Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.

For strongly undirected anisotropic processes such as coherence-enhancing diffusion...

. We present a framework for enhancing images while preserving either the edge or the orientation-dependent texture information present in them. We do this by treating images as manifolds in a feature-space. This geometrical interpretation leads to a natural way for grey level, color, movies, volumetric medical data, and color-texture image enhancement. Following this, we invoke the Polyakov action from high-energy physics, and develop a minimization procedure through a geometric flow. This flow, based on manifold volume minimization yields a natural enhancement procedure. We apply this framework to edgepreserving denoising of grey value and color images, for volumetric medical data, and orientation-preserving flows for grey level and color texture images. 1 Introduction In this paper, we present a general framework for processing images of various types like grey scale, color, and those that have orientation-dependent information such as textures. We do this by treating images as emb...

The segmentation of objects in video sequences constitutes a prerequisite for numerous applications ranging from computer vision tasks to second-generation video coding.

We study multivalued diffusion PDE's (Partial Differential Equations) and their application to color image processing. The analysis of classic scalar diffusion PDE's leads to a new multivalued regularization equation which is coherent with a local vector image geometry. Then, we are interested in constrained regularization problems, where vector norm constraints have to be considered. A general extension for unit vector regularization is then proposed. Finally, experimental results of color image restoration are presented.

In many applications computers analyse images or image sequences which are often contaminated by noise, and their quality can be poor (e.g. in medical imaging). We discuss how nonlinear partial differential equations (PDEs) can be used to automatically produce an image of much higher quality, enhance its sharpness, filter out the noise, extract shapes, etc. The models are based on the well-known Perona-Malik image selective smoothing equation and on geometrical equations of mean curvature flow type. Since the images are given on discrete grids, PDEs are discretized by variational techniques, namely by the semi-implicit finite element, finite volume and complementary volume methods in order to get fast and stable solutions. Convergence of the schemes to variational solutions of these strongly nonlinear problems and the extension of the methods to adaptive scheme strategies improving computational efficiency are discussed. Computational results with artificial and real 2D, 3D images and image sequences are presented.