Investigation On Deformable Models With Application To Cardiac Magnetic Resonance Images Analysis

Image understanding is the high level processing in machine vision and encompasses the set of activities required to identify objects in visual imagery and to establish 3D relationships between the objects themselves and the objects and the viewer. Because the image is discrete and also usually contaminated by noise during acquisition and transmission, the resulting data are incomplete so that many problems, such as object extraction and surface reconstruction, in machine vision are ill-posed. The mathematical solution for ill-posed problems is regularization. The computational foundation for deformable models is just regularization. The deformable model based image understanding is a top-down process, which integrates an initial estimate, desired contour/surface properties, image data and knlowdge-based constraints into a single process, and the deformable models provide a good solution for object extraction and surface reconstruction. Cardiac magnetic resonance images analysis is an important application in the field of machine vision, it requires to extract the epicardium and endocardium of the left ventricle (also the tag stripes which move along with the underlying tissues) and reconstruct the surface of the left ventricle( also the non-rigid motion corresponding to the tag stripes). In this paper, we investigate the deformable model theoretically and utilize the deformable model to extract the contours of the left ventricle and reconstruct the surface.The snake model is a two-dimensional deformable model, and we give a comprehensive review for the snake model under the framework of regularization of ill-posed problem, all the achievements are classified into seven categories as representation of the contour, numerical solution, initial contour estimation, regularization, image adoption, topology and motion tracking.The GVF snake model shows high performance at capture-range enlarging and boundary concavity convergence. In this paper, we point out that the desired external force field is not the converged solution of the Euler Equation derived from the GVF functional, but only an intermediate formulation. We also discuss the critic point problem encountered by the initial contours and summarize the causalities for the critical point problem; a reasonable external force field can be generated when considering the causalities carefully. Also, we prove that the theory foundation, i.e., the Navier-Stokes equation for viscous fluid flow, for the solution to the critical point problem in literatures is incorrect. When the restrictions are proper, a simple and effective solution to the critical point problem is presented as well.We also address the problem of extraction of the epicardium and endocardium of the left ventricle from cardiac MR images. We first analyze the characteristics of the cardiac MR images and point out the difficulties in extracting the epicardium and endocardium of the left ventricle. As to extract the epicardium, we introduce a two-step deformation snake which takes the deformation results of traditional snake as the prediction of the new contour position, and a priori shape knowledge of the LV is used to correct the predictive resultssuch that the snake contour deformed via prediction and correction. The experimental results validate the performance of this two-step-deformation snake for the LV epicardium segmentation of MR images.When taking into account the shape of the left ventricle, we introduce the polar coordinates transform to convert the quasi-cirle shape into a quasi-line; a snake-based algorithm associated with several merits is presented to track the contours of left ventricle. The high performance is validated by considerable experiments.This paper also exploits the 3D deformable model to reconstruct the inner and outer surface of the left ventricle from the segmented cardiac magnetic resonance images. From the requirements of non-rigid motion reconstruction based on tag stripes, the left ventricle is modeled as a cylinder with parametric functions. Under the framework of the physic...