Efficient and Reliable Methods for Direct Parameterized Image Registration

Abstract

This thesis examines methods for ecient and reliable image registration in the con- text of computer vision and medical imaging. Direct, parameterized image registration approaches work by minimizing a di erence measure between a xed reference image, and the image warped to match it. The calculation of this di erence 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. Eciency 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 di erence measure. The performance of a wide range of opti- mization 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 su ers from a potential loss of accuracy. An algorithm is presented which ap- plies formal deliberation control methods to managing this tradeo . 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 eciency without sacri cing 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. Fi- nally, (4) two existing ecient registration approaches, the inverse compositional, and ecient second order algorithms, rely on specialized optimizer update steps and spe- cialized parameterizations. A generalization of these methods is presented that both identi es the connections between them, and eliminates the need for these specialized components. Throughout the thesis, application speci c 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 ecient registration methods can be applied, alone or in combination, to a very wide range of problems.

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