Bézier Method For Image Processing

This project concerns about Bézier method in Computer Aided GeometricDesign (CAGD) involving Bézier Curve and Bézier Surface which widely related to the other theorem and method. The aim of this project is to introduce the basic of Bézier method and then generate the Bézier curves, Bézier surfaces, theory and properties and develop Bézier method in image processing application specifically image compression by using MATLAB

Body-fitting Meshes for the Discontinuous Galerkin Method

Abstract In this dissertation, a scheme capable of generating highly accurate, body fitting meshes and its application with the Discontinuous Galerkin Method is introduced. Unlike most other mesh generators, this scheme generates meshes consisting of quadrilateral or hexahedral elements exclusively. The high approximation quality is achieved by means of high order curved elements. The resulting meshes are highly suited for the application with high order methods, specifically the Discontinuous Galerkin Method, as large portions of the mesh are fully structured while matching the high order of the numerical method with a high order geometry representation at object and domain boundaries. The mesh scheme works in two steps. It chooses an interior volume that can be represented using a fully structured Cartesian mesh and connects it to the embedded objects and domain boundaries with a so called buffer-layer in a second step. Inside the layer, high order curved elements are applied for yielding high geometric representation accuracy. The resulting meshes are ideal for the application of high order methods. In the interior part the Cartesian structure can be exploited for obtaining high efficiency of the numerical method while the accuracy potential can be realized also in the presence of curved objects and boundaries. After introducing the mesh scheme, the Discontinuous Galerkin Method is described and applied for solving Maxwell’s equations. As a high order method it achieves exponential convergence under p-refinement. It is shown that using meshes produced by the novel scheme this property is achieved for curved domains as well. As an example, optimal convergence rates are demonstrated in a cylindrical cavity problem. In another example, the abilities of the method to produce correct spectral properties of closed resonator problems are investigated. To this end, a time-domain signal is recorded during the transient analysis. After applying the Fourier transform accurate frequency spectra are observed, which are free of spurious modes

Rate-Distortion Optimized Tree-Structured Compression Algorithms for Piecewise Polynomial Images

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymp- totic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D be- havior (D(R) ~ C02^-c1 R), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of 0(NlogN). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of 0(NlogN). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp

Automatic indexed calculation of wachspress' rational finite element functions

AbstractA numerical method of calculating all of the polynomial coefficients for Wachspress' rational finite element functions is presented. It requires only linear algebraic computations of matrix algebra and avoids the complicated constructions of geometric algebra used in the development of the rational elements