摘要
论文研究了计算机视觉中的基本问题:图像分割及目标边界提取。目标边界提取把图像中感兴趣的目标与背景区分开来，它是一类特殊的图像分割。实现图像分割和目标边界提取的重要方法之一是活动轮廓模型，该模型具有数值实现简单且可以提供闭合分割曲线的优点，目前是图像分割和目标边界提取领域中理论和应用方面的一个重要研究课题。在活动轮廓模型中，外部力在曲线演化过程中起主导作用。外部力向量场分为静态向量场和动态向量场。著名的静态向量场有梯度向量流，向量场卷积等，动态向量场有静磁场，流体向量流等，这些向量场在提取目标边界方面取得了极大的成功。然而，外部力向量场中仍存在一些关键的问题需要进一步研究。静态向量场不能提取深凹形边界问题以及在提取复杂几何边界时会遇到“平衡点”问题，动态向量场常需要用边缘检测算子得到边缘特征点来计算得到，对噪声较敏感。本文围绕复杂几何形状目标提取问题，在参数活动轮廓模型中的外部力向量场领域进行了研究，取得了以下研究成果：
首先，对有关向量场基本知识和基本理论进行了总结，在向量场理论框架下介绍了几种典型的向量场。基于传统的向量场，我们构造了一个新的向量场。构造的向量场由两部分组成。其中一部分是保守场起到扩大向量场捕获范围的作用，另一部分主要作用是驱使轮廓向凹形边界演化。基于两部分的不同作用，通过两个向量场的组合构造出了一个新的向量场。相比传统的向量场，该向量场在提取深凹形边界有了一定的改进。
其次，传统的轮廓演化方程是基于变分法和最速下降法最小化能量函数得到。梯度向量流和向量场卷积外部力并入到演化方程后，活动轮廓模型在提取复杂凹形边界时常出现过早收敛以及收敛速率较慢的问题。针对这些问题，通过对一些经典的向量场特征进行深入的分析并结合优化方法，提出了冲量梯度下降算法来优化能量泛函。利用冲量梯度下降算法，得到了活动轮廓模型的演化方程。和传统的演化方程相比，用冲量梯度下降算法得到的演化方程是在传统的演化方程中并入了自适应冲量项。该冲量项根据轮廓在向量场的变化能够自适应的变化，提出的自适应冲量方法中未引入新的参数。从向量场角度看，提出的方法相当于在传统的静态场中并入了一个动态外部力(冲量力)，冲量力基于静态场特征产生，因此提出的方法建立了静态场向量场和动态向量场之间的联系。
接着，文中在分析了向量场卷积中外部力之间的相关性基础上，提出了动态约束向量场卷积和偏向向量场卷积两种改进的向量场来分别解决深凹形边界和复杂几何边界提取这两个问题。针对深凹形边界提取，我们提出了动态约束向量场卷积。通过引入与演化轮廓曲线有关的特征函数，使得仅轮廓内部区域的边缘信息被用来产生外部力。这里，提出的向量场是多阶段向量场。此外，为了提取复杂几何边界，又提出了偏向向量场卷积。引入一个与演化轮廓曲线和窄带有关的特征函数，使得轮廓内部中的一些边缘信息被充分的来产生外部力。另外，为了更好的保护边缘，又引入了一个新的边缘映射，引入的边缘映射能够同时刻画边缘和角点特征。从向量场角度出发，通过引入一种特征函数，提出能逐渐去除向量场卷积中外部力之间相关性的两个向量场，这使得静态向量场和动态向量场有了更直观的联系。
最后，本文提出了一个基于多阶段向量场的活动轮廓模型，这一向量场不是基于原有向量场的改进，而是通过定义的映射来建立向量场。首先对引入的边缘映射二值化后，目标边界特征点有了明确的数值定义。在初始化轮廓后，通过轮廓的法方向，建立了轮廓点与边界特征点之间的映射。在轮廓点与对应边界点之间连线上的各点有相同的方向，均为该轮廓点的法方向，这些向量组成了一个向量场。轮廓在这一向量场演化到收敛状态，收敛状态下未收敛到目标边界的轮廓点继续建立新的映射和向量场，直到轮廓完全收敛到边界。由于提出向量场的多阶段性，向量场在每个阶段是静态向量场，且提出的基于映射产生的向量场是保守向量场。
实验表明，提出的冲量力场，动态约束向量场卷积，偏向向量场卷积和多阶段向量场均有效的克服了静态向量场中的“平衡点”问题，相对于传统方法，这些向量场方法均提高了凹形和复杂几何边界提取的能力。
The thesis has researched the basic problems in computer vision: image segmentationand object boundary extraction. Object boundary extraction is to distinguish the objectof interest from the image background, it is a special image segmentation. Active contourmodel (ACM) is one of important methods for image segmentation and extracting objectboundaries, it has many advantages, such as easy to implement and ofering closed curves,and it is an important research topic in thesis and application of image segmentation andobject boundary extraction. In active contour models, external force plays a leading rolein curve evolution. External vector felds are divided in static and dynamic vector felds.Famous static vector felds include gradient vector feld (GVF), vector feld convolution(VFC) and so on, dynamic vector felds include magnetostatic feld, fuid vector fow(FVF) and so on, these vector felds have got great success in object boundary extraction.However, there are some critical problems needed to be researched in vector felds. Staticvector felds could not extract the deep concavity, they could sufer from “equilibriumproblem” when extracting complex geometries. Dynamic vector feld always need to useedge detector to obtain the feature points and they are sensitive to noise. Around theproblems of object with complex geometry extraction, some research in vector feld ofparametric active contour model is worked and the main contributions of the thesis areas follows:
Firstly, the fundamental knowledge and theory about vector feld are summarized,and some typical vector felds are introduced under the framework of the theory of vectorfeld. Based on the traditional vector felds, we construct a new vector feld. The con-structed feld is composed by two parts. One part is a conservative feld and used to playthe role of enlarging the feld’s capture range, and another part is used to push contourevolve to concavity. Based on the diference efects of these two parts, a new feld isobtained by weighting these two parts. Compared with traditional felds, the constructedfeld improve the ability to extract concavity to some degree.
