The Basic Theory And Development Of Vector Fields In Active Contour Models

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.