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Solution of linear and nonlinear diffusion problems via stochastic differential equations

Bargieł M., Tory E. M.

Computer Science

2015

Vol. 16 (4)

415--428

The equation for nonlinear diffusion can be rearranged to a form that immediately leads to its stochastic analog. The latter contains a drift term that is absent when the diffusion coefficient is constant. The dependence of this coefficient on concentration (or temperature) is handled by generating many paths in parallel and approximating the derivative of concentration with respect to distance by the central difference. This method works for one-dimensional diffusion problems with finite or infinite boundaries and for diffusion in cylindrical or spherical shells. By mimicking the movements of molecules, the stochastic approach provides a deeper insight into the physical process. The parallel version of our algorithm is very efficient. The 99% confidence limits for the stochastic solution enclose the analytical solution so tightly that they cannot be shown graphically. This indicates that there is no systematic difference in the results for the two methods. Finally, we present a direct derivation of the stochastic method for cylindrical and spherical shells.

Integrated region-based segmentation using color components and texture features with prior shape knowledge

Emambakhsh M., Ebrahimnezhad H., Sedaaghi M. H.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

711-726

Segmentation is the art of partitioning an image into different regions where each one has some degree of uniformity in its feature space. A number of methods have been proposed and blind segmentation is one of them. It uses intrinsic image features, such as pixel intensity, color components and texture. However, some virtues, like poor contrast, noise and occlusion, can weaken the procedure. To overcome them, prior knowledge of the object of interest has to be incorporated in a top-down procedure for segmentation. Consequently, in this work, a novel integrated algorithm is proposed combining bottom-up (blind) and top-down (including shape prior) techniques. First, a color space transformation is performed. Then, an energy function (based on nonlinear diffusion of color components and directional derivatives) is defined. Next, signeddistance functions are generated from different shapes of the object of interest. Finally, a variational framework (based on the level set) is employed to minimize the energy function. The experimental results demonstrate a good performance of the proposed method compared with others and show its robustness in the presence of noise and occlusion. The proposed algorithm is applicable in outdoor and medical image segmentation and also in optical character recognition (OCR).

An improved diffusion driven watershed algorithm for image segmentation of cells

Tarnawski W., Kurzyński M.

Journal of Medical Informatics & Technologies

2007

Vol. 11

213--220

The image segmentation is one of the most crucial steps in automated analysis of medical and biological images. The segmentation process allows for a detection of object contours. Due to specificity of imaging technique, a correct detection of cell contours is problematic because of the fuzzy and broken edges. Moreover, the cells are very often connected. The modified watershed algorithm based on the diffusion model presented in this paper has been successfully applied to segmentation of cells where the mentioned difficulties appear. The method was tested in contact endoscopy, a novel technique in the diagnosis of the larynx.