A first parallel algorithm to compute the morphological tree of shapes of nD images

The tree of shapes is a self-dual tree-based image representation belonging to the field of mathematical morphology. This representation is highly interesting since it is invariant to contrast changes and inversion, and allows for numerous and powerful applications. A new algorithm to compute the tree of shapes has been recently presented: it has a quasilinear complexity; it is the only known algorithm that is also effective for nD images with n > 2; yet it is sequential. With the increasing size of data to process, the need of a parallel algorithm to compute that tree is of prime importance; in this paper, we present such an algorithm. We also give some benchmarks that show that the parallel version is computationally effective. As a consequence, that makes possible to process 3D images with some powerful self-dual morphological tools.