Efficient and reliable methods for direct parameterized image registration

This thesis examines methods for efficient and reliable image registration in the context of computer vision and medical imaging. Direct, parameterized image registration approaches work by minimizing a difference measure between a fixed reference image, and the image warped to match it. The calculation of this difference measure is the most computationally intensive part of the process and for faster registration it either has to be calculated faster, or calculated fewer times. Both possibilities are addressed in detail. Efficiency and reliability are addressed in four ways (1) Methods are presented for generalizing the Gauss-Newton Hessian approximation to the non-least squares case, and for the optimal selection of scaling factors for the transformation parameters. Both of these enhance performance by enabling optimization algorithms to perform fewer evaluations of the difference measure. The performance of a wide range of optimization algorithms is analyzed both theoretically and experimentally, and guidelines are presented for optimizer selection based on the characteristics of the registration problem. (2) Using only a portion of the available pixels results in faster calculation but suffers from a potential loss of accuracy. An algorithm is presented which applies formal deliberation control methods to managing this tradeoff. By managing the amount of image data used at every evaluation of the cost function, the algorithm adapts to the nature of the images and the stage of the optimization. This adaptive approach allows greater efficiency without sacrificing reliability. (3) It is shown that the scale used to compute the derivative is a critical factor to consider when selecting subsets of pixels for registration, that has largely been ignored in previous work. Finally, (4) two existing efficient registration approaches, the inverse compositional, and efficient second order algorithms, rely on specialized optimizer update steps and specialized parameterizations. A generalization of these methods is presented that both identifies the connections between them, and eliminates the need for these specialized components. Throughout the thesis, application specific approaches have been avoided. Both 2D and 3D images from both computer vision and medical imaging applications have been used throughout. Consequently each of the efficient registration methods can be applied, alone or in combination, to a very wide range of problems.