A Morphological Tree of Shapes for Color Images

In mathematical morphology the tree of shapes of a gray level image is a versatile representation that allows for multiple powerful applications. That structure is highly interesting because it is a self-dual representation invariant by contrast changes and since many authors state that object contours are well described by level lines. Such a representation has not yet been defined (thus used) on color images because a priori a total order on colors is required that really make sense on data. In this paper we propose a solution to obtain a tree of shapes on color images without resorting to an ordering of colors. To that aim we relax the definition of shapes and we show that relevant applications follow from our proposal.