Edge-preserving multi-scale image decomposition based on alpha-shape

We propose a new model of image decomposition for detail that inherently captures oscillations, a key property that distinguishes textures from individual edges. Inspired by techniques in computational geometry and morphological image analysis, we use the alpha-shape of the input image to extract information about oscillations: We define detail as oscillations between upper and lower envelop of the input image. Building on the key observation that the spatial scale of oscillations is characterized by the ? value, we develop an algorithm for decomposing images into multiple scales of superposed oscillations. Compared with traditional image decomposition methods, our method has three advantages as follows: 1) precisely control scale parameter; 2) preserve edge while decomposition; 3) decouple a noise layer from noise image. We compared our results with current existing edge-preserving image decomposition algorithms and demonstrate exciting applications with our methods.