Warplets: an image-dependent wavelet representation

A novel image-dependent representation, warplets, based on self-similarity of regions is introduced. The representation is well suited to the description and segmentation of images containing textures and oriented patterns, such as fingerprints. An affine model of an image as a collection of self-similar image blocks is developed and it is shown how textured regions can be represented by a single prototype block together with a set of transformation coefficients. Images regions are aligned to a set of dictionary blocks and their variability captured by PCA analysis. The block-to-block transformations are found by Gaussian mixture modelling of the block spectra and a least-squares estimation. Clustering in the April domain can be used to determine a April dictionary. Experimental results on a variety of images demonstrate the potential of the use of April for segmentation and coding.