基于水平集方法的主动轮廓模型理论研究及其应用
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摘要
基于PDE方程的主动轮廓模型,在求解过程中结合了水平集工具、曲线演化理论,适合处理形式多样、结构复杂的图像边界,与传统图像分割方法相比呈现出独特的优越性和广泛的适应性。但是,在这种基于PDE方程的主动轮廓模型中,有的能量泛函存在数学上的非凸性,有的存在局部极小值性。本文对当前主动轮廓模型中存在的问题做了进一步的研究与探讨。
作者在广泛学习、深入研究基于主动轮廓模型的图像分割方法基础上,对近十多年来国内外学者普遍研究的主动轮廓模型技术进行了系统的分类、综述。然后详细探讨了三类基于非参数化方法描述曲线的主动轮廓模型——结合区域信息的短线程主动轮廓模型、全局最小值主动轮廓模型和局部区域信息驱动的主动轮廓模型。在此基础上,提出和实现了几种分割模型的改进方法,并在实际应用过程中取得了满意的效果。本文研究工作的主要创新性体现在以下几个方面:
一、基于短线程主动轮廓模型GAC改进的GAC-CV模型。传统的GAC模型只利用了图像的梯度信息构建驱动曲线演化的能量,在对边界不清晰、边缘相邻的实物图像分割时,不能收敛到期望的边界处提取出所有的目标轮廓,对噪声敏感。针对GAC分割模型的这一不足,提出了融合图像区域信息、方向信息的GAC-CV模型,实现了快速、稳定的目标分割。
二、全局最小值主动轮廓模型的提出与实现。针对GAC模型能量泛函的非凸性,把非参数化的ROS模型与GAC-CV模型结合,提出了一个约束条件下的全局最小值主动轮廓模型GMGAC,并证明了模型全局最小值的存在性。并基于对偶形式的总变分TV-norm算法实现能量泛函的快速求解。对合成图像、含噪声医学图像的分割实验结果表明,GMGAC模型对噪声具有很强的鲁棒性,能够准确提取出图像中的几何结构信息,分割速度快。
三、基于CV模型的扩展性研究。针对CV模型是一个前景、背景分割的2相模型,作者对当前的多相分割模型做了系统研究,并提出了一个基于单水平集曲线实现多相分割模型。然后,分析了CV模型能量函数的局部局限性,对CV模型中的数据拟合项做了改进,引入了竞争移位函数,提出了一个快速的双模态图像分割方法,并证明了算法全局最小值的存在性。在该双模态图像分割算法中,初始化曲线可以设置为任意的二值函数,迭代演化过程中不需要对曲线执行重新初始化操作,实验结果表明本文算法效率比CV模型得到了极大提高。
四、局部区域信息驱动的主动轮廓模型。大多数基于区域信息驱动的主动轮廓模型,对图像的灰度信息都存在一致性分布,或整体服从某种统计分布的前提性假设,这种假设不能很好解决灰度分布不一致性对象的分割问题。作者基于局部描述子的概念,推导了一个演化曲线附近局部图像信息驱动的主动轮廓模型。分别从图像坐标空间、图像像素空间定义局部模板,并推导了该模型的曲线演化方程。对灰度不一致、边缘模糊的图像分割结果表明,本文提出的基于局部能量驱动主动轮廓模型能够获得很好的分割效果。
Compared with the traditional image segmentation method, the active contour models based on the PDE equation which combine the level set method and the curve evolution theory, have shown unique advantage and comprehensive applicability in the segmentation of images with various styles and complicated structures. But there are some questions in the active contour model, such as the un-convex and local minimum of the energy functional. How to perfect its theory and settle the questions in the image segmentation is the main task of this dissertation.
Previous research works in recent years on the active contour model for image segmentation and its numerical difference methods are studied extensively and classified. Then three kind of active contour model in which the curve is described by the way of non-parameter: Geodesic active contour based on the region information, active contour model with a global minimum and active contour model driven by the local energy, are studied in detail and its corresponding improved method are provied.
The main research work and contribution of this dissertation can be summarized as follows:
1). The traditional GAC whose curve is driven by the information of image gradient, is sensitive to noise and can not converge to the expected object boundary when the edges of image are blur. To realize the drawback of GAC, a novel improved model of GAC ,named as GAC-CV model which is integrated with image region information and direction information is proposed. The GAC-CV model has faster and more stable segmentation result compared with the traditional GAC.
2). To overcome the non-convex of the energy functional in the GAC, a new GMGAC model which combines the classical non-parameter ROS model with the GAC-CV model, is established and the existence of a global minimum of the new model is provided. The fast algorithm based on the dual formulation of TV-norm is deduced. The experiments on the synthetic images and noised medical images demonstrate that the GMGAC model is robust to noise and accurately segment the whole geometry structures in the image and the speed is very high.
3). The extended studies on the CV model. The methods of multi-phase image segmentation are studied in detail and a novel segmentation based on the classic CV model is proposed. To handle the local limitation of the energy functional of CV, a fast method for bi-model segmentation is offered, in which the data fitting terms in the CV model are adjusted and a shifted competition function is introduced. In this novel model the curve can be initialized to a arbitrarily function with two reverse values and the re-initialization is not needed. The experiment results show that it is superior to the traditional CV.
