数字图像的修复方法研究
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摘要
数字图像的修复具有重要的理论研究意义及广阔的应用前景。本文从分析修复问题的数学模型出发,从贝叶斯推理的角度对图像修复和图像融合的方法以及修复技术在图像压缩中的应用进行了深入的研究,主要工作和创新有:
1.针对小缺损区域的修复,分析了“宏观修复机制”偏微分方程和“微观修复机制”偏微分方程两类修复方法,并提出了一种综合了两类方法优点的修复方法:宏观上,方法定义的能量函数中的先验项能够反映图像模型;微观上,求解能量函数所对应的偏微分方程能较好地描述图像微观变化。针对大缺损区域的修复,分析了基于纹理合成的修复方法,并给出了3条修复规则,据此将修复问题表示成一个全局离散优化问题;采用一种期望值最大算法进行优化,同时解决了基于纹理合成修复方法中的两个关键问题——样本块匹配和样本块合成。
2.针对压缩图像在传输中的块损失问题,提出了一种基于凸集投影的块修复方法。方法充分利用了有效图像区域信息和信道先验估计信息,通过对损失块的局部边缘方向估计,采用一种结合频域和空域的凸集投影方法进行修复。该方法能较好地修复图像中的复杂边缘和纹理,与RIBMAP方法相比,在修复质量和方法稳定性上具有明显提高。
3.分析了当前梯度场重构的方法,提出了一种基于整体变分模型的梯度场重构方法,并将方法应用于图像融合的两个应用领域——图像编辑和图像拼接。提出了一种统一的梯度域拼接方法,并与当前的融合方法如羽化、最优接缝方法以及其他梯度域方法进行了理论和实验上的讨论和比较。讨论并分析了梯度域技术在图像融合中存在的问题,提出了一种基于边界优化的融合方法,有效克服了融合中存在的模糊和结构形变问题。
4.研究了修复技术在图像压缩中的应用。从数学上探讨了压缩问题和修复问题的关系,给出了一个面向修复的图像压缩框架,并描述了一种结合边缘和梯度场的图像表示和压缩方法。
The recovery of digital images is of significance in both theoretical research and practical applications. Form Bayesian inference point of view, this dissertation analyzes the mathematical model of recovery problem, and focuses on some key issues in the topic of image inpainting, image fusion, and recovery-oriented compression applications. The main work and innovations are listed as following:
1. According to the analysis on two main PDE-based inpainting methods, that are "macro-inpainting mechanisms" and "micro-inpainting mechanisms" PDE-based, respectively, a combined inpainting method aiming to restore small gap is proposed. Macroscopically, the prior term in proposed energy function mirrors image model. Microscopically, the associated PDEs simulate the generation of image. According to the analysis on texture synthesis-based completion methods, three completion rules are proposed. These rules turn the completion problem into a globally discrete optimization problem which is solved via an EM-like algorithm. The algorithm unifies two key procedures in the completion—patch matching and patch synthesis.
2. To fill-in blocks of missing data in wireless image transmission, a POCS-based approach which makes use of the information from both surrounding available blocks and channel estimation is presented. According to the computed edge orientation of a missing block, an adaptive recovery algorithm which combines frequency and spatial domain information is proposed. The proposed approach can restore image edge and complex texture satisfactorily. Improvement in restored image quality and robustness achieves when comparing with RIBMAP.
3. According to the analysis on current methods in reconstruction from gradient field, a reconstruction method based on total variation (TV) model is proposed. Editing and stitching applications in image fusion area are introduced. A unified gradient domain stitching approach is presented. We compare our proposed approach with state-of-the-art approaches mathematically and experimentally. Some key issues of gradient domain image fusion are discussed, and an improved method based on boundary optimization is presented. This method can handle both blurring and geometry deformation effectively.
4. The compression applications using image recovery technology are studied. We investigate the relation between the compression problem and the recovery problem from mathematical point of view, and present a recovery-oriented compression framework. An image compression scheme guided by this framework is described.
1.针对小缺损区域的修复,分析了“宏观修复机制”偏微分方程和“微观修复机制”偏微分方程两类修复方法,并提出了一种综合了两类方法优点的修复方法:宏观上,方法定义的能量函数中的先验项能够反映图像模型;微观上,求解能量函数所对应的偏微分方程能较好地描述图像微观变化。针对大缺损区域的修复,分析了基于纹理合成的修复方法,并给出了3条修复规则,据此将修复问题表示成一个全局离散优化问题;采用一种期望值最大算法进行优化,同时解决了基于纹理合成修复方法中的两个关键问题——样本块匹配和样本块合成。
2.针对压缩图像在传输中的块损失问题,提出了一种基于凸集投影的块修复方法。方法充分利用了有效图像区域信息和信道先验估计信息,通过对损失块的局部边缘方向估计,采用一种结合频域和空域的凸集投影方法进行修复。该方法能较好地修复图像中的复杂边缘和纹理,与RIBMAP方法相比,在修复质量和方法稳定性上具有明显提高。
3.分析了当前梯度场重构的方法,提出了一种基于整体变分模型的梯度场重构方法,并将方法应用于图像融合的两个应用领域——图像编辑和图像拼接。提出了一种统一的梯度域拼接方法,并与当前的融合方法如羽化、最优接缝方法以及其他梯度域方法进行了理论和实验上的讨论和比较。讨论并分析了梯度域技术在图像融合中存在的问题,提出了一种基于边界优化的融合方法,有效克服了融合中存在的模糊和结构形变问题。
4.研究了修复技术在图像压缩中的应用。从数学上探讨了压缩问题和修复问题的关系,给出了一个面向修复的图像压缩框架,并描述了一种结合边缘和梯度场的图像表示和压缩方法。
The recovery of digital images is of significance in both theoretical research and practical applications. Form Bayesian inference point of view, this dissertation analyzes the mathematical model of recovery problem, and focuses on some key issues in the topic of image inpainting, image fusion, and recovery-oriented compression applications. The main work and innovations are listed as following:
1. According to the analysis on two main PDE-based inpainting methods, that are "macro-inpainting mechanisms" and "micro-inpainting mechanisms" PDE-based, respectively, a combined inpainting method aiming to restore small gap is proposed. Macroscopically, the prior term in proposed energy function mirrors image model. Microscopically, the associated PDEs simulate the generation of image. According to the analysis on texture synthesis-based completion methods, three completion rules are proposed. These rules turn the completion problem into a globally discrete optimization problem which is solved via an EM-like algorithm. The algorithm unifies two key procedures in the completion—patch matching and patch synthesis.
2. To fill-in blocks of missing data in wireless image transmission, a POCS-based approach which makes use of the information from both surrounding available blocks and channel estimation is presented. According to the computed edge orientation of a missing block, an adaptive recovery algorithm which combines frequency and spatial domain information is proposed. The proposed approach can restore image edge and complex texture satisfactorily. Improvement in restored image quality and robustness achieves when comparing with RIBMAP.
3. According to the analysis on current methods in reconstruction from gradient field, a reconstruction method based on total variation (TV) model is proposed. Editing and stitching applications in image fusion area are introduced. A unified gradient domain stitching approach is presented. We compare our proposed approach with state-of-the-art approaches mathematically and experimentally. Some key issues of gradient domain image fusion are discussed, and an improved method based on boundary optimization is presented. This method can handle both blurring and geometry deformation effectively.
4. The compression applications using image recovery technology are studied. We investigate the relation between the compression problem and the recovery problem from mathematical point of view, and present a recovery-oriented compression framework. An image compression scheme guided by this framework is described.
引文
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