Modeling regular textures in images using the Radon transform

The Radon transform is a major integral transform in computed tomography and a widely applied technique in computer vision and image analysis used to detect linear structures and regular textures. Its application is based on the property of the integrals of the direct problem to accumulate the image brightness along the contours under study. The back-projection operation, one of the main components of tomographic algorithms, results in ridge functions having the directions in which they participated in the direct operator. In the present paper, we examine the ridge functions and their orientation as the features for describing the anisotropy of regular textures. These features are involved in the regular texture model as a sum of ridge functions. Many textures are visually perceived as a superposition of linear structures and are therefore examined using the Radon transform. The paper presents a computational scheme for the singular value decomposition of a regular texture into a sum of informative ridge functions. The results are given of numerical experiments with the textures of industrial fabrics. The algorithm can be used in processing the visual data in computer vision systems, textile industry, robotics, and crystallography.