Implicit method for nonlinear complex diffusion with applications to image denoising

In this paper we focus on the development and implementation of an implicit finite difference method for solving a complex diffusion differential equation with applications to noise filtering in images. We give a complete characterization of the implementation of the fully implicit method, including the characterization of the derivatives for Newton's method at each step. In order to show the feasibility of the method, we compare the implicit method with the semi-implicit and apply it to both in vivo images of the human retina by optical coherence tomography (OCT) and standard images (Lena and the Cameraman). We compute noise removal performance metrics to show the effect of several parameters in the performance of the method.info:eu-repo/semantics/publishedVersio

Cross-diffusion systems for image processing: II. The nonlinear case

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration

A multi-view approach to cDNA micro-array analysis

The official published version can be obtained from the link below.Microarray has emerged as a powerful technology that enables biologists to study thousands of genes simultaneously, therefore, to obtain a better understanding of the gene interaction and regulation mechanisms. This paper is concerned with improving the processes involved in the analysis of microarray image data. The main focus is to clarify an image's feature space in an unsupervised manner. In this paper, the Image Transformation Engine (ITE), combined with different filters, is investigated. The proposed methods are applied to a set of real-world cDNA images. The MatCNN toolbox is used during the segmentation process. Quantitative comparisons between different filters are carried out. It is shown that the CLD filter is the best one to be applied with the ITE.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the National Science Foundation of China under Innovative Grant 70621001, Chinese Academy of Sciences under Innovative Group Overseas Partnership Grant, the BHP Billiton Cooperation of Australia Grant, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050 and the Alexander von Humboldt Foundation of Germany

Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.Comment: 10 page

Adaptive pre-filtering techniques for colour image analysis

One important step in the process of colour image segmentation is to reduce the errors caused by image noise and local colour inhomogeneities. This can be achieved by filtering the data with a smoothing operator that eliminates the noise and the weak textures. In this regard, the aim of this paper is to evaluate the performance of two image smoothing techniques designed for colour images, namely bilateral filtering for edge preserving smoothing and coupled forward and backward anisotropic diffusion scheme (FAB). Both techniques are non-linear and have the purpose of eliminating the image noise, reduce weak textures and artefacts and improve the coherence of colour information. A quantitative comparison between them will be evaluated and also the ability of such techniques to preserve the edge information will be investigated

Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement

The goal of many early visual filtering processes is to remove noise while at the same time sharpening contrast. An historical succession of approaches to this problem, starting with the use of simple derivative and smoothing operators, and the subsequent realization of the relationship between scale-space and the isotropic dfffusion equation, has recently resulted in the development of "geometry-driven" dfffusion. Nonlinear and anisotropic diffusion methods, as well as image-driven nonlinear filtering, have provided improved performance relative to the older isotropic and linear diffusion techniques. These techniques, which either explicitly or implicitly make use of kernels whose shape and center are functions of local image structure are too computationally expensive for use in real-time vision applications. In this paper, we show that results which are largely equivalent to those obtained from geometry-driven diffusion can be achieved by a process which is conceptually separated info two very different functions. The first involves the construction of a vector~field of "offsets", defined on a subset of the original image, at which to apply a filter. The offsets are used to displace filters away from boundaries to prevent edge blurring and destruction. The second is the (straightforward) application of the filter itself. The former function is a kind generalized image skeletonization; the latter is conventional image filtering. This formulation leads to results which are qualitatively similar to contemporary nonlinear diffusion methods, but at computation times that are roughly two orders of magnitude faster; allowing applications of this technique to real-time imaging. An additional advantage of this formulation is that it allows existing filter hardware and software implementations to be applied with no modification, since the offset step reduces to an image pixel permutation, or look-up table operation, after application of the filter

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE