Pyramidal image representation with deformation: Reformulation of domain transform and filter designs
Edge-preserving smoothing is one of the most important topics for image and video processing. Recently, we presented a multiscale image decomposition method based on domain transform, which is an efficient edge-preserving smoothing method. It is robust to noise compared with the original domain transform. In this paper, we generalize the scheme so that it can be applied to not only domain transform but also any deformation (warping) of pixels (or nonuniformly sampled signals) through showing the facts that the domain transform is a specific method of mesh deformation with a simple cost function. We also propose construction methods of filters by using arbitrary continuous filters or graph spectral filters in order that various filters can be accommodated by our method. To evaluate the proposed method, we performed experiments on pencil drawing and stylization. These results show that our approach easily changes the smoothing strength in accordance with the applications due to its multiscale scheme.