Abstract
The Tree of Shapes (ToS) is a morphological tree that provides an high-level hierarchical representation of the image suitable for many image processing tasks. When dealing with color images, one cannot use the ToS because its definition is ill-formed on multivariate data. Common workarounds such as marginal processing, or imposing a total order on data are not satisfactory and yield many problems (color artifacts, loss of invariances…) In this paper, we highlight the need for a self-dual and contrast invariant representation of the image and provide a method that builds a single ToS by merging the shapes computed marginally and preserving the most important properties of the ToS. This method does not try to impose an arbitrary total ordering on values but uses only the inclusion relationship between shapes and the merging strategy works in a shape space. Eventually, we show the relevance of our method and our structure through several applications involving color and multispectral image analysis.