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Dissertation
Wavelet-based nonlinear multi-dimensional registration
Doctor of Philosophy (Ph.D.), Drexel University
Sep 2002
DOI:
https://doi.org/10.17918/00000770
Abstract
This thesis deals with image registration. Image registration is a widely used procedure in multi-dimensional data visualization and analysis. In medicine image alignment is used mainly to fuse complementary information, construct a probabilistic map, and automatically segment experimental data. The focus of this thesis is on the application of brain mapping, where large anatomical variability exists between any two specimens. An elastic deformation model is used to compensate for nonlinear morphological differences. In the first phase of this research a wavelet methodology for elastic registration was developed. An algorithm for nonlinear alignment of elastic objects based on known external surface correspondences was proposed. Wavelet bases were used to represent the elastic deformation which was modeled by the static homogenous Navier Partial Differential Equation (PDE). A wavelet-Galerkin method was used to discretize the PDE. Analytic expressions for the connection coefficients were developed and a principle of threefold orthogonality was introduced to simplify the resulting system of linear equations. The use of wavelet bases produces a system that is sparse, embodies locality, and multiresolution analysis leading to a computationally efficient algorithm. In the second phase of the research a surface-based registration algorithm was developed Alignment was achieved by minimization of the Euclidian distance between a reference and a test brains' surfaces as well as minimization of the elastic bending energy. The elastic bending energy minimization was shown to be equivalent to solving the homogenous Navier PDE, whereas the minimization of the Euclidian distance was shown to be equivalent to imposing boundary conditions. A progressive coarse-to-fine approach that reduces algorithm complexity was adopted. The performance of the algorithm was evaluated by the alignment of sections from mouse brains located in the olfactory bulbs as well as by the alignment of rat brain volumes.
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Details
- Title
- Wavelet-based nonlinear multi-dimensional registration
- Creators
- Smadar Gefen
- Contributors
- Oleh John Tretiak (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xi, 99 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Electrical (and Computer) Engineering [Historical]; Drexel University
- Other Identifier
- 991014970200404721