A Method Of Image Segmentation Based On Sparse Theory

Image segmentation is the process of dividing the image into different non-overlapping sub-regions and each has a certain significance. Image segmentation helps one get the interested or important part, through the analysis of the area to obtain the overall comprehension or understanding of the target. Thus it is an important part in image analysis, and is the basis in study of computer vision and pattern recognition.With the development and the maturity of the subspace theory, subspace clustering methods are further applied into image segmentation. The basic idea is to divide the data into their respective subspaces, and the subspaces are independent with each other.We get the clustering aims by accurate partitioning of the data. For an image, we divide it into different regions, and extract features from each region, partitioning the regions with similar features into the same subspace, and obtain the clustering results. Among all the methods, there are two more effective methods, one is the low rank subspace clustering, it mainly considers the global property of the data instead of the internal relationship among the local regions, while another one is the sparse subspace clustering can take into account the relation among the local regions, however, since the data of the dictionary of different parts are almost the same, so the sparse clustering can be thought of as a implicit global method.This thesis presents two models based on the theory of sparse and subspace clustering.First, a weighted spare subspace clustering segmentation model is given, weighting by gaussian similarity between data. The weight compels the data be represented by elements in its own subspace, while the contribution of data from other subspaces as little as possible, as a result, the sparse representation coefficients matrix is more and more sparse between the classes, which can benefit the final clustering and segmentation. Second, a subspace clustering segmentation model based the joint representation of nonconvex low rank and nonconvex sparse is proposed. The nonconvex low-rank representation can make the model nicely approximate the discrete rank, the nonconvex sparse representation can make the corresponding vectors have as little 0-norm as possible, through joint the two representations, we can make the subspace representation coefficients simultaneously possess the properties of inter-class sparse and inter-class dependence, which can benefit the subspace representation and the image segmentation. Because of the nonconvex, the model can not solved by using the general optimization algorithms, so we propose a simple threshold shrinkage algorithm. To demonstrate the superiority of our models, we conduct a large number of simulation experiments to the artificial synthetic data and the real images as well. The results show that the two new models can obtain more satisfactory clustering and segmentation effects. Moreover, the non-convex model has superior results in dealing with images with more disturbance and high similarity in different regions, perform much better than the existing methods.