Abstracts of reference papers in the field of edge detection are proposed: (Marr and Hildreth, 1980) and (Perona and Malik, 1990), as well as surveys on edge detection (Ziou and Tabbone, 1998; Basu, 2002) and old forgotten papers (Fram and Deutsch, 1975). Personal remarks are sometimes included.s of reference papers in the field of edge detection are proposed: (Marr and Hildreth, 1980) and (Per...

• Restoration by energy minimization (Section 2): We detail the discretization of the divergence term, which can also be found for the Perona and Malik equation. • Enhancement by Osher and Rudin’s shock filters (Section 3): The main interest is to use a flux limiter called minmod. • Curve evolution with level sets and especially segmentation with geodesic active contours (Section 4). For the sa...

We introduce a family of rst-order multi-dimensional ordinary diierential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diiusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations \stabilized inverse diiusion equatio...

The Perona–Malik (PM) model, or the anisotropic diffusion, shows good performance for image restoration. However, it suffers from the so-called staircasing effect if the contrast parameter is small and otherwise cannot preserve edges. This paper proposes a modified Perona–Malik (MPM) model based on directional Laplacian, which diffuses image along the edge direction of the original image. A sli...

A novel nonlinear PDE based image denoising and restoration approach is provided in this article. The proposed anisotropic diffusion based technique is derived from the influential Perona-Malik nonlinear diffusion scheme, representing an enhanced version of that scheme. Our model is based on new versions of the edge-stopping function and the conductance parameter. The proposed PDE-based filteri...

In this paper we give a general, robust, and efficient approach for numerical solutions of partial differential equations (PDEs) arising in image processing and computer vision. The well-established variational computational techniques, namely, finite element, finite volume, and complementary volume methods, are introduced on a common base to solve nonlinear problems in image multiscale analysi...

We introduce a family of first-order multi-dimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations “stabilized inverse diffusion eq...