A contrario hierarchical image segmentation

Hierarchies are a powerful tool for image segmentation, they produce a multiscale representation which allows to design robust algorithms and can be stored in tree-like structures which provide an efficient implementation. These hierarchies are usually constructed explicitly or implicitly by means of region merging algorithms. These algorithms obtain the segmentation from the hierarchy by either using a greedy merging order or by cutting the hierarchy at a fixed scale. Our main contribution is to enlarge the search space of these algorithms to the set of all possible partitions spanned by a certain hierarchy, and to cast the segmentation as a selection problem within this space. The importance of this is two-fold. First, we are enlarging the search space of classic greedy algorithms and thus potentially improving the segmentation results. Second, this space is considerably smaller than the space of all possible partitions, thus we are reducing the complexity. In addition, we embed the selection process on a statistical a contrario framework which allows us to reduce the number of free parameters of our algorithm to only one.