基于Gap统计的图像分割理论与算法研究
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摘要
图像处理与模式识别是一门前沿的交叉学科,其中边缘检测、图像分割以及目标的表达等都是该学科的主要研究方向。而图像分割又是图像处理、模式识别和人工智能等领域中一个十分重要的研究课题,也是图像理解的基础和计算机视觉领域低层次视觉的经典研究难题。本文结合“基于IBR的仿真图像生成理论与技术研究”、“仿真实时图像生成和分析系统”及“基于图像的虚拟战场环境生成技术研究”等项目,以Gap统计方法为主线,系统深入地研究了基于Gap统计方法的图像分割理论与算法,所取得的主要研究成果与创新之处为:
(1)全面分析与总结了前人关于图像分割的随机统计模型、几何分析模型和神经网络模型等,首次提出了基于“Gap Statistic”的思想来研究图像分割的理论与算法;
(2)提出了函数Gap的一般概念,依据边缘判断的不同特征或标准,定义了几种具体的函数Gap,分析了不同函数Gap之间的关系。并利用函数Gap的理论,首次研究了图像的Gap统计特性,提出了边缘检测的Gap统计模型;
(3)提出了图像中点Gap的概念,研究了图像中边缘的点Gap特征,导出了广义阶跃边缘和广义屋脊边缘的表示方法,建立了图像多尺度边缘检测的点Gap模型,并提出了点分布Gap的图像多尺度边缘检测算法,进一步研究了点顺序秩和Gap及其理论在边缘检测中的应用;
(4)基于Gap统计理论,利用图像像素之间的近程和远程相关性,提出了加权Gap的概念;提出了多尺度加权邻域的图像边缘检测模型与算法,并分析了Gap算子与Sobel边缘检测算子的关系;
(5)提出了函数特征、间隙、总间隙及全间隙等概念,建立了图像分割的Gap统计模型,并给出了较为详细的算法。分析了图像分割Gap统计模型中正则部分和奇异部分的特点,导出了区域特征自相似函数的分割结果与模型调节参数的关系。比较了用于图像分割的Gap统计模型与Mumford-Shah模型,结果表明图像分割Gap统计模型的复杂度明显低于Mumford-Shah模型。
Image processing and pattern recognition are the stratosphere of an interdisciplinary field. It is well known that edge detection, image segmentation and object description are the mainly research subjects in such field. In addition image segmentation plays a very important role in the field of image processing, pattern recognition, and it is classical difficult problem of the lower level computer vision as well as the fundamental step for image understanding. Based on the projects named "Research of IBR based simulate image synthesis theory and techniques ", "Real-time digital scene generation and analysis system" and "Research of the virtual environment generation in the battlefield based on image rendering ", this dissertation focuses on the research on the theory and application of Gap statistic for image segmentation. A systematic study is made for the theory and algorithms of image segmentation based on Gap statistic. The primary works and creative contribution of the paper are:(1) The paper takes a systematic research on the random statistical model, geometrical analysis model and neural network model, etc. The Gap statistic is firstly introduced to study the theory and algorithms of image segmentation.(2) A new conception of "function gap" is originally proposed in this paper. Based on the different feature and criteria of edge in image, several types of function gap are defined and the relationships among them are discussed. Furthermore, utilizing the theory of function gap, we creatively take an investigation on the Gap statistical properties of images. Finally, the gap statistical models for edge detection are proposed.(3) After presenting the new conception of "point gap", we study the Gap features of the edges in image and develop a formalism of generalized step edges and roof edges. A point Gap model of multi-scale edge detection is presented and the corresponding algorithm is advanced. Furthermore, we put our study forward on the theory and application of another Gap named "order rank sum Gap".(4) Using the long range and short range dependency among image pixels respectively, we propose the conception of weighted Gap and present a new multi-scale weighted neighborhood based edge detection model and corresponding algorithms. The difference between Gap operator and Sobel operator is also analyzed.(5) Several new conceptions including function feature, total Gap and full Gap are proposed and the Gap statistical model for image segmentation is established and the detail
(1)全面分析与总结了前人关于图像分割的随机统计模型、几何分析模型和神经网络模型等,首次提出了基于“Gap Statistic”的思想来研究图像分割的理论与算法;
(2)提出了函数Gap的一般概念,依据边缘判断的不同特征或标准,定义了几种具体的函数Gap,分析了不同函数Gap之间的关系。并利用函数Gap的理论,首次研究了图像的Gap统计特性,提出了边缘检测的Gap统计模型;
(3)提出了图像中点Gap的概念,研究了图像中边缘的点Gap特征,导出了广义阶跃边缘和广义屋脊边缘的表示方法,建立了图像多尺度边缘检测的点Gap模型,并提出了点分布Gap的图像多尺度边缘检测算法,进一步研究了点顺序秩和Gap及其理论在边缘检测中的应用;
(4)基于Gap统计理论,利用图像像素之间的近程和远程相关性,提出了加权Gap的概念;提出了多尺度加权邻域的图像边缘检测模型与算法,并分析了Gap算子与Sobel边缘检测算子的关系;
(5)提出了函数特征、间隙、总间隙及全间隙等概念,建立了图像分割的Gap统计模型,并给出了较为详细的算法。分析了图像分割Gap统计模型中正则部分和奇异部分的特点,导出了区域特征自相似函数的分割结果与模型调节参数的关系。比较了用于图像分割的Gap统计模型与Mumford-Shah模型,结果表明图像分割Gap统计模型的复杂度明显低于Mumford-Shah模型。
Image processing and pattern recognition are the stratosphere of an interdisciplinary field. It is well known that edge detection, image segmentation and object description are the mainly research subjects in such field. In addition image segmentation plays a very important role in the field of image processing, pattern recognition, and it is classical difficult problem of the lower level computer vision as well as the fundamental step for image understanding. Based on the projects named "Research of IBR based simulate image synthesis theory and techniques ", "Real-time digital scene generation and analysis system" and "Research of the virtual environment generation in the battlefield based on image rendering ", this dissertation focuses on the research on the theory and application of Gap statistic for image segmentation. A systematic study is made for the theory and algorithms of image segmentation based on Gap statistic. The primary works and creative contribution of the paper are:(1) The paper takes a systematic research on the random statistical model, geometrical analysis model and neural network model, etc. The Gap statistic is firstly introduced to study the theory and algorithms of image segmentation.(2) A new conception of "function gap" is originally proposed in this paper. Based on the different feature and criteria of edge in image, several types of function gap are defined and the relationships among them are discussed. Furthermore, utilizing the theory of function gap, we creatively take an investigation on the Gap statistical properties of images. Finally, the gap statistical models for edge detection are proposed.(3) After presenting the new conception of "point gap", we study the Gap features of the edges in image and develop a formalism of generalized step edges and roof edges. A point Gap model of multi-scale edge detection is presented and the corresponding algorithm is advanced. Furthermore, we put our study forward on the theory and application of another Gap named "order rank sum Gap".(4) Using the long range and short range dependency among image pixels respectively, we propose the conception of weighted Gap and present a new multi-scale weighted neighborhood based edge detection model and corresponding algorithms. The difference between Gap operator and Sobel operator is also analyzed.(5) Several new conceptions including function feature, total Gap and full Gap are proposed and the Gap statistical model for image segmentation is established and the detail
引文
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