This paper presents a new technique based on anisotropic diffusion for segmenting color images. This operation is accomplished through two independent anisotropic diffusion processes: one involving only the chromatic information, conveniently embedded in a complex function, and the other affecting the lightness information. The results of the two diffusions are separately segmented and their co...

We investigate a generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface. The exact solution of the relevant mixed boundary-value problem was found for different ratios of the intrinsic rate constants. The results obtaine...

Anisotropic Diffusion is widely used for noise reduction with simultaneous preservation of vascular structures in maximum intensity projected (MIP) angiograms. However, extension to minimum intensity projected (mIP) venograms in Susceptibility Weighted Imaging (SWI) poses difficulties due to spatially varying baseline. Here, we introduce a modified version of the directional anisotropic diffusi...

This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems of vector and tensor calculus on nonorthogonal, nonsmooth, structured and unstructured computational grids. We provide e...

In this paper we discuss application of an anisotropic diffusion equation in processing Posterior Capsular Opacification (PCO) Images. Such images are recorded to monitor the state of a patient’s vision after cataract surgery. Nonlinear filtering using an anisotropic diffusion equation generates segmentation-like results by enhancing edges represented by the high value of the gradient and smoot...

In this paper we discuss application of an anisotropic diffusion equation in processing Posterior Capsular Opacification (PCO) Images. Such images are recorded to monitor the state of a patient’s vision after cataract surgery. Non-linear filtering using an anisotropic diffusion equation generates segmentation-like results by enhancing edges represented by the high value of the gradient and smoo...

Anisotropic diffusion has been widely used in image processing for its efficiency of smoothing the noisy images while preserving the sharp edges. In this paper we will explore a general version of anisotropic diffusion schemes for vectorvalued images, based on the polar-coordinate representation of the vectors. As an example, we will apply our method to color images and show its ability of edge...

This paper presents an edge-enhancing super-resolution algorithm using anisotropic diffusion technique. Because we solve the super-resolution problem by incorporating anisotropic diffusion, our technique does more than merely reconstruct a high-resolution image from several overlapping noisy lowresolution images and preserve them. In addition to reducing image noise during the restoration proce...

Implementation of anisotropic diffusion for removal of noise from Chest CT data. ii Acknowledgements I would like to thank my supervisor Prof. Paul Whelan for his guidance, enthusiasm and commitment to this project. I would also like to express my deep appreciation to Dr. Tarik Chowdhury and Dr. Ovidiu Ghita for who have been very supportive during this project and have given me precious advice...

Understanding the generalization of deep learning has raised lots of concerns recently, where the learning algorithms play an important role in generalization performance, such as stochastic gradient descent (SGD). Along this line, we particularly study the anisotropic noise introduced by SGD, and investigate its importance for the generalization in deep neural networks. Through a thorough empi...