Curvature-preserving regularization of multi-valued images using PDE's

Abstract

We are interested in diffusion PDE's for smoothing niulti-valued images in an anisotropic manner. By pointing out the pros and cons of existing tensor-driven regularization methods, we introduce a new constrained diffusion PDE that regularizes image data while taking curvatures of image structures into account. Our method has a direct link with a continuous formulation of the Line Integral Convolutions, allowing us to design a very fast and stable algorithm for its implementation. Besides, our smoothing scheme numerically performs with a sub-pixel accuracy and is then able to preserves very thin image structures contrary to classical PDE discretizations based on finite difference approximations. We illustrate our method with different applications on color images. © Springer-Verlag Berlin Heidelberg 2006.