基于偏微分方程的图像分割与配准研究
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摘要
图像分割与图像配准是图像工程中两个关键的基础性任务,是机器视觉、模式识别等领域的重要组成部分。图像的分割和配准问题自图像产生便已存在,诸多研究者提出了大量处理方法,但图像间的差异性和用户需求的特殊性,使得图像分割和图像配准一直是图像工程中的研究热点。偏微分方程理论因其具有完备的数学理论基础和良好的可扩展性等优点成为当前最为流行的图像处理基本理论之一,已深入到图像处理的各个方面且取得了良好的效果,基于活动轮廓模型的图像分割方法与基于光流场等物理模型的图像配准方法是偏微分方程理论在图像处理中的典型应用。本文基于偏微分方程理论,从亮度不一致图像分割、非刚性图像配准、配准-分割耦合模型三个方面进行了理论和方法的研究。本文的主要工作和研究成果如下：
(1)LBF模型是一种有效的亮度不一致图像分割模型,但该模型存在易于陷入局部极值的问题,本文针对该问题提出给模型的拟合函数加入对比度约束的改进方法。LBF模型利用图像的局部信息定义拟合函数,拟合函数的局部化属性能够克服亮度不一致问题的同时,回导致模型易于陷入局部极值。本文基于目标边界两侧的图像亮度存在对比度的假设,提出对拟合函数加入对比度约束以避免能量陷入局部极值的改进方法,模型中还加入了气球作用力以扩大外力的作用范围。本文提出的对比度约束LBF模型能够有效克服原始LBF模型易于陷入局部极值的问题,且具有更强的初始化鲁棒性。
(2)针对全局化实现方法会严重影响LBF模型的实现效率和分割性能的问题,本文提出基于窄带活跃点更新的LBF模型。LBF模型在实现过程中需要进行大量的卷积运算,因而全局化的实现方法十分耗时；另外,LBF模型全局化的实现方法与模型局部化的定义形式不一致,导致能量易于陷入局部极值、对初始化敏感等问题。为此,本文提出采用窄带方法实现LBF模型,并在窄带基础上,进一步将更新点的范围缩小到窄带上的活跃点。本文提出的基于窄带活跃点更新的LBF模型能够显著提高模型的计算效率,彻底解决模型易于陷入局部极值的问题,且能实现感兴趣区域的分割；另外,该模型可以直接推广到向量LBF模型,实现亮度不一致向量图像的有效分割。
(3)针对基于光流场模型的图像配准方法会造成图像模糊的问题,本文提出具有图像特征保持能力的改进光流场模型。基于光流场模型的图像配准方法能够对存在非刚性形变的图像实现配准,但由于微分光流场模型采用简单的光滑性约束来解决孔径问题,而光滑性约束不具有保持图像特征的能力,因而会造成图像严重模糊和细节丢失的问题。本文将具有图像结构自适应性的扩散滤波方法引入图像配准,定义具有特征保持和一致性增强能力的各向异性扩散函数作为模型的正则项。基于改进光流场模型的图像配准方法能够有效保持图像特征,实现对大脑等复杂图像的有效配准。
(4)针对彩色图像配准中经常存在的大色差和大位移问题,本文在抽象匹配流框架下定义了彩色图像的配准模型。模型由互相关相似度函数和基于彩色结构张量的各向异性扩散正则项组成。新模型能够有效综合图像各通道的信息,且具有良好的图像特征保持能力,因而能够有效避免各通道的色彩混叠,实现对大色差和大位移图像的有效配准。
(5)针对当前耦合模型中普遍存在的参数化的配准项与非参数化的分割项定义形式不一致、模型定义不直观等问题,本文提出了一种耦合配准与分割的水平集演化模型。新定义的模型由基于抽象匹配流的配准项、基于活动轮廓模型的分割项和通过水平集函数直接定义的耦合项构成,模型实现了配准项与分割项定义形式和实现方法的统一,整个模型直接定义在水平集函数上,定义直观,实现简单。
Image segmentation and image registration are two fundamental tasks in image processing and analysis. The two problems have been existed since the birth of image. Many researchers have proposed a large number of methods to implement image segmentation and registration, however, the difference between images and applications make the research of the two problems be hot all the time. Partial differential equation is one of the most popular theories for image processing. Image segmentation methods based on active contour model, and non-rigid image registration methods based on physical models are the typical applications of partial differential equation in image project. This paper studies several special problems of image segmentation and image registration based on the theory of partial differential equation. The primary work and remarks of this paper are as follows:
(1) This paper presents a more robust and efficient level set method than the original LBF model for image segmentation under a constrained energy minimization framework. LBF model is able to address intensity inhomogeneities, but it often suffers from the problem of being stuck in local minima. LBF model formulates image segmentation as a problem of seeking an optimal contour and two fitting functions that best approximate local intensities on the two sides of the contour. The local property enables the model to deal with intensity inhomogenities, however, it makes the model tend to stick in local minima. We introduce a contrast constraint on the fitting functions to effectively prevent the contour from being stuck in spurious local minima, which thereby makes our model more robust to the initialization of contour. Comparisons with the LBF model and the piecewise smooth (PS) model demonstrate the superior performance of our model in terms of robustness, accuracy, and efficiency.
