Image Segmentations Based On Partial Differential Equations

Image segmentation has always been a fundamental problem in the field of image processing and computer vision. Its goal is to partition a given image into several dissimilar parts in each of which the intensity is homogeneous. Up to now, a wide variety of algorithms have been proposed to solve the image segmentation problem, in which partial differential equation based methods (active contour models) have been proved to be an efficient framework for image segmentation.Active contour models can be classified as parametric and geometric active contour models according to the representation of the evolving curve. Geometric contour active models can be classified into edge-based and region-based according to the use of image feature.This dissertation focuses on geometric active contour models; the main results are summarized as follows:1. The edge stopping function is very important in edge-based active contour models. It is typically the composition of a strictly monotonically decreasing positive function and the gradient magnitude of Gaussian smoothed image. The active contour models based on this type of edge stopping function have the drawbacks of long evolving time and need for Gaussian filter. Although Gaussian filter smoothes noise, it may also smooth edges; it is possible for the active contour models to inaccurately locate the edges. In this paper, a new edge stopping function without Gaussian smoothing is proposed to overcome the two drawbacks above. Experimental results show that an active contour model based on the new edge stopping function is about 50% faster than the original mode.2. A problem with most of geometric active contour models is contours initialization. That is, the segmentation results depend typically on the selection of initial contours. In order to address this problem, we proposed a new geometric active contour model. With our model, the level-set function can be initialized to a constant function, which completely eliminates the need of initial contours. Numerical results on synthetic and real digital images are given to show effectiveness and reliability of the proposed method. Besides, our model is especially suitable for segmentation of document images produced by cameras.