A hierarchical segmentation algorithm based on hepta-tree

This paper is concerned with a Hierarchical Markov Random Field (HMRF) algorithm for image segmentation, based on samples belonging to a hexagonal grid. Most of image segmentation algorithms use the topology based on the classical Z
²
grid, i.e., the squared grid, because this is an extension from the one-dimensional case. Nevertheless, the Z
²
grid is not optimal according to the Shannon sampling theorem: the optimal one for image sampling is the hexagonal grid [16, 1]. In this paper, we adapt to hexagonal topology a hierarchical image segmentation algorithm developed previously on a Z
²
grid. We present here a new structure, called the hepta-tree, adapted to hexagonal grids. Unsu-pervised segmentation results are compared on synthetic images issued from the both sampling grids.