(2) We propose a novel and efficient narrow band level set evolution algorithm based on the LBF model. The full domain implementation of the LBF model is computationally expensive and makes the model often suffer from the problem of being stuck in local minima. Thus, we propose a novel narrow band level set evolution algorithm to implement the LBF model. Com-putational efficiency is further improved by avoiding unnecessary computation for updating the level set function at those points where the level set function has converged after a number of iterations. Therefore, the proposed algorithm only updates the level set function at those points where the level set function still actively evolve. These points, called active points, typically consist of only a small portion of the narrow band. Computation time is therefore dramatically reduced by confining the computation to the active points. The narrow band implementation offers more localized computation of the fitting functions in the LBF model. Compared with the original LBF algorithm, the enhanced localization property of the narrow band algorithm leads to the following desirable features:1) more accurate segmentation of images with inten-sity inhomogeneities; 2) more stable performance; 3) allows for the segmentation of regions of interest only. Our algorithm has been validated on synthetic and real images with desirable results.
(3) An improved optical flow model within the differential framework is employed in non-rigid image registration. Aiming at eliminating the severe image blurring caused by the Horn model, the anisotropic flow-driven diffusion is used as the regularization term to keep the image feature during the evolution, and the proposed diffusion tensor possesses the capability of edge preserving and coherence enhancing. The data term employs the nonquadratic penalization function to improve the robustness to image noise. The improved model is validated on complex brain images.
(4) A color image registration model within the framework of abstract matching flow is proposed to deal with the problem of serious color difference and large displacement between images to be registered. The model is composed of a data term and a regularization term. The data term employs the cross correlation as the similarity measurement to deal with the serious color difference between images. We bring the theory of anisotropic diffusion to the defini-tion of the regularization term. The regularization term is defined as a flow-driven anisotropic diffusion function based on the vector-valued structure tensor. New defined diffusion function integrates the intensity and structure information of multi-channels, and possesses the property of preserving image features during image evolution.
(5) A novel variational model for integrating registration and segmentation via level set evolution is proposed. A non-parametric registration method based on the abstract matching flow model is used as the registration term to go along with the non-parametric segmentation term. An edge-based active contour model is used to segment the region of interested, and the model is improved by adding region statistic information to deal with the problem of sensitivity to the initialization. The integrated model is defined by the level set function and can be im-plemented straightforward. Comparisons with classic method demonstrate the advantage of the proposed method in terms of accuracy.
(1)LBF模型是一种有效的亮度不一致图像分割模型,但该模型存在易于陷入局部极值的问题,本文针对该问题提出给模型的拟合函数加入对比度约束的改进方法。LBF模型利用图像的局部信息定义拟合函数,拟合函数的局部化属性能够克服亮度不一致问题的同时,回导致模型易于陷入局部极值。本文基于目标边界两侧的图像亮度存在对比度的假设,提出对拟合函数加入对比度约束以避免能量陷入局部极值的改进方法,模型中还加入了气球作用力以扩大外力的作用范围。本文提出的对比度约束LBF模型能够有效克服原始LBF模型易于陷入局部极值的问题,且具有更强的初始化鲁棒性。
(2)针对全局化实现方法会严重影响LBF模型的实现效率和分割性能的问题,本文提出基于窄带活跃点更新的LBF模型。LBF模型在实现过程中需要进行大量的卷积运算,因而全局化的实现方法十分耗时；另外,LBF模型全局化的实现方法与模型局部化的定义形式不一致,导致能量易于陷入局部极值、对初始化敏感等问题。为此,本文提出采用窄带方法实现LBF模型,并在窄带基础上,进一步将更新点的范围缩小到窄带上的活跃点。本文提出的基于窄带活跃点更新的LBF模型能够显著提高模型的计算效率,彻底解决模型易于陷入局部极值的问题,且能实现感兴趣区域的分割；另外,该模型可以直接推广到向量LBF模型,实现亮度不一致向量图像的有效分割。
(3)针对基于光流场模型的图像配准方法会造成图像模糊的问题,本文提出具有图像特征保持能力的改进光流场模型。基于光流场模型的图像配准方法能够对存在非刚性形变的图像实现配准,但由于微分光流场模型采用简单的光滑性约束来解决孔径问题,而光滑性约束不具有保持图像特征的能力,因而会造成图像严重模糊和细节丢失的问题。本文将具有图像结构自适应性的扩散滤波方法引入图像配准,定义具有特征保持和一致性增强能力的各向异性扩散函数作为模型的正则项。基于改进光流场模型的图像配准方法能够有效保持图像特征,实现对大脑等复杂图像的有效配准。
(4)针对彩色图像配准中经常存在的大色差和大位移问题,本文在抽象匹配流框架下定义了彩色图像的配准模型。模型由互相关相似度函数和基于彩色结构张量的各向异性扩散正则项组成。新模型能够有效综合图像各通道的信息,且具有良好的图像特征保持能力,因而能够有效避免各通道的色彩混叠,实现对大色差和大位移图像的有效配准。
(5)针对当前耦合模型中普遍存在的参数化的配准项与非参数化的分割项定义形式不一致、模型定义不直观等问题,本文提出了一种耦合配准与分割的水平集演化模型。新定义的模型由基于抽象匹配流的配准项、基于活动轮廓模型的分割项和通过水平集函数直接定义的耦合项构成,模型实现了配准项与分割项定义形式和实现方法的统一,整个模型直接定义在水平集函数上,定义直观,实现简单。
