Anisotropic Data-Specific Wavelets for Structure-aware Image Processing

This paper proposes a novel anisotropic data-specific wavelets (ADW) for structure-preserving image analysis and processing. Our ADW is founded upon the rigorous mathematical derivation of hierarchical heat diffusion coupled with graph Laplacian, which not only inherits powerful properties from Mexican hat wavelets in spirit but also intrinsically encodes multi-level image properties. First, we construct anisotropic heat kernel by embedding the intrinsic image properties into graph Laplacian, and on such basis, ADW is derived from the heat kernel difference of adjacent layers in image pyramid, which is equivalent to the negative first-order derivative of the fundamental solution of heat diffusion equation with respect to time. At the application fronts of ADW, we perform various image processing experiments and conduct quantitative comparisons with other state-of-the-art methods to demonstrate the versatility and superiority of our method.