Shape registration: toward the automatic construction of deformable shape and appearance models
Authors: Hung-Tat Tsui, Qing-Hu Max Meng
Venue:  (2007)

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.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.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. 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.For both methods, the model generalization errors&mdash;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.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.