Image Segmentation Technology Based On Partiail Differential Equation

Image segmentation based on partial differential equations combines physics, mathematics, information, computing science and other knowledge, which shows a strong vitality. It receives extehsive attention of scholars, and becomes one of the most popular image segmentation methods. The basic idea is:according to image features, partial differential equation with initialization and boundary conditions is directly designed or got by minimizing the energy functional to meet customer needs. The level set function evolves under the control of PDE, and stays finally at the boundary of the target.The thesis focuses on image segmentation based on partial differential method, The main work is described as follows:1. Proposes a distance regularization model based on signed pressure force function to tackle the problem of DRLSE model which does not have direction self-adaptive and cannot effectively segment intensity inhomogeneities images.DRLSE model overcomes the problem of the traditional active contour that the level set function must be initialized periodically. But DRLSE model has some shortcomings:(1)the evolution of the curve is in one direction only; (2) the model is sensitive to initial contour; (3) the model easily falls into local minimum. To those issues, the paper constructs a signed pressure force(SPF) function combining local and global information, then proves the signs of SPF function is dissimilar inside and outside the regions of interest. The improved model has direction self- adaptive and can effectively segment images with intensity inhomogeneities.2. Studying on the periodical initialization problem of level set function, we propose a more general variational level set model.In the traditional level set evolution(LSE), non-regularization of LSE can cause numerical error and undermine the stability of LSE. The solution is re-initialization, but this process requires solving a nonlinear PDE. This paper solves the problem of re-initialization by introducing a penalty energy term, which penal the deviation between LSE and signed distance function, and can be applied to other models.3. Proposes an active contour model based on Fuzzy C-means.SPF model is simple in numerical implement, excellent in anti-noise performance, but also has the following disadvantages:(1) edge leakage is easily occur; (2) the initial method of level set function(LSF) is less flexible, for example, LSF is initialized to a constant function or a point; (3) the initial position of LSF is not flexible, and different initial position may gets different segmentation result. To solve those problem, this paper proposes an active contour model based on fuzzy C-mean (FSPF), The initial method and position of the level set function of FSPF are more flexible, The edge leakage problem of SPF model is solved and slightly intensity inhomogeneities images can be segmented.4. Proposes an active contour model based on fuzzy energy.FSPF model has better performance on segmenting images with intensity inhomogeneities than SPF model, but fails to segment strong intensity inhomogeneities images. In this paper, the concept of Fuzzy c-means is introduced into the active contour model, and the integration of local and global fuzzy energy can improve the ability of the model to segment intensity inhomogeneities images and the robustness of contour initialization.