This paper proposes a new class of nonlinear PDEs called the Gibbs Reaction And Di usion Equation GRADE for a variety of applications in computer vision image processing and graphics In two previous papers the authors have been studying a minimax entropy theory based on which a new class of Gibbs distributions are learned in a fully non parametric form from a set of observed images such as text...

There exists a large number of techniques for content-aware smoothing. Despite its simplicity, the PeronaMalik Anisotropic Diffusion method is among the most employed ones. In this work we study this method in detail and propose a generalization of its diffusion scheme using restricted dissimilarity functions to measure the intensity differences between neighbouring pixels. This generalization ...

Noise filtering of images is basically a smoothing process, and it is a subject that has been addressed for many years. The idea of adaptive smoothing is being investigated a long time and many different approaches have been proposed over the years. Mastin (1985) reported superior performance of nonlinear such as medina filtering over linear techniques applied for adaptive image smoothing. Zuck...

Segmentation of images holds an important position in the area of image processing. It becomes more important while typically dealing with medical images where pre-surgery and post surgery decisions are required for the purpose of initiating and speeding up the recovery process [5] Computer aided detection of abnormal growth of tissues is primarily motivated by the necessity of achieving maximu...

Vision systems require fundamental algorithms of image processing and vision computing. Algorithms of edge detection, grouping and stereo disparity detection are typical examples. Marr and his collaborators proposed several effective algorithms of edge detection and stereo disparity detection, in particular, in a computational approach (Marr, 1982). Marr and Hildreth had previously proposed an ...

Abstract. Let u ∈ BV(Ω) solve the total variation denoising problem with L2-squared fidelity and data f . Caselles et al. [Multiscale Model. Simul. 6 (2008), 879–894] have shown the containment Hm−1(Ju \ Jf ) = 0 of the jump set Ju of u in that of f . Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to high...

This work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accura...