Schrödinger Transform of Image: A New Tool for Image Analysis

Image segmentation is the process of separating or grouping an image into different parts . These parts normally correspond to something that human beings can easily separate and view as individual objects. Computers have no means of intelligently for recognizing objects, and a large number of different methods have been developed in order to segment images, ranging from the simple thresholding method to advanced graph-cut methods. The segmentation process is based on various features found in the image. Those features might be histograms information, information about the pixels that indicate edges or boundaries or texture information and so on. Approaches of Image processing and analysis based on partial differential equation, such as deformable models or snakes (Terzopoulos et al., 1987; Kass, et al., 1987), balloon models (Cohen, L. D., 1991; Cohen, L. D. & Cohen, I., 1993), geometric models (Caselles et al., 1993), discrete dynamic contour models (Lobergt & Viegever, 1995), geodetic active contours (Caselles et al., 1995) and topology adaptive deformable model (McInerney & Terzopoulos, 1999), whose physical background is principle of minimum action or force equilibrium in classical mechanics, are being extensively applied to image segmentation, image smooth, image inpainting, extraction of boundary and so on. Xu and Prince analyzed the reason why snake methods have poor convergence to boundaries with large curvatures and replaced the gradient field with the gradient vector field (GVF), which has a larger capture region and slowly changes away from the boundaries (Xu & Prince, 1998). Consequently, the dependence on initial positions is decreased but the field can attract the moving contour to the right position. Parametric deformable models have high computational efficiency and can easily incorporate a priori knowledge. However, these models cannot naturally handle topological changes and are sensitive to initial conditions. Geometric deformable models are based on the level set method (Osher & Sethian, 1988), which was initially proposed to handle topological changes during the curve evolution. Geometric deformable models have the advantage of naturally handling the topological