Multidimensional spline interpolation theory and surfaced-based alignment of brains

Maria Gabrani

doi:10.17918/00000733

This thesis deals with the problem of image registration, that is bringing in correspondence images of the same or similar objects. The images could be obtained from different geometric angles, acquisition methods, time instances, or even different scenes. This problem appears in numerous applications in Computer Vision, Pattern Recognition, Medical Image Analysis, and Remotely Sensed Image Processing. The present study is focused on registration techniques for biomedical images. In clinical diagnosis, therapy planning and evaluation, and in medical research, information in images from different modalities (MRI, CT, PET), or different patients, or obtained at different chronological instances need to be integrated. However, these images are not registered. Moreover, in images from different individuals there is a shape and scale variability that requires nonlinear registration. In this dissertation we deal with the development of a new nonlinear registration technique. In the literature authors address the problem of handling local variability by introducing elastic transformations. The underlying idea is the following. Since one wants to bring the two objects in a meaningful correspondence, one makes the assumption that the one object is a deformed version of the other. According to the theory of mechanics the deformed object has an energy that is a function of strains, stresses, and displacements. If one wants to bring the objects in alignment, one has to bring the object in equilibrium, that is minimize its energy. The main focus of this thesis is in the development of a new nonlinear registration technique. We have developed a new class of nonlinear transformations. The transformations are defined by a minimization problem of an energy functional that was inspired from the elasticity theory but has a general form and admits new classes of interpolation solutions. The two major contributions of the proposed transformations are the following; they consist of polynomials whose degree is decoupled from the dimensionality of the problem, and they have a vector valued closed form solution. We have developed two new interpolation problems to describe each property separately, and studied their solutions, and their conditions of uniqueness and existence. Even though the transformations are in terms of fiducial points we developed a scheme to support surface-based alignment. We have studied some techniques that support the initialization selection and provide the conditions under which the proposed techniques are effective. We tested the performance of the proposed transformations in the alignment of images of brains from different rats. The experiments have shown that the proposed transformations, for the given data, are stable and promising.

Multidimensional spline interpolation theory and surfaced-based alignment of brains

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Multidimensional spline interpolation theory and surfaced-based alignment of brains

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