Distance Regularized Level Set Evolution For Image Segmentation Based On AOS Scheme

Among the most widely applied techniques is image processing, in which imagesegmentation is a crucial procedure, through which target object of interest is ex-tracted from the image, in order to further analyze and interpret the image. Thereare a variety of approaches to image segmentation, in which segmentation methodbased on partial diferential equation has developed and gained popularity in therecent two decades. Active contour models, typical segmentation methods basedon partial diferential equation, can be divided into two categories: edge-based andregion-based. Snakes, the earliest active contour models, verify the target boundaryvia the evolution of a parametric curve driven by partial diferential equations ofenergy minimization. Due to the parametric form of snakes, however, topologicalvariation cannot be naturally controlled. The introduction of level set method en-ables control of topological variation of active contour models. Its essential idea isto embed the evolution curve into a function of a higher dimension as its zero levelset, and then to acquire the evolution of the zero level set, or the evolution curve,through the evolution of the function. Both geometric active contour model andgeodesic active contour model are edge-based active contour models utilizing levelset method, so that they can automatically control the topological variation of thecontour, but require stricter initial position of the contour. Mumford-Shah modeland its simplified form, C-V Model, are region-based active contour models do notdepend on the selection of the contour.s initial position, but inaccuracy in boundarydetermination may occur owing to their lack of boundary information. In traditionallevel set methods, the periodical reinitialization is called for, because the curve canturn irregular during evolution. Chunming Li proposed an active contour model thatrequires no reinitialization, i.e. distance regularized level set evolution, based on theproperties of signed distance function. This model is complemented with a distanceregularization term, describing deviations of level set functions from signed distancefunctions, and obtaining the approximation of signed distance functions by minimiz-ing such deviations. Distance regularized level set evolution removes in essence thecomplex and expensive reinitialization, and thus optimizes computation time. AOS scheme is a deformation of the semi-implicit scheme targeting the nonlineardifusion filtering, which decomposes multi-dimensional problems into multiple one-dimensional problems, which are treated equally and solved with the same method.The linear system under the deformation of AOS scheme, the coefcient matrix ofwhich is strictly diagonally dominant tridiagonal matrix, is solvable by the Thomasalgorithm. The Thomas algorithm is low in computing complexity, thus simplifyingthe calculation, and due to the unconditional stability of AOS scheme, longer timesteps can be used to further expedite the evolution.The distance regularized level set evolution based on AOS scheme proposed bythis paper not only avoids reinitialization, but also simplifies the complex divergenceterms using AOS scheme, thus solving, through the Thomas algorithm, linear sys-tems with strictly diagonally dominant tridiagonal matrices as coefcient matrices,increasing time steps, and expediting the evolution. The first chapter of this paperintroduces the relevant contexts of image segmentation and image segmentation ofpartial diferential equation; the second chapter discusses the relevant informationof level set method; the third chapter describes the active contour models of imagesegmentation; the fourth chapter presents the introduction of AOS scheme; the fifthchapter talks over the distance regularized level set evolution based on AOS schemeproposed by this paper; and the last chapter summarizes the whole article.