Morphlets: a new class of tree-structured morphological descriptors of image shape

In this paper, we present a new class of tree-structured morphological descriptors of image shape. The notion of a Haar-like function is formalized. It is demonstrated that Pytiev morphology of centered images can be described in terms of a Haar-like basis. The morphology of localized mosaic shapes and corresponding localized Haar-like wavelet systems are described. The formal way for generating a hierarchical structure of localized mosaic shapes and corresponding tree of localized Haar-like wavelets is reported. The notion of “morphlets” as Haar-like wavelets corresponding to the mosaic shape of some image is introduced. Some constructive schemes for the generation of morphlet-based image descriptors are considered.