Secondly, the equation of contour evolution is always obtained based on calculus ofvariations and gradient descent method. After GVF and VFC are integrated with theequation of contour evolution, premature convergence and slow convergence problems ap-pear when extracting complex concavities. Addressing to these problems, integrating withthe optical methods and deeply analyzing the features of typical vector felds, then thegradient descent with momentum method to minimize the energy functional is proposed.Based on gradient descent with momentum method, the equation of contour evolution is obtained. Compared with traditional evolution equation, the evolution equation basedon gradient descent with momentum method is obtained by incorporating the adaptivemomentum term into traditional evolution equation. The momentum term adaptivelychanges as the contour deforms in vector felds, it does not introduce any other new pa-rameter. According to the view of vector felds, proposed method is obtained seems thata dynamically external force (momentum force) is integrated in traditionally static vectorfelds. Therefore, the relationship between static vector feld and dynamical vector feldis built based on proposed method.
Then, based on the correlative analysis with respect to the external forces of VFC,dynamically constrained vector feld convolution (DCVFC) and biased vector feld con-volution (BVFC) are proposed to address the problems of deep concavity and complexgeometries extraction. Addressing to the problem of deep concavity extraction, DCVFCwas proposed. By introducing an indication function with respect to evolving contour,the edge information inside the evolving contour is utilized. DCVFC is a multistage vec-tor feld. Furthermore, in order to extract complex geometries, BVFC is presented. Anindication function with respect to evolving contour and a narrow band is introduced, afew of edge information inside evolving contour is made use of generating external forces.Besides, another novel edge map is also introduced to protect the object boundary, thisintroduced edge map could describe both the edges and corners equally. By introduc-ing the indication functions, two vector felds which removed the correlation of externalforces in VFC is proposed, and the relationship between static and dynamical vector feldsbecomes more intuitive.
Finally, a multistage vector feld based active contour model is proposed. This vectorfeld is not the improvement of original vector felds, it is obtained by defning a map.Image binaryzation for the introduced edge map is frstly performed, the object boundarypoints clearly have numerical defnition. After setting the initial contour, the map is buildbetween the contour points and object boundary points based on the normal direction ofthe contour. The points located the segment between the contour point and correspondingobject boundary point have the same direction, the direction of vectors at these points arethe normal direction of contour point. These vectors constitute a vector feld. Contourevolves to convergence in this vector feld. The points which does not converge to theobject boundary continue to set a new map and vector feld, the map and vector feld arenot set until the contour points completely converge to object boundary. Because of themultiple stage of proposed vector feld, vector feld in every stage is static, and the feldobtained based on the defned map is conservative.
Experimental results show that proposed momentum force feld, DCVFC, BVFCand multistage vector feld efectively get rid of the “equilibrium problem” which alwaysexists in static vector feld, and all these methods improve the abilities in extracting deepconcavity and complex geometry compared with traditional methods.
引文
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