Research On The Key Techniques In The Pre-Processing Of Topological Texture Image

The topological texture image, as a branch of texture image, contains many serpentine curves, regular or irregular geometric shapes, symmetrical or unsymmetrical patterns. All kinds of jacquard patterns in textile CAD, tissue textures in medical images, handwritten images, and ancient mural images belong to the research objects of topological texture image. More and more scholars and experts work at the domain of preprocessing for texture image, yet there are still many challenging problems in this field. For example, image denoising, image restoration, image segmentation and image inpainting are the four key techniques related to the system performance of topological texture images. This dissertation aims at the specialties of complex topological shapes in the edges of texture curves. It deeply deals with four key problems in the preprocessing of topological texture images, namely, edge-preserved image denoising method, color-preserved image restoration method, accurate image segmentation method, and fine image inpainting method. A lot of new ideas and approaches for numerical algorithms are proposed and better results are achieved. For example, Allen-Cahn equation in phase field theory and Mumford-Shah functional in free discontinuity problem were introduced to model the appearance of texture curves. The main contributions in this dissertation can be summarized as follows:Considering the problem of shape distortion and the poor adaptation to topological evolution in denoising of topological textures under noisy environment, a novel noise removal algorithm for topological textures was proposed, and a level set formulation for the Allen-Cahn equation was discussed. For nonlocal Allen-Cahn equation could generate an area-preserving motion by mean curvature flow, it can perfectly preserve shapes of the topological texture while in the process of denoising. First, the Allen-Cahn equation was put forward to generate area-preserving mean curvature motion. Then a level set formulation was developed to evolve curves arising in texture image. The proposed level set formulation also provided easier and more robust edge estimation and threshold strategies.An image restoration algorithm was proposed on the basis of space interaction among multi-color bands in degraded color images. It specified a Markov Random Field (MRF) model for the prior probability distribution of the degraded color image.The line process for an 8-point neighborhood system was developed to characterize and extract the spatial interaction between different color bands. The traditionally admissible solution space of classical simulated annealing procedure for the model is quite large. This dissertation presented a robust scheme for estimating the MRP line process and intensity configuration. The convergence speed of the estimation algorithm was improved by decisive search strategy, which enabled obtaining the sub-optimal solution of the degraded color image quickly.This dissertation dealed with the problem of low accuracy in segmentation of topological texture images under noisy environment. A novel iterative relaxation algorithm based on Mumford-Shah model was proposed for the segmentation of noisy topological texture images. In this algorithm, the Mumford-Shah model was approximated in the sense of F-convergence by a sequence of discrete models defined on piecewise affine spaces of adaptive triangulation. During each iteration, an adjustment procedure for the triangulation was enforced to characterize the essential contour structure of a topological texture pattern. Then, a quasi-Newton algorithm was applied to find the absolute minimum of the discrete model at the current iteration.In view of low accuracy in digital inpainting of topological texture images under noisy environment, a novel inpainting algorithm based on the Mumford-Shah model was proposed. For a successful completing action depended on its ability to evolve discontinuities along smooth contours, the Mumford-Shah model was improved by imposing some explicit smooth constrains on the formation of discontinuities. First, the paper presented the minimization problem for the Mumford-Shah based inpainting model. Then, a sequence of functionals F-convergent to the inpainting model was proposed. Finally, the gradient flow equation associated to the kth functional of the sequence was defined, and the finite difference approximation for numerical solving of the gradient flow equation was also presented. No limitations were imposed on the topology of the missing regions to be inpainted. Experimental results on noisy topological texture images demonstrate the effectiveness of the proposed inpainting algorithm.