Point-based Nonrigid Registration: Application to Object Recognition and Medical Image Registration

Image registration is an important problem in computer vision and has many diverse applications. Registration is the method of aligning two or more images into the same coordinate system to achieve a one-to-one correspondence. While registration of images has been studied in the past, an area that is less explored is nonrigid registration. It turns out that nonrigid registration is very appropriate when complex deformations are involved. In this thesis, we focus on point-based nonrigid registration and develop algorithms for solving nonrigid registration problems. With nonrigid registration as the goal, new point-based shape descriptor for object classification has been developed. The shape descriptor is based on principal curvatures and their directions. High curvature boundary points are first extracted in a multi-scale environment. The shape descriptor is then extracted by taking the k nearest neighborhood boundary points around a point of interest and calculating the central moments of the distribution of different properties of these neighborhood points. The choice of scale and the number of nearest neighbors provides a global as well as a local description of the neighborhood. Compared to previous techniques for shape matching and classification, experiments show that the proposed algorithm is more robust to deformation and invariant to rotation, scaling and translation. We also present a robust registration method based on geometric invariant features using multiscale weighted quaternion sub-division. The geometric invariant features are based on selective crest points which are robust to deformation. The k-nearest neighbor approach combined with multi-scale provides a new adaptive method for collecting features. The size of the neighborhood is increased if fewer features are present and is decreased when features are abundant. A feature of quaternion fitting approach is that it provides a fast method for registering points during sub-division registration, and the associated feature weights help remove any outlier effect on the result of the registration. A rigid body deformable registration scheme is also presented which is robust to noise, intensity variation and missing features. Hausdorff distance has been used as a similarity measure. The registration technique focuses on multi-modal medical images which have significant intensity variations and different levels of SNR. A huge amount of feature mismatch is also present between modalities as different modalities depict different tissues differently. We have analyzed the robustness and sensitivity of our algorithm with respect to various CT and MRI images of different quality.