A primary investigation on the selection of texture representations for the appearance modeling is also enclosed in this thesis, as a useful piece of work toward the automatic construction of deformable appearance models. / For both methods, the model generalization errors---the criteria directly evaluating deformable models, are adopted to quantitatively evaluate the registration results. The proposed methods are compared with state-of-the-art ones on both synthetic and real biomedical data. Their abilities to construct 2D and 3D shape models with better quality are demonstrated. Based on the STS method, an Active Boundary Model is also proposed for 3D images segmentation. / In recent years, the deformable shape models have been playing important roles in medical image analysis. A key problem involved in their construction is the shape registration: to establish dense correspondences across a group of different shapes. / So the second method, named STS (Segments tied to splines), is further proposed. It can directly take point sets as input shapes, which is able to handle shapes of complicated topologies in high dimensions. STS employs the same number of segments to gradually and concurrently model different point sets, achieving their registration by maintaining a correspondence that is naturally established at the coarsest stage of modeling. It formulates the registration problem in a Bayesian framework, where a constrained Gaussian Mixture Model (GMM) is taken to measure the likelihood, and an item derived from the bending energy of the Thin Plate Spline (TPS) is assumed to be the prior. This problem is efficiently solved by an Expectation-Maximum (EM) algorithm, which is embedded in a coarse-to-fine scheme. / The first method, called CAP (Coding all the points), employs a set of landmarks along the shape contours to establish the correspondence between shapes. Shape registration is formulated as an optimal coding problem, where not only the position of landmarks, but also the shape contours themselves are coded. The resultant description length is minimized by a new optimization approach, which utilizes multiple optimization techniques and a propagation scheme. However, CAP has difficulty to handle shapes in high dimensions, especially with complicated topologies. This is because it needs to parameterize the shapes under registration, so as to manipulate the trajectories of landmarks. / Two basic elements are normally embedded in a shape registration algorithm: a shape representation model and a transformation model. To our best knowledge, most existing methods treat them separately, where the representations for each shape are obtained first, and then the correspondence is established by only optimizing transformations. From the view of building deformable shape models, this leads to sub-optimal results, because a shape model is a coupled one of both representation and transformation. In this thesis, two new methods have been developed, both achieving the registration by simultaneously optimizing the shape representation and transformation, and thus have the potential to build optimal deformable shape models. Neither of them depend on any specific feature detection. / Jiang, Yifeng. / "September 2007." / Advisers: Hung-Tat Tsui; Qing-Hu Max Meng. / Source: Dissertation Abstracts International, Volume: 69-08, Section: B, page: 4844. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 161-172). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

First of all, the PDE form of the classical level set function phi is parameterized with an analytical form of Radial Basis Function (RBF), which is real-valued and continuously differentiable. Such that the upwind scheme, extension velocity and reinitialization algorithms in solving the discrete Hamilton-Jacobi equation can be waived in the numerical process, the whole framework is transformed into a standard mathematical programming problem in which the linear objective function can be directly optimized by a gradient algorithm - shape sensitivity. The minimization of the mean compliance is studied and presented to demonstrate the advantages of the parametrical method. / Parametrization substantially reduces the complexity of the original discrete PDE level set method. However, the result shows that the high number of RBF knots leads to dense coefficient matrices. Thus, it induces numerical instabilities, slow convergence and less accuracy in the process. Consequently, we then study the distribution of knots density for faster computation. By updating the movement of the knot, the knot moves towards the position where the change is directly determined by the shape sensitivity. In such case, we may use lesser number of knots to describe the properties of the system while the smoothness of the implicit function is satisfied. The sensitivity study is evaluated carefully and discussed in detail. Results show a significant improvement in the computational speed and stability. / The study found significant improvement obtained in the structural optimization with the parametric level set method, both the stability and efficiency were given as the benefits of using the method of the parametrization. / Traditional structural optimization approaches can be referred to as sizing optimization, since their design variables are the proportions of the structure or material. A major restriction in the sizing problem is that the shape and the topology of the structure are fixed a priori. Undoubtedly, changes in shape (e.g., curved boundary) and topology (e.g., holes in a member) could produce more significant improvement in dynamic performance than modifications in size alone. A recent development of shape and topology optimization based on the implicit moving boundaries with the use of the renowned level set method is regarded as one of the most sophisticated methods in handling the change of the structural topology. In this thesis, we study the parametrization of the classical level set method for the structural optimization and the associated computational methodology. / Usually, a large-scale model will lead to bulk coefficient matrices in the RBF optimization and the linear function normally require O (N3) flops and O (N2) memory while processing. It is becoming impractical to solve as N goes over 10,000. In fact, the dense system equation matrix frequently leads to the numerical instabilities and the failure of the optimization. Finally, we introduce the method of Partition of Unity (POU) to deal with this problem. POU is often used in 3D reconstruction of implicit surfaces from scattered point sets. It breaks the global domain into smaller overlapping subdomains such that the implicit functions can be more efficiently interpolated. Meanwhile, the global solution is obtained by blending all the local solutions with a set of weighting functions. The algorithm of POU is presented here, and we analyze and discuss the numerical results accordingly. / Ho, Hon Shan. / Adviser: Michael Y. Wang. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 106-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.