Geometry carries the key features of visual information. The challenges in exploring geometry in image processing come from the discrete nature of the data, as well as the issues of robustness and efficiency. We present a discrete-space framework for the construction of multiscale geometric image transforms that can be applied to sampled images. The resulting contourlet transform is based on multidimensional filter banks and sampling lattices. Contourlets provide a seamless connection between the continuous and discrete domains using a multiresolution analysis that is similar to wavelets. This property allows the geometrical smoothness of object boundaries to be captured precisely using sampled image data. Finally, we present numerical results on the application of the contourlet transform to several image processing tasks.
This is a joint work with Martin Vetterli (EPFL and UC Berkeley), Arthur Cunha, Yue Lu, Jianping Zhou (UIUC), and Duncan Po (Mathworks).
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