Bandelet-Based Anisotropic Diffusion

Visual tasks often require a hierarchical representation of images in scales ranging from coarse to fine. A variety of linear and nonlinear smoothing techniques, such as Gaussian smoothing, anisotropic diffusion, regularization, wavelet thresholding etc... have been proposed. In this work, we propose a geometrical multiscale anisotropic diffusion based on the geometrical flow for denoising multivalued images. The geometrical flow is determined by the Bandelet transform of the image being processed. Consequently, the image is segmented into a quadtree where each square regroups pixels sharing the same geometrical flow direction. The motivation of this work is to introduce a new multiscale multistructure bandelet-based diffusion tensor to adjust the anisotropic diffusion toward the direction of the optimal geometrical flow. Therefore, multiple dyadic squares in the quadtree have multiple structure tensors. Hence, a more accurate geometrically driven noise suppression is obtained where the homogeneity of different image regions is well maintained.