An adaptive noise removal approach for restoration of digital images corrupted by multimodal noise

Data smoothing algorithms are commonly applied to reduce the level of noise and eliminate the weak textures contained in digital images. Anisotropic diffusion algorithms form a distinct category of noise removal approaches that implement the smoothing process locally in agreement with image features such as edges that are typically determined by applying diverse partial differential equation (PDE) models. While this approach is opportune since it allows the implementation of feature-preserving data smoothing strategies, the inclusion of the PDE models in the formulation of the data smoothing process compromises the performance of the anisotropic diffusion schemes when applied to data corrupted by non-Gaussian and multimodal image noise. In this paper we first evaluate the positive aspects related to the inclusion of a multi-scale edge detector based on the generalisation of the Di Zenzo operator into the formulation of the anisotropic diffusion process. Then, we introduce a new approach that embeds the vector median filtering into the discrete implementation of the anisotropic diffusion in order to improve the performance of the noise removal algorithm when applied to multimodal noise suppression. To evaluate the performance of the proposed data smoothing strategy, a large number of experiments on various types of digital images corrupted by multimodal noise were conducted.Keywords — Anisotropic diffusion, vector median filtering, feature preservation, multimodal noise, noise removal

Analysis of motion in scale space

This work includes some new aspects of motion estimation by the optic flow method in scale spaces. The usual techniques for motion estimation are limited to the application of coarse to fine strategies. The coarse to fine strategies can be successful only if there is enough information in every scale. In this work we investigate the motion estimation in the scale space more basically. The wavelet choice for scale space decomposition of image sequences is discussed in the first part of this work. We make use of the continuous wavelet transform with rotationally symmetric wavelets. Bandpass decomposed sequences allow the replacement of the structure tensor by the phase invariant energy operator. The structure tensor is computationally more expensive because of its spatial or spatio-temporal averaging. The energy operator needs in general no further averaging. The numerical accuracy of the motion estimation with the energy operator is compared to the results of usual techniques, based on the structure tensor. The comparison tests are performed on synthetic and real life sequences. Another practical contribution is the accuracy measurement for motion estimation by adaptive smoothed tensor fields. The adaptive smoothing relies on nonlinear anisotropic diffusion with discontinuity and curvature preservation. We reached an accuracy gain under properly chosen parameters for the diffusion filter. A theoretical contribution from mathematical point of view is a new discontinuity and curvature preserving regularization for motion estimation. The convergence of solutions for the isotropic case of the nonlocal partial differential equation is shown. For large displacements between two consecutive frames the optic flow method is systematically corrupted because of the violence of the sampling theorem. We developed a new method for motion analysis by scale decomposition, which allows to circumvent the systematic corruption without using the coarse to fine strategy. The underlying assumption is, that in a certain neighborhood the grey value undergoes the same displacement. If this is fulfilled, then the same optic flow should be measured in all scales. If there arise inconsistencies in a pixel across the scale space, so they can be detected and the scales containing this inconsistencies are not taken into account

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described