Stochastic textures modeling and its application in texture structure decomposition

Natural stochastic textures coexist in images with complementary edge-type structural elements that constitute the cartoon-type skeleton of an image. Separating texture from the structure of natural image is an important inverse problem in image analysis. In this decomposition, the textural layer, which conveys fine details and small-scale variations, is separated from the image macrostructures (edges and contours). 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, which is suitable model for pure natural stochastic textures. We use it as a reconstruction prior to extract the corresponding textural element and show that this separation is crucial for improving the execution of various image processing tasks such as image denoising. Lastly, we highlight how manifold-based representation of texture-structure data, can be implemented in extraction of geometric features and construction of a classification space.