This article shows how the dynamics extinction value can be used to compute the decomposition of a function as a sum of simpler components. We show that this decomposition induces a hierarchical segmentation of the domain of definition, and a new partial ordering on nonnegative functions. Removing some of the components according to different criteria leads to new morphological operators. Their properties are discussed and illustrated in the last section. In particular, we see that thresholding on the supports' areas simplifies textured zones, while retaining perceptually salient elements of the image.