Computational geometry-based scale space for edge-preserving multiscale image decomposition

Recently many computational photography applications need to decompose an image into a piecewise smooth base layer, containing large-scale variations in intensity, and a residual detail layer capturing the smaller-scale details in the image. In these applications, the image decomposition method requires multiscale ability to avoid visual artifacts. In this paper, we propose a new model of image decomposition that has the properties of edge-preserving and multiscale ability. Inspired by techniques in computational geometry and morphological image analysis, we use the α -scale space of the input image to extract information about oscillations. We define detail as oscillations between upper and lower envelope of the input image. Building on the key observation that the spatial scale of oscillations is characterized by the α 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 controls scale parameter; (2) preserves edge while decomposing; and (3) decouples noise layer from noisy image. Finally, we compare our results with current existing edge-preserving image decomposition algorithms and demonstrate applications.