Study of non-rigid image registration algorithms

Abstract

In this thesis, we study several non-rigid dense image registration algorithms, and a special attention is given to over-fitting and under-fitting problems, which have identified as two major causes to limit accuracy of non-rigid image registration. In order to eliminate their impacts, two essential factors, leading to over-fitting and under-fitting, are specifically analysed in this thesis. They are ill-poseness and low expression power of geometric transformation. After that, we propose three new algorithms in this thesis, namely (a) two-phase probabilistic second-order Demons Algorithm, (b) learning varying dimension radial basis functions (LVDRBF), and (c) Cross-cumulative residual entropy (CCRE) based LVDRBF. Two-phase probabilistic second-order Demons Algorithm: In this algorithm, a divide-and-conquer strategy is presented to reduce effects of under-fitting and over-fitting through addressing ill-poseness and low expression power of geometric transformation. Firstly, ill-poseness is successfully solved with incorporating priori information into probabilistic second-order Demons Algorithm. After that, registration errors caused by low expression of the rectangle free-form transformation are rectified by a two-phase deformation strategy. This two-phase probabilistic Second-order Demons Algorithm extends the applications of Demons Algorithm from homogenous region to texture-rich image. Learning varying dimension radial basis functions (LVDRBF): Different from divide-and-conquer strategy in two-phase probabilistic second-order Demons Algorithm, "learning varying dimension RBF", can tackle ill-poseness and low expression power of geometric transformation, simultaneously. To achieve this purpose, a matched data-pairing set is established via Lucas-Kanade-Tomasi feature tracking algorithm to be a latent control point library. Then, the "best" RBF transformation with the optimal number and the appropriate locations of control point is found by an iterative learning process based on this latent control point library, in order to eliminate impacts of low expression of the rectangle free-form transformation. Meanwhile, ill-poseness is solved by incorporating Bayesian framework into warping parameter estimation in this iterative learning process. This new algorithm not only increases the accuracy of image registration, but also provides a strategy to establish the "best" RBF transformation and search for optimal corresponding warping parameters. Cross-cumulative residual entropy (CCRE) based LVDRBF: Because the need for multi-modality image registration occurs in many applications including computer vision, remote sensing, and especially medical image processing, thus we present an improved "CCRE based learning varying dimension RBF" for multi-modality dense image registration. CCRE as a similarity measure not only contributes to the extension of application of learning varying dimension RBF from single-modality to multi-modality image registration, but also increases its robustness owing to property of CCRE. Show more