Study On Active Contour Model And Gaussian Model In Image Processing

Image processing plays an increasingly important role in the life. A study has beenmade of the three facts, image smoothing, image segmentation and edge detection ofimage processing.Firstly, the C-V model is studied. It is the simple form of the Mumfor-Shah model.The model utilizes the global intensity information of image to evolve the activecontour, which will stop on the desired boundary. Since, the stopping term of C-Vmodel does not depend on the gradient of the image, it can properly segment the imagewith weak edge or blurred seriously by noise. The C-V model is not sensitive to theinitial value of the level set function and can detect the outer and inner edges of targetswith inner hole. It extends the speed to all level set functions, but the edge far awayfrom the active contour would be seriously suppressed by the Dirac function. The levelset function of C-V model is presented by discrete form. The geometric characteristicsanalytical solution of active contour is hard to be calculated. In order to obtain anaccurate and stable solution, the C-V model implies the upwind difference, the smalltime steps and periodical re-initialization of the level set function. This slows the speedof segmentation and reduces the flexibility of structure. The curvature term of partialdifference equation has ability to suppress the noise, but in the case of low SNR, the C-V model can not get the good results. In order to solve these problems, we propose analternative approach based on continuous level-set. The level-set function is modeled asa continuous parametric function using the line combination of two-dimensionLagrange basis. The difference equation is derived by minimizing the energyformulation. As a consequence, the minimization of the energy formulation is directlyobtained in term of the Lagrange coefficient. The fast segmentation of image with lowSNR value is implemented by the numerical solution of the coefficient differenceequation that is solved by simple finite-difference methods.Secondly, the anisotropic diffusion model, the kernel anisotropic diffusion modeland the anisotropic diffusion based on hierarchical implementation of multiphasepiecewise constant segmentation method are studied. The noise image with high SNRcan be effectively smoothed by the anisotropic diffusion model with appropriateparameters. For the low SNR images, the model does not work. The reason is that in thecase of low SNR, the diffusivity function can not effectively distinguish between edgeand noise. The kernel anisotropic diffusion model solves the problem, but it does notsolve the limit value of the diffusivity function. Although the anisotropic diffusion based on hierarchical implementation of multiphase piecewise constant segmentationmethod is able to avoid the drawback of diffusivity function, it can not effectivelysmooth the low SNR images. The reason is that the C-V model can not effectivelysegment the low SNR images. In order to effectively preserve low SNR image edgesand smooth the noise, a kernel method-based Selective anisotropic diffusion algorithmis proposed based on anisotropic diffusion model of multiphase hierarchy segmentationmethod. The image data is generally non-linearly separable. Firstly, the data term ofmultiphase hierarchy segmentation method is promoted from low-dimensional space tohigh-dimensional space by the kernel method. In the high-dimensional space the imageis segmented by the multiphase hierarchy segmentation method. Then, the diffusioncoefficient of P-M model is improved based on gradient information of the homogenousregion. Finally, the proposed P-M model is used to smooth noise in the homogenousregion. The proposed algorithm has capabilities of reducing noise and preserving edgeefficiently.Thirdly, the algorithm of edge detection based on Gaussian filter is studied. Anedge in an image corresponds to a discontinuity of intensity in the scene. Edges usuallyconvey the most relevant information of an image [1-2] and their detection is anessential goal in computer vision and image processing [3-4]. Although identifying andlocalizing edges have been researched for more than50years, they are still a verychallenging task in a variety of applications such as3-D reconstruction, shaperecognition, image compression, enhancement, and restoration [5]. Hence, the detectionof edges in an image is still an important problem until now. There have existed manydifferent types of approach for edge detection, but the Gaussian-based methods may bethe most commonly used. Since the Gaussian-based edge detection methods aregenerally simple and easily implemented, and have relatively good performance, theywill be mainly considered in this paper. The well-known isotropic Gaussian filter (IGF)also called Canny operator has been most extensively used in edge detection andprovides very good performance. It is easily observed that geometrically structuralinformation of a boundary of image includes three desirable characteristics, continuity,elongation, and anisotropy formed by the multiple edge pixels. A boundary of imagecan be well approximated by some edge-line segments (ELS) in which each must beconstructed by several (at least three) edge pixels. It should be seen that the IGF doesnot deal with anisotropic information of the image data near an edge, and not fullyexploit structure information of elongation of a boundary (CEB). In some cases, the IGF G (x, y)is not sufficient. The existing anisotropic Gaussian filter (AGF) has slowvariation along edge direction, and it can more efficiently perform edge detection andprevent the detected edges from blurring. The AGF exploits anisotropic information ofthe image data near an edge. However, it does not fully consider structure informationof boundary. In order to further improve performance of AGF and fully take advantageof structural information of a boundary, we propose a multi-pixel AGF (MAGF) todetect edges or ELS from low signal-to-noise ratio images. MAGF more efficientlytakes use of the continuity and CEB, leading to more effective edge detection. MAGFcan be separated into the multiplication between a1D parallel filter and a1D verticalone. The elaborately-designed parallel filter is expected to more fully exploit CEB. Thevertical filter perpendicular to the ELS is typically taken as a1D Gaussian derivativefilter. Moreover, unlike IGF and AGF, MAGF can simultaneously detect multiple edgepixels or ELS within a window. Threshold for MAGF to detect the ELS has beenobtained by comparing the response of MAGF with that of Canny operator. In order todecrease computational complexity of MAGF, Canny operator is first used forestimating an approximate direction of an ELS, and then MAGF can search moreaccurate ELS direction by a few of directional filter masks near such an approximatedirection. In the sense of noise reduction, good localization, and edge continuity, theMAGF can achieve better performance than the relative edge-detection methods.Finally, the segmentation algorithm of brain MR image is studied. Segmentation ofbrain tissues in MR images into gray matter (GM), white matter (WM), andcerebrospinal fluid (CSF) is pivotal for quantitative brain analyses [1]. It can serve as atool to help neurosurgeons, physicians, and researchers to investigate and diagnose thestructure and function of the brain. Since manual segmentation of brain MR imagesperformed by medical professionals is exceedingly time-consuming, highly subjective,irreproducible, and impractical for large scale group study, automated segmentationalgorithms with high accuracy have attracted extensive research attention, Statisticalsegmentation techniques have been widely used for brain MR images. In thesealgorithms, voxel values are usually characterized by the Gaussian mixture model(GMM)[16], which is a weighted sum of finite Gaussian components with eachcomponent modeling the distribution of voxels from one tissue type and each weightrepresenting the prior probability of the corresponding tissue type. The parameters ofGMM are traditionally estimated by using the expectation-maximization (EM)algorithm. However, the EM-based segmentation algorithm is more sensitive to the initialization. To avoid the initialization problem, we propose a new global optimizationalgorithm for the GMM parameter estimation problem. Firstly, a new three phasesimage segmentation method is proposed based on the C-V model and the features of thebrain MR image. Then, the initialization of EM is got from the segmentation results ofthe new segmentation method. Finally, the Bayes classifier is applied to obtain theclassified label of each pixel. The tissue classification results obtained by our methodare shown to be consistently more accurate than that with the traditional parameterestimation methods. In addition, a method for low SNR image is proposed based on theresults of the algorithm above-mentioned.