10,187 research outputs found

    Discontinuity Preserving Noise Removal Method based on Anisotropic Diffusion for Band Pass Signals

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    nonlinear discontinuity-preserving method for noise removal for band pass signals such as signals modulated with Binary Phase-Shift Keying (BPSK) modulation is proposed in this paper. This method is inspired by the anisotropic diffusion algorithm to remove noise and preserve discontinuities in band pass signals modulated with a single frequency. It is demonstrated here that nonlinear noise removal method for a real valued band pass signal requires a solution for a nonlinear partial differential equation which is of fourth order in space and second order in time. The results presented in this work show better performance in nonlinear noise removal for real valued band pass signals in comparison with the previous work in the literature

    A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

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    To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total α\alpha-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total α\alpha-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total α\alpha-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

    Learning shape correspondence with anisotropic convolutional neural networks

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    Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks

    Discretization schemes and numerical approximations of PDE impainting models and a comparative evaluation on novel real world MRI reconstruction applications

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    While various PDE models are in discussion since the last ten years and are widely applied nowadays in image processing and computer vision tasks, including restoration, filtering, segmentation and object tracking, the perspective adopted in the majority of the relevant reports is the view of applied mathematician, attempting to prove the existence theorems and devise exact numerical methods for solving them. Unfortunately, such solutions are exact for the continuous PDEs but due to the discrete approximations involved in image processing, the results yielded might be quite unsatisfactory. The major contribution of This work is, therefore, to present, from an engineering perspective, the application of PDE models in image processing analysis, from the algorithmic point of view, the discretization and numerical approximation schemes used for solving them. It is of course impossible to tackle all PDE models applied in image processing in this report from the computational point of view. It is, therefore, focused on image impainting PDE models, that is on PDEs, including anisotropic diffusion PDEs, higher order non-linear PDEs, variational PDEs and other constrained/regularized and unconstrained models, applied to image interpolation/ reconstruction. Apart from this novel computational critical overview and presentation of the PDE image impainting models numerical analysis, the second major contribution of This work is to evaluate, especially the anisotropic diffusion PDEs, in novel real world image impainting applications related to MRI
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