|M.Sc Student||Khawaled Samah|
|Subject||Models of Stochastic Textures in Image Processing|
|Department||Department of Electrical Engineering||Supervisor||Professor Emeritus Yehoshua Zeevi|
|Full Thesis text|
Natural stochastic texture (NST) coexists in images with complementary edge-type structural elements, that constitute the cartoon-type skeleton of an image. Separating texture from structure of a natural image is an important inverse problem in image analysis. In this study, we propose a variational texture-structure separation scheme. Our approach involves texture modeling by a stochastic field. The 2D fractional Brownian motion (fBm), a non-stationary Gaussian self-similar process that has been shown to be a suitable model for pure NST. We use it as a reconstruction prior to extract the corresponding textural element and show the applicability of this decomposition in image denoising. We proceed to present a novel manifold-based representation of the texture-structure space, where we extract its volumetric features to construct a classification space. Textural and structural features can be regraded as "two-view" feature sets. Inspired by the recent progress in multi-view learning, we propose a two-view classification method that models each feature set and optimizes the process of merging these views efficiently. Examples of implementation of this approach in classification of real-world data, with special emphasis on medical images, are presented.
Unlike fBm governed by a unique parameter (Hurst exponent), piecewise fractional Brownian motion (p-fBm) is defined by three parameters: the Hurst exponent in low frequencies, the Hurst exponent in high frequencies and the threshold frequency, which separates the two regimes. In this work, we present a synthesis method that generates a finite approximation of both 1D and 2D p-fBm signals. Moreover, we test the Gaussianity of both p-fBm and p-fGn and explore an approach to estimation of the process Hurst parameters. Our contribution is relevant to modeling and analysis of certain textures that are characteristic of certain medical and other natural images.