of the distance maps, each level set being traversed in parallel. Under some reasonable assumptions about the graph and sets to be dilated, our parallel algorithm runs in O(n/p + K log 2 p) where n, p, and K are the size of the graph, the number of available processors, and the number of distinct level-sets of the distance map, respectively

Parallelization Strategy for Elementary Morphological Operators on Graphs: Distance-Based Algorithms and Implementation on Multicore Shared-Memory Architecture

“…This article extends an article [34] published in a conference. In particular, it contains the proof of the properties presented in [34].…”

“…This article extends an article [34] published in a conference. In particular, it contains the proof of the properties presented in [34]. The three last sections dedicated to the implementation of the proposed parallel algorithm and its assessment are also completely original.…”