Some Differential Equations Based Topics In Image Analysis

We discuss three blocks in this dissertation. First, we establish a geometry frame to analyze SPMVIF; Second, we use level set to get Hamilton-Jacobi equation of Snakes based Laplacian operator; Third, we introduce EDEK algorithm and investigate the evaluation of segmentation effect. We expand theory analysis on SPMVIF, Snakes, and other models in mathematical technology and engineering thinking. Some important conclusions are drawn. In the last part of this dissertation, we discuss how to model an image is discussed and how to segment an image by EDEK.Zero-Cross principle is a classical concept in signal processing. We generalize the concept to be zero normal curvature after the geometry frame built. Furthermore, we present the explanation to choose the dual parameters in SPMVIF. And we research why the Laplacian gradient superior to edge gradient.Due of an equivalent external force, we deduce a novel equation of Snakes, which is different to the forms in reference because it has clear geometric and physical background. Under the novel form, we can explain the auto-direction to evolving, speed decaying, and position of initial curves in traditional Snakes naturally.We discuss engineering details in EDEK model. And we use cost function to obtain image information at each pixel considered from both direction: tangential and normal. We compute energy line and average gradient to evaluate segmentation.A theorem on discrete data system is introduced. And we prove it to be true whenever the data number is finite or infinite. Obviously, it is true when we change it under another condition. In the end we generalize the theorem for continuous data system. The theorem is useful in seed choice at EDEK algorithm experiment.