拓扑纹理图像的关键预处理技术研究
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摘要
拓扑纹理图像是一类包含许多蜿蜒的曲线、规则与不规则的几何图形、对称与不对称的图案的纹理图像,纺织CAD中的各种提花织物图案、医学图像中的器官图像、手写体图像以及古代文物绘画图像等都属于拓扑纹理图像的范畴。虽然在纹理分析方面已经有大量的研究工作,但是拓扑纹理图像预处理领域仍然存在着很多挑战性问题。论文针对拓扑纹理图像中包含很多拓扑形状复杂的曲线边缘的特点,采用相变理论中的Allen-Cahn水平集曲线运动方程和自由不连续理论中的Mumford-shah泛函模型等数学工具,探讨支持含噪拓扑纹理图像在预处理过程中的保边去噪、保色彩恢复、精确分割、精细修补等四个共性关键问题的理论方法,研制相应的数值求解算法,为推进拓扑纹理图像在上述应用领域中的深入应用提供理论指导。
目前对上述四个关键预处理技术的研究难点和着眼点,大致可以总结为如下四个问题:一是,研究支持拓扑纹理图像的保细节去噪模型,以有效提高对复杂纹线拓扑形变的自适应能力;二是,研究支持表征和提取彩色拓扑纹理图像中多色彩通道间相关性的保色彩恢复模型,以有效避免色彩混迭,提高退化彩色拓扑纹理图像的色彩恢复质量;三是,研究支持对拓扑纹理曲线形变复杂度具有良好适应性的精确分割模型,提高对拓扑纹理图像的局部分割定位和整体分割提取;四是,研究支持对拓扑纹理图像中的不连续点集曲线具有较好光滑度约束的精细修补模型,使修补行为不受修补破损区域的拓扑形状的限制。
在拓扑纹理图像的保细节去噪模型研究方面,论丈针对含噪拓扑纹理图像在去噪过程中存在的形状失真和拓扑演变适应性差的问题,研究含噪拓扑纹理图像中不规则纹理的保边去噪模型,并重点讨论相变理论中的Allen-Cahn模型的水平集方法,以有效提高模型对复杂纹线拓扑形变的自适应能力。论文提出一种新的拓扑纹理图像去噪算法,算法利用非局部Allen-Cahn方程在平均曲率流中的面积保留特性,在去噪过程中较好地保留了拓扑纹线的形状。采用水平集对Allen-calan方程进行数值演化,有效提高了算法对复杂纹线拓扑形变的自适应能力。为减小对水平集进行有限差分计算的开销,采用改进快速行进算法确定适宜的相邻水平集扩张速度。
在拓扑纹理图像的保色彩恢复模型研究方面,论文针对彩色拓扑纹理图像在各个色彩通道的波长不相近时导致的色彩混迭不足,研究能对多色彩通道间相关性进行有效表征和提取的马尔可夫随机场模型。论文还针对经典模拟退火算法在对马尔可夫随机场模型求解时的时间复杂性过高的不足,研究能对经典模拟退火
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.
目前对上述四个关键预处理技术的研究难点和着眼点,大致可以总结为如下四个问题:一是,研究支持拓扑纹理图像的保细节去噪模型,以有效提高对复杂纹线拓扑形变的自适应能力;二是,研究支持表征和提取彩色拓扑纹理图像中多色彩通道间相关性的保色彩恢复模型,以有效避免色彩混迭,提高退化彩色拓扑纹理图像的色彩恢复质量;三是,研究支持对拓扑纹理曲线形变复杂度具有良好适应性的精确分割模型,提高对拓扑纹理图像的局部分割定位和整体分割提取;四是,研究支持对拓扑纹理图像中的不连续点集曲线具有较好光滑度约束的精细修补模型,使修补行为不受修补破损区域的拓扑形状的限制。
在拓扑纹理图像的保细节去噪模型研究方面,论丈针对含噪拓扑纹理图像在去噪过程中存在的形状失真和拓扑演变适应性差的问题,研究含噪拓扑纹理图像中不规则纹理的保边去噪模型,并重点讨论相变理论中的Allen-Cahn模型的水平集方法,以有效提高模型对复杂纹线拓扑形变的自适应能力。论文提出一种新的拓扑纹理图像去噪算法,算法利用非局部Allen-Cahn方程在平均曲率流中的面积保留特性,在去噪过程中较好地保留了拓扑纹线的形状。采用水平集对Allen-calan方程进行数值演化,有效提高了算法对复杂纹线拓扑形变的自适应能力。为减小对水平集进行有限差分计算的开销,采用改进快速行进算法确定适宜的相邻水平集扩张速度。
在拓扑纹理图像的保色彩恢复模型研究方面,论文针对彩色拓扑纹理图像在各个色彩通道的波长不相近时导致的色彩混迭不足,研究能对多色彩通道间相关性进行有效表征和提取的马尔可夫随机场模型。论文还针对经典模拟退火算法在对马尔可夫随机场模型求解时的时间复杂性过高的不足,研究能对经典模拟退火
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.
引文
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