Research On Image Segmentation Based On Variational Methods And Fuzzy Clustering Algorithms

Image segmentation is a challenge and difficult task in image processing, and thefoundation of image analysis and identifying. This thesis mainly focus on gray imagesegmentation problems, i.e., noise restraining and characteristic keeping, segmentationfor images with intensity inhomogeneity, texture segmentation. The main work and inno-vation are embodied as follows.1. Two image segmentation algorithms were proposed based on the homogeneousBesovspace,inspiredbygeodesicactivecontoursmethodswithglobalminimizers. Mean-while the existence of the solution was proved. These new algorithms can be resolved ef-ficiently through wavelet soft threshold thanks to the connections between wavelet trans-form and Besov space semi-norm. And the split Bregman method was also adopted in oneof the two algorithms. Due to the multiresolution character of wavelet, they are proper tosegment images containing more fine information.2. This thesis researched the segmentation for images corrupted by intensity inho-mogeneity via variational methods. Firstly, a new constrained convex variational modelbased on PS MS model and fuzzy clustering was proposed. Meanwhile, we designedtwo fast algorithms by combining the split Bregman method, Gauss-Seidel algorithm andGaussian convolution. Secondly, based on the general assumption of the intensity inho-mogeneity, a variational multiphase segmentation model for simultaneously performingbias correction and segmentation was proposed. The energy functional of the proposedmethod was formulated in terms of a fuzzy clustering based data fidelity term and someregularization terms. To suppress the noises, a total variation regularization term wasadapted. Meanwhile, the first and second gradient smooth terms are used to ensure thebias field to be both slowing varying and smooth. Experimental results for synthetic andreal images showed desirable performance of the proposed method.3. The well-known MS model and the CV model have gained great successes in im-age segmentation. However, the successes of those models are mainly founded on the as-sumption that the images are corrupted by some additive Gaussian noises. Inspired by thevariational denoising methods for non-Gaussian images, three variational segmentationmodels were proposed to address the segmentation tasks under different noisy conditions. Experimental results for synthetic and real images showed that the proposed algorithmsare very efficient and effective.4. Traditional fuzzy c-means (FCM) clustering algorithm is sensitive to noise. Amodified FCM algorithm was presented in this thesis by utilizing local contextual infor-mation and structure information. A similarity measure model was established based onimage patch difference. Based on the similarity measure, a new distance measure namedneighborhood weighted(NW) distance was defined. The NW distance was then adoptedto replace the Euclidean distance in the objective function of FCM. Experiments resultsshowed that this method is very robust to noise and other image artifacts. This thesisalso proposed a fuzzy clustering-based segmentation method for intensity inhomogeneityimages. A weight function defined on a local window was introduced into the objectivefunction of FCM. The local weight makes the prototype for every pixel depend only onthe information in local regions, which is more reasonable for the considered problem.5. A two-phase texture segmentation method based on active contour was proposed.Firstly, the texture feature extraction approach based on semi-local image informationwas analyzed, which revealed that it could not represent texture's orientation informa-tion. In order to segment texture images containing periodic and orientational character, afour-channel texture feature was obtained by combing semi-local image information withnonlinear structure tensor. Then Gaussian mixture model was adopted to describe theprobability density function of the features. Experimental results for both nature and syn-thetic texture images showed that our method cope with complex segmentation tasks verywell.