No description available.

No description available.

Spherical Harmonics (SPHARM) and Singular Value Decomposition (SVD) utilize the orthogonal relations of its parameters to represent and process images. The process involve mapping of the image from its original parameter domain to a new domain where the processing is performed. This process induces distortion and smoothing is required. The image now mapped to the new parameter domain is descripted using SPHARM and SVD using one at a time. The least significant values for the SPHARM coefficients and singular values of SVD are truncated which induces compression in the reconstructed image keeping the memory allocation in view. In this thesis, we have applied SPHARM and SVD tools to represent and reconstruct an image. The image is first mapped to the unit sphere (a sphere with unit radius). The image gets distorted that is maximum at the north and south poles, for which smoothing is approached by leaving 0.15*π space blank at each pole where no mapping is done. Sampling is performed for the θ and φ parameters and the image is represented using spherical harmonics and its coefficients are calculated. The same is then repeated for the SVD and singular values are computed. Reconstruction is performed using the calculated parameters, but defined over some finite domain, which is done by truncating the SPHARM coefficients and the singular values inducing image compression. Results are formulated for the various truncation choices and analyzed and finally it is concluded that SPHARM is better as compared with SVD as compression tool as there is not much difference in the quality of the reconstructed image with both tools, though SVD seem better quality wise, but with much higher memory allocation than SPHARM.

Thesis (doctoral)--University of Helsinki, 2007. / Includes bibliographical references. Also available on the World Wide Web.

It is well known that the n-th eigenfunction to one-dimensional Sturm-Liouville eigenvalue problems has exactly n-1 nodes, i.e. non-degenerate zeros. For higher dimensions, it is much more complicated to obtain general statements on the zeros of eigenfunctions. The author states a new conjecture on the number of nodal domains of spherical harmonics, i.e. of connected components of S^2 \ N(u) with the nodal set N(u) = (x in S^2 : u(x) = 0) of the eigenfunction u, and proves it for the first six eigenvalues. It is a sharp upper bound, thus improving known bounds as the Courant nodal domain theorem, see S. Y. Cheng, Comment. Math. Helv. 51, 43-55 (1976; Zbl 334.35022). The proof uses facts on real projective plane algebraic curves (see D. A. Gudkov, Usp. Mat. Nauk 29(4), 3-79, Russian Math. Surveys 29(4), 1-79 (1979; Zbl 316.14018)), because they are the zero sets of homogeneous polynomials, and the spherical harmonics are the restrictions of spherical harmonic homogeneous polynomials in the space to the plane. / Series: Preprint Series / Department of Applied Statistics and Data Processing

<p>Image rendering is the process of creating realistic computer images from  geometric models and physical laws of light and reflection. This master thesis deals mainly with the numerical intricacies of implementing an image renderer using spherical harmonics. It investigates how to calculate the reflection of light in a surface using the Phong model, and employs ray tracing to create a realistic image of a geometric model. Further, it investigates different ways of calculating the spherical harmonic representation of a function defined on the sphere. The thesis also deals with the implementation of self-shadowing, and the effects of adding this component to the rendering equation.</p>

Image rendering is the process of creating realistic computer images from  geometric models and physical laws of light and reflection. This master thesis deals mainly with the numerical intricacies of implementing an image renderer using spherical harmonics. It investigates how to calculate the reflection of light in a surface using the Phong model, and employs ray tracing to create a realistic image of a geometric model. Further, it investigates different ways of calculating the spherical harmonic representation of a function defined on the sphere. The thesis also deals with the implementation of self-shadowing, and the effects of adding this component to the rendering equation.

Thesis (M.S.)--Brigham Young University. Dept. of Physics and Astronomy, 2008. / Includes bibliographical references (p. 79-82).

No description available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. Description based on print version record. Includes bibliographical references.