Quadtree representation and compression of spatial data

Spatial data representation and compression has become a focus issue in computer graphics and image processing applications. Quadtrees, as one of hierarchical data structures, basing on the principle of recursive decomposition of space, always offer a compact and efficient representation of an image. For a given image, the choice of quadtree root node plays an important role in its quadtree representation and final data compression. The goal of this thesis is to present a heuristic algorithm for finding a root node of a region quadtree, which is able to reduce the number of leaf nodes when compared with the standard quadtree decomposition. The empirical results indicate that, this proposed algorithm has quadtree representation and data compression improvement when in comparison with the traditional method.

Solid state NMR chemical shifts as an alternative to diffraction data in the determination of SIC polytypic structures

Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites which agree well with the experiment, provided that contributions from bonds up to 100 A are included in the calculation. The calculated chemical shifts depend on three factors: the layer stacking sequence, electrical centre of gravity, and the spacings between silicon and carbon layers. The assignment of peaks to lattice sites is proved possible for three polytypes (6H, 15R, and 3C). The fact that the calculated chemical shifts are very sensitive to layer spacings provides us a potential way to detennine and refine a crystal structure. In this work, the layer spacings of 6H SiC have been calculated and are within X-ray standard deviations. Under this premise, the layer spacings of 15R have been detennined. 29Si and 13C single crystal nmr studies of 6H SiC polytype indicate that all silicons and carbons are magnetically anisotropic. The relationship between a magnetic shielding tensor component and layer spacings has been derived. The comparisons between experimental and semi-empirical chemical shielding tensor components indicate that the paramagnetic shielding of silicon should be included in the single crystal chemical shift calculation.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Determining rotational direction of rotation structures using prolate shaped grains within till

Micromorphology is used to analyze a wide range of sediments. Many microstructures have, as yet, not been analyzed. Rotation structures are the least understood of microstructures: their origin and development forms the basis of this thesis. Direction of rotational movement helps understand formative deformational and depositional processes. Twenty-eight rotation structures were analyzed through two methods of data extraction: (a) angle of grain rotation measured from Nikon NIS software, and (b) visual analyses of grain orientation, neighbouring grainstacks, lineations, and obstructions. Data indicates antithetic rotation is promoted by lubrication, accounting for 79% of counter-clockwise rotation structures while 21 % had clockwise rotation. Rotation structures are formed due to velocity gradients in sediment. Subglacial sediments are sheared due to overlying ice mass stresses. The grains in the sediment are differentially deformed. Research suggests rotation structures are formed under ductile conditions under low shear, low water content, and grain numbers inducing grain-to-grain interaction.