Geometric Image Models And Application In Medical Image Processing

Many problems in image processing or computer vision, such as segmentation, enhancement, or tracking, are more often than not ill-conditioned. The minimization of some energy measure translates some problems into an optimization problem depending on the unknown variables (which are function) in mathematics. When energy measure functional is differentiable, the calculus of variations leads to a partial differential equation. Variational methods can offer strong frameworks to correctly formulate image processing problems. A property of these mathematical frameworks is to state well-posed problems to guarantee existence uniqueness and regularity of solutions. In this thesis, we study mainly geometric curve evolution models and their application in medical images. We solved some problems of image segmentation, image enlargement and image denoising.The property of parametric active contour model and geometric active contour model is analyzed. The combine gradient vector force field with potential force field takes for new exterior force field on snake model. New model is the same about segmenting concave regions edges and capture range as GVF snake do. The potential force field act mainly on model when contour curve close target region edges. Experiments demonstrate that the model curve is driven to the object boundary by the new forces even if the initial estimate is not close and the object is nonconvex or has a high local curvature on left ventricle MAI. We propose a prior shape parametric active contour model. The prior shape force is computed using prior shape. We can incorporate prior shape force field into active contour model. The novel model can avoid computing the distance of prior shape contour to active contour and take from complexity. The model curve is driven to the object boundary by the new forces even if the initial estimate is not close edges and the object is nonconvex or has weak edges and noise on medical images. The adaptive balloon forces active contour model is proposed. The adaptive balloon forces relating to target region information was introduced in the geodesic active contour. The model provides an accurate segmentation to weak edges and noise image and speeds curve convergence to target region boundary. Experimental results of applying the scheme to real images including objects with weak edges and medical data imagery demonstrate its segmentation power. It is a novel approach for integrating prior shape to active contour model.The surface interpolating or fitting is a method for images enlarging in common use. We present two methods for image enlargement and enhancement. It is based upon scale relation of resolution analysis in wavelet. Let W_u0 denote that the original image can be deduced from enlarged image by a wavelet sub-sampling. (1) We use the total variation of the image as measure of regularity. The Euler-Lagrange equations with constraints W_u0 that is deduced from the variational principle by the minimum of total variation. (2) Using Lagrange method, Anisotropic diffusion equation are deduced from the variational...