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Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2010. / Committee Chair: Guzdial, Mark; Committee Member: Abowd, Gregory; Committee Member: Mynatt, Elizabeth; Committee Member: Smith, Michael; Committee Member: Thomas, John. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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In this thesis, new methods for the efficient segmentation of images are presented. The proposed methods are based on the deformable model approach, and can be used efficiently in the segmentation of complex geometries from various imaging modalities. A novel deformable model that is based on a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions is presented. This external force field is based on hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contributes to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and give the deformable model a high invariance in initialization configurations. The voxel interactions across the whole image domain provides a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force held allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries. In addition, it is shown that by enhancing the geometrical interaction field with a nonlocal edge-preserving algorithm, the new deformable model can effectively overcome image noise. A comparative study on the segmentation of various geometries with different topologies from both synthetic and real images is provided, and the proposed method is shown to achieve significant improvements against several existing techniques. A robust framework for the segmentation of vascular geometries is described. In particular, the framework consists of image denoising, optimal object edge representation, and segmentation using implicit deformable model. The image denoising is based on vessel enhancing diffusion which can be used to smooth out image noise and enhance the vessel structures. The image object boundaries are derived using an edge detection technique which can produce object edges of single pixel width. The image edge information is then used to derive the geometric interaction field for optimal object edge representation. The vascular geometries are segmented using an implict deformable model. A region constraint is added to the deformable model which allows it to easily get around calcified regions and propagate across the vessels to segment the structures efficiently. The presented framework is ai)plied in the accurate segmentation of carotid geometries from medical images. A new segmentation model with statistical shape prior using a variational approach is also presented in this thesis. The proposed model consists of an image attraction force that propagates contours towards image object boundaries, and a global shape force that attracts the model towards similar shapes in the statistical shape distribution. The image attraction force is derived from gradient vector interactions across the whole image domain, which makes the model more robust to image noise, weak edges and initializations. The statistical shape information is incorporated using kernel density estimation, which allows the shape prior model to handle arbitrary shape variations. It is shown that the proposed model with shape prior can be used to segment object shapes from images efficiently.

Airborne laser bathymetry, a relatively new state-of-the-art technology for the mapping of sea depth by using active airborne laser ranging systems, has proved successful for charting shallow waters worldwide including Canada, Australia, and the United States. In order to improve the reliability and efficiency of using airborne laser ranging systems, in particular, the Canadian LARSEN 500 airborne system, for the estimation of sea depth, one- and two-dimensional (1-D and 2-D) signal processing algorithms are developed. The processing involved is carried out in a two-phased approach. In phase I, 1-D signal processing is explored. Specifically, 1-D digital smoothing is applied to the laser waveforms for noise reduction. Results show that this process can remove noise while preserving the important characteristics of the laser signal. In order to analyze the laser reflections quantitatively, a mathematical model function that can be used to characterize the smoothed laser waveforms received by the LARSEN 500 under diverse circumstances is established. Two algorithms are also developed for the detection of the peak of the laser pulse reflected from the sea surface and bottom. The algorithms have been implemented and tested extensively with real-world LARSEN waveforms. Tests show that the algorithms can reject noise pulses and pulses arising from turbid layers in the sea and locate the correct pulse in the presence of varying degrees of noise. In order to separate the surface and bottom reflections independently of the degree of their overlap, a waveform-decomposition technique based on a robust optimization method is developed. An initialization scheme is also developed in conjunction with the decomposition technique which can reduce the amount of computation required in the decomposition quite significantly. Comparison resuits obtained from statistical analysis show that the proposed technique offers considerable potential in improving the depth estimates particularly when the resolution between the surface and bottom reflections is low. In addition, it can be used to automate the depth estimation process. In phase II, 2-D signal processing is used to improve the reconstruction of ocean topography from individual depth estimates. A type of 2-D interpolating filter is introduced to suppress impulsive noise present in the scattered measurements. It is found that as a result of the filtering, the representation of the sea floor, which can be in the form of 2-D contour maps or 3-D surface plots, becomes a more accurate representation of the ocean bottom. To improve the accuracy in the reconstruction, a sophisticated triangle based 2-D interpolation technique designed using the finite-element method is applied. To increase the reliability of the reconstruction, optimal triangulated irregular networks are constructed before carrying out the interpolation. In order to assess the accuracy of the decomposition results when the resolution between the laser reflections is very low, a procedure which incorporates the 2-D interpolation technique is developed. To further enhance the reconstructed profiles, an adaptive 2-D filtering procedure is introduced. This procedure is developed using 2-D power spectral analysis of the depth profiles. In areas where the signal characteristics of the bathymetric data vary rapidly, 2-D filtering based on minimum mean-squared error estimation is explored. It is shown that the derived filter is a 2-D space-variant filter and its application to bathymetric profiles collected by the LARSEN 500 system is also implemented. Results obtained show that these two filtering procedures are useful in reducing random noise inherent in the reconstructed profiles which is difficult to detect and eliminate in 1-D processing. / Graduate

M.Sc. (Computer Science) / Please refer to full text to view abstract