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In this dissertation, a new cubic-spline interpolation (CSI) for both one-dimensional and two-dimensional signals is developed to sub-sample signal, image and video compression data. This new interpolation scheme that is based on the least-squares method with a cubic-spline function can be implemented by the fast Fourier transform (FFT). The result is a simpler and faster interpolation scheme than can be obtained by other conventional means. It is shown by computer simulation that such a new CSI yields a very accurate algorithm for smoothing. Linear interpolation, linear-spline interpolation, cubic-convolution interpolation and cubic B-spline interpolation tend to be inferior in performance. In addition it is shown in this dissertation that the CSI scheme can be performed by a fast and efficient computation. The proposed method uses a simpler technique in the decimation process. It requires substantially fewer additions and multiplications than the original CSI algorithm. Moreover, a new type of overlap-save scheme is utilized to solve the boundary-condition problems that occur between two neighboring subimages in the actual image. It is also shown in this dissertation that a very efficient 9-point Winograd discrete Fourier transform (Winograd DFT) can be used to replace the FFT needed to implement the CSI scheme. Furthermore, the proposed fast new CSI scheme is used along with the Joint Photographic Experts Group (JPEG) standard to design a modified JPEG encoder- decoder for image data compression. As a consequence, for higher compression ratios the proposed modified JPEG encoder-decoder obtains a better quality of reconstructed image and also requires less computational time than both the conventional JPEG method and the America on Line (AOL) algorithm. Finally, the new fast CSI scheme is applied to the JPEG 2000, MPEG-1 and MPEG-2 algorithms, respectively. A computer simulation shows that in the encoding and decoding, the proposed modified JPEG 2000 encoder-decoder speeds up the JPEG 2000 standard, respectively, and still obtains a good quality of reconstructed image that is similar to JPEG 2000 standard for high compression ratios. Additionally, the reconstructed video using the modified MPEG encoder-decoder indicates a better quality than the conventional MPEG-1 and MPEG-2 algorithms for high compression ratios or low-bit rates.

Orientador: Sérgio Antonio Tozoni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-22T06:19:51Z (GMT). No. of bitstreams: 1 Lopes_RaquelVieira_M.pdf: 1141005 bytes, checksum: 8091e673668abab031630ae7fd1b7436 (MD5) Previous issue date: 2013 / Resumo: Os sk-splines são uma generalização natural dos splines polinomiais, os quais foram introduzidos e tiveram sua teoria básica desenvolvida por Alexander Kushpel nos anos de 1983-1985. Estas funções são importantes em várias aplicações e seu espaço é gerado por translações discretas de uma única função núcleo. Neste trabalho, estudamos condições necessárias e suficientes para a existência e unicidade de sk-splines interpolantes de funções periódicas. Além disso, estudamos a aproximação de funções de determinadas classes por sk-splines nos espaços Lp. Como aplicação estudamos a aproximação de funções infinitamente diferenciáveis e finitamente diferenciáveis por sk- splines / Abstract: The sk-splines are a natural generalization of polynomial splines. They were introduced and their basic theory developed by Alexander Kushpel between 1983 and 1985. These functions are important in many applications and the space of sk-splines is the linear span of shifts of a single kernel K. In this work, we study necessary and sufficient conditions for the existence and uniqueness of sk-splines interpolants of periodic functions. Furthermore, we study the approximation in several classes of functions by sk-splines in the Lp spaces. As an application we study the approximation of infinitely and finitely differentiable functions by sk-splines / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

This work approaches the problem of triangulating algebraic curves/surfaces with a subdivision-style algorithm using A-Patches. An implicit algebraic curve is converted from the monomial basis to the bivariate Bernstein-Bezier basis while implicit algebraic surfaces are converted to the trivariate Bernstein basis. The basis is then used to determine the scalar coefficients of the A-patch, which are used to find whether or not the patch contains a separation layer of coefficients. Those that have such a separation have only a single sheet of the surface passing through the domain while one that has all positive or negative coefficients does not contain a zero-set of the surface. Ambiguous cases are resolved by subdividing the structure into a set of smaller patches and repeating the algorithm. Using A-patches to generate a tessellation of the surface has potential advantages by reducing the amount of subdivision required compared to other subdivision algorithms and guarantees a single-sheeted surface passing through it. This revelation allows the tessellation of surfaces with acute features and perturbed features in greater accuracy.

Real-valued functions have wide applications in various areas within computer graphics. In this work, we examine three representation of shapes using functions. In particular, we study the classical B-spline representation of piece-wise polynomials in the univariate domain. We provide a generalization of B-spline to the bivariate domain using intuition gained from the univariate construction. We also study the popular scheme of representing 3D density distribution using a uniform, rectilinear grid, where we provide a novel contouring scheme that culls occluded inner geometries. Lastly, we examine a ray-based representation for 3D indicator functions called ray-rep, for which we present a novel meshing scheme with multi-material extensions.

This work approaches the problem of triangulating algebraic curves/surfaces with a subdivision-style algorithm using A-Patches. An implicit algebraic curve is converted from the monomial basis to the bivariate Bernstein-Bezier basis while implicit algebraic surfaces are converted to the trivariate Bernstein basis. The basis is then used to determine the scalar coefficients of the A-patch, which are used to find whether or not the patch contains a separation layer of coefficients. Those that have such a separation have only a single sheet of the surface passing through the domain while one that has all positive or negative coefficients does not contain a zero-set of the surface. Ambiguous cases are resolved by subdividing the structure into a set of smaller patches and repeating the algorithm. Using A-patches to generate a tessellation of the surface has potential advantages by reducing the amount of subdivision required compared to other subdivision algorithms and guarantees a single-sheeted surface passing through it. This revelation allows the tessellation of surfaces with acute features and perturbed features in greater accuracy.

Conventional Cobb-Douglas and Transcendental Logarithmic production functions widely used in Stochastic Production Frontier Estimation and Inefficiency Analysis have merits and deficiencies. The Cobb-Douglas function imposes monotonicity and concavity constraints required by microeconomic theory. However it is inflexible and implies undesired assumptions as well. The Trans-log function is very flexible and does not imply undesired assumptions, yet it is very hard to impose both monotonicity and concavity constraints. The first essay introduced a class of stochastic production frontier estimation models that impose monotonicity and concavity constraints and suggested models that are very flexible. Researchers can use arbitrary order of polynomial functions or any function of independent variables within the suggested frameworks. Also shown was that adopting suggested models could greatly increase predictive accuracy through simulations. In the second essay we generalized the suggested models with the Inefficiency Analysis technique. In the last essay we extended the models developed in the previous two essays with regression spline and let the data decide how flexible or complicated the model should be. We showed the improvement of deterministic frontier estimation this extension could bring through simulations, as well. Works in this dissertation reduced the gap between conventional structural models and nonparametric models in stochastic frontier estimation field. This dissertation offered applied researchers Stochastic Production Frontier models that are more accurate and flexible than previous ones. It also preserves constraints of economic theory.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 136-138).

No description available.

Zugl.: Passau, Univ., Diss., 2007