Image segmentation and image registration are two fundamental tasks in image processing and analysis. The two problems have been existed since the birth of image. Many researchers have proposed a large number of methods to implement image segmentation and registration, however, the difference between images and applications make the research of the two problems be hot all the time. Partial differential equation is one of the most popular theories for image processing. Image segmentation methods based on active contour model, and non-rigid image registration methods based on physical models are the typical applications of partial differential equation in image project. This paper studies several special problems of image segmentation and image registration based on the theory of partial differential equation. The primary work and remarks of this paper are as follows:
(1) This paper presents a more robust and efficient level set method than the original LBF model for image segmentation under a constrained energy minimization framework. LBF model is able to address intensity inhomogeneities, but it often suffers from the problem of being stuck in local minima. LBF model formulates image segmentation as a problem of seeking an optimal contour and two fitting functions that best approximate local intensities on the two sides of the contour. The local property enables the model to deal with intensity inhomogenities, however, it makes the model tend to stick in local minima. We introduce a contrast constraint on the fitting functions to effectively prevent the contour from being stuck in spurious local minima, which thereby makes our model more robust to the initialization of contour. Comparisons with the LBF model and the piecewise smooth (PS) model demonstrate the superior performance of our model in terms of robustness, accuracy, and efficiency.
(2) We propose a novel and efficient narrow band level set evolution algorithm based on the LBF model. The full domain implementation of the LBF model is computationally expensive and makes the model often suffer from the problem of being stuck in local minima. Thus, we propose a novel narrow band level set evolution algorithm to implement the LBF model. Com-putational efficiency is further improved by avoiding unnecessary computation for updating the level set function at those points where the level set function has converged after a number of iterations. Therefore, the proposed algorithm only updates the level set function at those points where the level set function still actively evolve. These points, called active points, typically consist of only a small portion of the narrow band. Computation time is therefore dramatically reduced by confining the computation to the active points. The narrow band implementation offers more localized computation of the fitting functions in the LBF model. Compared with the original LBF algorithm, the enhanced localization property of the narrow band algorithm leads to the following desirable features:1) more accurate segmentation of images with inten-sity inhomogeneities; 2) more stable performance; 3) allows for the segmentation of regions of interest only. Our algorithm has been validated on synthetic and real images with desirable results.
(3) An improved optical flow model within the differential framework is employed in non-rigid image registration. Aiming at eliminating the severe image blurring caused by the Horn model, the anisotropic flow-driven diffusion is used as the regularization term to keep the image feature during the evolution, and the proposed diffusion tensor possesses the capability of edge preserving and coherence enhancing. The data term employs the nonquadratic penalization function to improve the robustness to image noise. The improved model is validated on complex brain images.
(4) A color image registration model within the framework of abstract matching flow is proposed to deal with the problem of serious color difference and large displacement between images to be registered. The model is composed of a data term and a regularization term. The data term employs the cross correlation as the similarity measurement to deal with the serious color difference between images. We bring the theory of anisotropic diffusion to the defini-tion of the regularization term. The regularization term is defined as a flow-driven anisotropic diffusion function based on the vector-valued structure tensor. New defined diffusion function integrates the intensity and structure information of multi-channels, and possesses the property of preserving image features during image evolution.
(5) A novel variational model for integrating registration and segmentation via level set evolution is proposed. A non-parametric registration method based on the abstract matching flow model is used as the registration term to go along with the non-parametric segmentation term. An edge-based active contour model is used to segment the region of interested, and the model is improved by adding region statistic information to deal with the problem of sensitivity to the initialization. The integrated model is defined by the level set function and can be im-plemented straightforward. Comparisons with classic method demonstrate the advantage of the proposed method in terms of accuracy.
引文
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