Some Applications Of Geometric Heat Flow In Digital Image Processing

The main pursuit of this dissertation is derived from a practical problem that how to segment desired objects from a given color image, regardless of other objects. We transform this problem to a variational problem, and modify the traditional geodesic active contour method and the Chan-Vese model. Moreover, we prove the existence and uniqueness of the solution of these new evolving equations. The work partly complete the theoretical researches of geometric heat flow in image processing fields by researching two particular curvature evolution. At the same time, the experiment results show that our method is very efficient for segmenting desired objects. The main research results are as follows:1. Modified geodesic active contours.Using the statistical analysis method, we analysis the sample pixels chosen from the desired objects and construct a discrimination function. The discrimination function is coupled in the traditional stopping function. The new stopping function depends on not only the image gradient but also the discrimination function derived from the color information of desired objects. The stopping function in the geodesic active contour method is replaced by this new stopping function. The evolving curve will stop only when it achieves at boundaries of the desired objects via the new stopping function. Our modified active contours method can detect desired objects but without unwanted objects. Since the level set evolution equation is a curvature evolution equation, we also can prove the existence, uniqueness and stability of the solution by viscosity solution theory and classical geometric analysis methods, for example the gradient estimation, maximum principal, and so on. However, this method can not segment the interior boundaries, which is can be solved by the methods presented in the next.2. Modified Chan-Vese modelA new variational formulation is presented by corporate the new stopping function to the Chan-Vese model. This model can segment the exterior and interior boundaries of desired objects because this model combines the new stopping function and the overall character of Chan-Vese model. It is different from the traditional Chan-Vese model that our model has no longer the Dirac function. Therefore, the uncertainty of numerical computation derived by all kinds of approximation of Dirac function is avoided. Applying the viscosity solution theory, the theory in classical partial differential equation, and the Schauder fixed point theorem, we discuss the existence and uniqueness of solution of the evolution equations.