4). Most active contour models based region information depend on the supposing or the condition that the image intensity conform to homogeneity or a statistical distributing, which result in a inaccurate result. Based on the local descriptor which is studied respectively from the image Cartesian coordinate space and the image pixel intensity space, a novel region-based active contour model is propose whose curve is driven by the local image information around the curve. The experiment for real images and medical images results demonstrate that the active contour model driven by the local image information can cope with the image segmentation with intensity inhomogeneity and show desirable performances.
作者在广泛学习、深入研究基于主动轮廓模型的图像分割方法基础上,对近十多年来国内外学者普遍研究的主动轮廓模型技术进行了系统的分类、综述。然后详细探讨了三类基于非参数化方法描述曲线的主动轮廓模型——结合区域信息的短线程主动轮廓模型、全局最小值主动轮廓模型和局部区域信息驱动的主动轮廓模型。在此基础上,提出和实现了几种分割模型的改进方法,并在实际应用过程中取得了满意的效果。本文研究工作的主要创新性体现在以下几个方面:
一、基于短线程主动轮廓模型GAC改进的GAC-CV模型。传统的GAC模型只利用了图像的梯度信息构建驱动曲线演化的能量,在对边界不清晰、边缘相邻的实物图像分割时,不能收敛到期望的边界处提取出所有的目标轮廓,对噪声敏感。针对GAC分割模型的这一不足,提出了融合图像区域信息、方向信息的GAC-CV模型,实现了快速、稳定的目标分割。
二、全局最小值主动轮廓模型的提出与实现。针对GAC模型能量泛函的非凸性,把非参数化的ROS模型与GAC-CV模型结合,提出了一个约束条件下的全局最小值主动轮廓模型GMGAC,并证明了模型全局最小值的存在性。并基于对偶形式的总变分TV-norm算法实现能量泛函的快速求解。对合成图像、含噪声医学图像的分割实验结果表明,GMGAC模型对噪声具有很强的鲁棒性,能够准确提取出图像中的几何结构信息,分割速度快。
三、基于CV模型的扩展性研究。针对CV模型是一个前景、背景分割的2相模型,作者对当前的多相分割模型做了系统研究,并提出了一个基于单水平集曲线实现多相分割模型。然后,分析了CV模型能量函数的局部局限性,对CV模型中的数据拟合项做了改进,引入了竞争移位函数,提出了一个快速的双模态图像分割方法,并证明了算法全局最小值的存在性。在该双模态图像分割算法中,初始化曲线可以设置为任意的二值函数,迭代演化过程中不需要对曲线执行重新初始化操作,实验结果表明本文算法效率比CV模型得到了极大提高。
四、局部区域信息驱动的主动轮廓模型。大多数基于区域信息驱动的主动轮廓模型,对图像的灰度信息都存在一致性分布,或整体服从某种统计分布的前提性假设,这种假设不能很好解决灰度分布不一致性对象的分割问题。作者基于局部描述子的概念,推导了一个演化曲线附近局部图像信息驱动的主动轮廓模型。分别从图像坐标空间、图像像素空间定义局部模板,并推导了该模型的曲线演化方程。对灰度不一致、边缘模糊的图像分割结果表明,本文提出的基于局部能量驱动主动轮廓模型能够获得很好的分割效果。
Compared with the traditional image segmentation method, the active contour models based on the PDE equation which combine the level set method and the curve evolution theory, have shown unique advantage and comprehensive applicability in the segmentation of images with various styles and complicated structures. But there are some questions in the active contour model, such as the un-convex and local minimum of the energy functional. How to perfect its theory and settle the questions in the image segmentation is the main task of this dissertation.
Previous research works in recent years on the active contour model for image segmentation and its numerical difference methods are studied extensively and classified. Then three kind of active contour model in which the curve is described by the way of non-parameter: Geodesic active contour based on the region information, active contour model with a global minimum and active contour model driven by the local energy, are studied in detail and its corresponding improved method are provied.
The main research work and contribution of this dissertation can be summarized as follows:
1). The traditional GAC whose curve is driven by the information of image gradient, is sensitive to noise and can not converge to the expected object boundary when the edges of image are blur. To realize the drawback of GAC, a novel improved model of GAC ,named as GAC-CV model which is integrated with image region information and direction information is proposed. The GAC-CV model has faster and more stable segmentation result compared with the traditional GAC.
2). To overcome the non-convex of the energy functional in the GAC, a new GMGAC model which combines the classical non-parameter ROS model with the GAC-CV model, is established and the existence of a global minimum of the new model is provided. The fast algorithm based on the dual formulation of TV-norm is deduced. The experiments on the synthetic images and noised medical images demonstrate that the GMGAC model is robust to noise and accurately segment the whole geometry structures in the image and the speed is very high.
3). The extended studies on the CV model. The methods of multi-phase image segmentation are studied in detail and a novel segmentation based on the classic CV model is proposed. To handle the local limitation of the energy functional of CV, a fast method for bi-model segmentation is offered, in which the data fitting terms in the CV model are adjusted and a shifted competition function is introduced. In this novel model the curve can be initialized to a arbitrarily function with two reverse values and the re-initialization is not needed. The experiment results show that it is superior to the traditional CV.
4). Most active contour models based region information depend on the supposing or the condition that the image intensity conform to homogeneity or a statistical distributing, which result in a inaccurate result. Based on the local descriptor which is studied respectively from the image Cartesian coordinate space and the image pixel intensity space, a novel region-based active contour model is propose whose curve is driven by the local image information around the curve. The experiment for real images and medical images results demonstrate that the active contour model driven by the local image information can cope with the image segmentation with intensity inhomogeneity and show desirable performances.
引文
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