Improvement Of PDE Segmentation Models By Changing Dynamically The Local Window Sizes And The Implementation By Using Bregman Method

Image segmentation is an important task in image processing and computer vision, its purpose is to separate the interesting parts (foreground) of image from the rest of the image (background) for the high-level image analysis. The traditional image segmentation methods are sensitive to noise, and the results of segmentation may have discontinuous edges. The image segmentation methods based on partial differential equation models are the state-of-the-art methods due to the high precision of edge detection and the continuity of boundaries.This article focuses on the classical PDE image segmentation models:Chan-Vese (CV) model, Geodesic Active Contours (GAC) model, Region-Scalable Fitting (RSF) model, and their corresponding global convex segmentation models.The Split Bregman algorithm of the convex optimization is also introduced in details.In view of the idea of a non-convex segmentation model translated to a global convex segmentation model, this paper presents CSLIF model.This model is based on local image fitting (LIF) model which applied to inhomogeneous images.A globally convex version of the LIF model is proposed.To detect the object boundaries, an edge detection function is incorporated in the proposed model. The split Bregman method is used to solve the model in a more efficient way. Experiments show that this model is more efficient than the RSF model and the LIF model while with similar segmentation results.However, the CSLIF model inherited LIF model’s nature of being sensitive to initial contours, different initial contour may yield different segmentation results. To solve this problem, we return to the most primitive model which used to segment the inhomogenous images-RSF model, and find the reason of the RSF model’s sensitivity to the initial contour. Then, this paper presents the second improved model-the DRSF model.In the DRSF model, the window size of the Gaussian kernel function is changing according to the intensity variance information. In the regions with intensity homogeneity, a larger window size may be chosen to get a local fitting energy; while in the regions with intensity inhomogeneity, a smaller window may be chosen. The window changing dynamically is based on the edge stopping function. Experiments by using different sizes and different locations of initial contours for three RSF-based models are implemented and compared in this paper. The experimental results show that the proposed model is robust to initial contours. The DRSF model incorporating a larger window Gaussian kernel increases computation time, we improved the DRSF model into the CSDRSF model, which is a global convex segmentation model based on the DRSF model, and then use the split Bregman algorithm to minimize the CSDRSF model. The experiments illustrates CSDRSF model inheriting the DRSF model’s nature of being not sensitive to the initial contour position, and greatly improves efficiency.