Multi-scale image enhancement and representation is an important part of biological and machine early vision systems. The process of constructing this representation must be both rapid and insensitive to noise, while retaining image structure at all scales. This is a complex task as small scale structure is diicult to distinguish from noise, while larger scale structure requires more computatio...

We are developing a regularization technique for Perona–Malik diffusion equations that relies on multiresolution techniques. The main result of this paper is to show that the chosen discretization overcomes the ill-posedness of the nonlinear Perona–Malik model. The resulting algorithm is tested and the results are compared with pixel–based methods. keywords, phrases: Nonlinear diffusion, regula...

We study well-posed perturbations of formally ill-posed diffusion equations which are used in image processing, such as the Perona–Malik equation. Our perturbation technique is to consider the diffusion equations as L gradient flows on integral functionals and then modify the inner product from L to a Sobolev inner product. We show that the functional differential equations obtained in this way...

A generalization of the regularized (in the sense of Cattt, Lions, Morel and Coll) Perona-Malik anisotropic diiusion equation is proposed for image analysis. We present a numerical method for solving the above nonlinear degenerate diiusion problem, together with existence and convergence results. Numerical experiments are disscussed.

Multi-scale image enhancement and representation is an important part of biological and machine early vision systems. The process of constructing this representation must be both rapid and insensitive to noise, while retaining image structure at all scales. This is a complex task as small scale structure is difficult to distinguish from noise, while larger scale structure requires more computat...

We rigorously prove that the semidiscrete schemes of a Perona-Malik type equation converge, in a long time scale, to a suitable system of ordinary differential equations defined on piecewise constant functions. The proof is based on a formal asymptotic expansion argument, and on a careful construction of discrete comparison functions. Despite the equation has a region where it is backward parab...

We introduce a new model for multiscale analysis of space-time echocardiographic sequences. The proposed nonlinear partial diierential equation, representing the multiscale analysis, lters the sequence with keeping of the space-time coherent structures. It combines the ideas of regularized Perona-Malik anisotropic diiusion and Galilean invariant movie multiscale analysis of Alvarez, Guichard, L...