KEYWORDS: Image enhancement, Image filtering, Smoothing, Nonlinear filtering, Algorithm development, Image processing, High dynamic range imaging, Control systems, Digital filtering, 3D image processing
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.
The Reeb graph provides a structure that encodes the topology of a shape, and it has been gaining in popularity in shape analysis and understanding. We introduce a spectral clustering method to compute the Reeb graph. Given a 3-D model embedded in the Euclidean space, we define the Morse function according to the connected components of the 3-D model in a spectral space. The spectral clustering formulation gives rise to a consistent Reeb graph over pose changes of the same object with meaningful subparts and yields a hierarchical computation of the Reeb graph. We prove that this method is theoretically reasonable, and experimental results show its efficiency.