The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

Abstract—In this work, we use partial differential equation techniques to remove noise from digital images. The removal is done in two steps. We first use a total-variation filter to smooth the normal vectors of the level curves of a noise image. After this, we try to find a surface to fit the smoothed normal vectors. For each of these two stages, the problem is reduced to a nonlinear partial differential equation. Finite difference schemes are used to solve these equations. A broad range of numerical examples are given in the paper. Index Terms—Anisotropic diffusion, image denoising, nonlinear partial differential equations (PDEs), normal processing. I.

We are interested in PDE’s (Partial Differential Equations) in order to smooth multi-valued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE’s, we point out the pros and cons of the different equations proposed in the literature. Then, we introduce a new tensor-driven PDE, regularizing images while taking the curvatures of specific integral curves into account. We show that this constraint is particularly well suited for the preservation of thin structures in an image restoration process. A direct link is made between our proposed equation and a continuous formulation of the LIC’s (Line Integral Convolutions by Cabral and Leedom [11]). It leads to the design of a very fast and stable algorithm that implements our regularization method, by successive integrations of pixel values along curved integral lines. Besides, the scheme numerically performs with a sub-pixel accuracy and preserves then thin image structures better than classical finite-differences discretizations. Finally, we illustrate the efficiency of our generic curvature-preserving approach- in terms of speed and visual quality- with different comparisons and various applications requiring image smoothing: color images denoising, inpainting and image resizing by nonlinear interpolation.

Abstract—Vessel plaque assessment by analysis of intravascular ultrasound sequences is a useful tool for cardiac disease diagnosis and intervention. Manual detection of luminal (inner) and mediaadventitia (external) vessel borders is the main activity of physicians in the process of lumen narrowing (plaque) quantification. Difficult definition of vessel border descriptors, as well as, shades, artifacts, and blurred signal response due to ultrasound physical properties trouble automated adventitia segmentation. In order to efficiently approach such a complex problem, we propose blending advanced anisotropic filtering operators and statistical classification techniques into a vessel border modelling strategy. Our systematic statistical analysis shows that the reported adventitia detection achieves an accuracy in the range of interobserver variability regardless of plaque nature, vessel geometry, and incomplete vessel borders. Index Terms—Anisotropic processing, intravascular ultrasound (IVUS), vessel border segmentation, vessel structure classification.

A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems.

Abstract. We are interested in diffusion PDE’s for smoothing multi-valued images in an anisotropic manner. By pointing out the pros and cons of existing tensor-driven regularization methods, we introduce a new constrained diffusion PDE that regularizes image data while taking curvatures of image structures into account. Our method has a direct link with a continuous formulation of the Line Integral Convolutions, allowing us to design a very fast and stable algorithm for its implementation. Besides, our smoothing scheme numerically performs with a sub-pixel accuracy and is then able to preserves very thin image structures contrary to classical PDE discretizations based on finite difference approximations. We illustrate our method with different applications on color images. 1

The years 1985-2000 have seen the emergence of several nonlinear P.D.E. models in image restoration and image analysis. Before that date, the heat equation and the reverse heat equation had been considered as relevant, one as a model of image smoothing compatible with Shannon conditions, and one as a restoration model proposed by Gabor. We try in this review to organize the P.D.E. models according to their genealogy from the initial heat equation and according to their very diverse use : some are useful for image denoising, some for image deblurring, some for invariant smoothing in view of shape recognition. Some permit to de ne easily active contours (snakes), some may be used for a nonlinear interpolation of sparse images. We show many experiments illustrating these dierent applicative aspects.

The adventitia layer appears as a weak edge in IVUS images with a non-uniform grey level, which difficulties its detection. In order to enhance edges, we apply an anisotropic filter that homogenizes the grey level along the image significant structures (ridges, valleys and edges). A standard edge detector applied to the filtered image yields a set of candidate points prone to be unconnected. The final model is obtained by interpolating the former line segments along the tangent direction to the level curves of the filtered image with an anisotropic contour closing technique based on functional extension principles. 1.