Registration is the process of extracting spatial correspondences between different data sets such as digital images or sets of points and obtaining their spatial trans-formations from the extracted spatial correspondences. The information provided by these transformations is very useful in areas such as morphing in computer graphics, fusion of medical images from different modalities, and finding the pose of an object in an image or between different objects....[ Read more ]

Registration is the process of extracting spatial correspondences between different data sets such as digital images or sets of points and obtaining their spatial trans-formations from the extracted spatial correspondences. The information provided by these transformations is very useful in areas such as morphing in computer graphics, fusion of medical images from different modalities, and finding the pose of an object in an image or between different objects.

One of the essential criteria in registration is inverse consistency, i.e. to make the registration source-destination symmetric so that the forward and backward mapping matrices extracted are inverse to each other. Conventional approaches enforce con-sistency in deterministic fashions, either through the incorporation of sub-objective cost function that impose consistent property during the registration process or by the construction of diffeomorphic mapping on predetermined landmarks sets. How-ever, deterministic techniques for establishing the consistency means that the errors inherited from the discrete nature of the information sources are not considered. In this thesis, we present a stochastic framework that yields perfect inverse consistent registration from the initial forward and backward matching matrices. These ini-tial forward and backward transformation matrices can be computed by any image registration or point matching algorithms, which are input to our system. Then an optimization process is developed to compute the perfect source-destination symmet-ric mapping between the forward and backward transformation matrices. The errors of the registration matrices and the imperfectness of the consistent constraint are both modelled such that the whole optimization process is stochastic in nature. An itera-tive generalized total least square (GTLS) strategy has been developed such that the source-destination symmetric criterion is optimally established. Experiments based on point sets matching where ground truths are available, and synthetic as well as real image registration problems have been performed. Both show very promising results.