A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and thus its utility in detecting the modes of the density. The equivalence of the mean shift procedure to the Nadaraya–Watson estimator from kernel regression and the robust M-estimators of location is also established. Algorithms for two low-level vision tasks, discontinuity preserving smoothing and image segmentation are described as applications. In these algorithms the only user set parameter is the resolution of the analysis, and either gray level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. In this paper, we introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a ‘stream function ’ for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vector field defined by the stream function. The resulting algorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The method is directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.

One physical process involved in many computer vision problems is the heat diffusion process. Such Partial differential equations are continuous and have to be discretized by some techniques, mostly mathematical processes like finite differences or finite elements. The continuous domain is subdivided into sub-domains in which there is only one value. The diffusion equation comes from the energy conservation then it is valid on a whole domain. We use the global equation instead of discretize the PDE obtained by a limit process on this global equation. To encode these physical global values over pixels of different dimensions, we use a computational algebraic topology (CAT)-based image model. This model has been proposed by Ziou and Allili and used for the deformation of curves and optical flow. It introduces the image support as a decomposition in terms of points, edges, surfaces, volumes, etc. Images of any dimensions can then be handled. After decomposing the physical principles of the heat transfer into basic laws, we recall the CAT-based image model and use it to encode the basic laws. We then present experimental results for nonlinear graylevel diffusion for denoising, ensuring thin features preservation.

Image smoothing based on anisotropic diffusion provides better performance than classical linear filtering. One difficulty is to compare and evaluate the different models proposed. Since the basic model arises from fluid mechanics, we propose to track anisotropic diffusion using an optical flow technique through a new physics based image model. Consequently to this, we propose a new choice for the conductance function which is easier to control. We demonstrate with the optical flow tracking that this function has a better behavior concerning the gradient threshold than the known conductance functions. 1

This paper proposes an alternative to partial differential equations (PDEs) for the solution of diffusion (Perona and Malik scheme), using the heat transfer problem. Traditionally, the method for solving such physics-based problems is to discretize and solve a PDE by a mathematical process. We propose to use the global heat equation and decompose it into simpler laws. Some of these laws admit an exact global version since they arise from conservation principles while the assumptions on the others can be made wisely, taking into account knowledge about the problem. A computational algebraic topology-based image model allows us to write directly discrete equations. The numerical scheme is derived in a straightforward way from the problem modeled. It thus provides a physical explanation of each solving step in the solution. Finally, we present results for non linear diffusion.