The objective of the proposed research is to develop high performance, low computational complexity resolution enhancement and demosaicing algorithms. Our approach to both problems is to find creative ways to incorporate edge information into the algorithm design. However, in contrast with the usual edge directed approaches, we do not try to detect edge presence and orientation explicitly. For the image interpolation problem, we study the relationship between low resolution and high resolution pixels, and derive a general interpolation formula to be used on all pixels. This simple interpolation algorithm is able to generate sharp edges in any orientation. We also propose a simple 3 by 3 filter that quantifies local luminance transition and apply it to the demosaicing problem. Additionally, we propose a gradient based directional demosaicing method that does not require setting any thresholds. We show that the performance of this algorithm can be improved by using multiscale gradients. Finally, we address the low spectral correlation demosaicing problem by proposing a new family of hybrid color filter array (CFA) patterns and a local algorithm that is two orders of magnitude faster than a comparable non-local solution while offering the same level of performance.

[Truncated abstract] Image transition effects are commonly used on television and human computer interfaces. The transition between images creates a perception of continuity which has aesthetic value in special effects and practical value in visualisation. The work in this thesis demonstrates that better image transition effects are obtained by incorporating properties of projective geometry into image transition algorithms. Current state-of-the-art techniques can be classified into two main categories namely shape interpolation and warp generation. Many shape interpolation algorithms aim to preserve rigidity but none preserve it with perspective effects. Most warp generation techniques focus on smoothness and lack the rigidity of perspective mapping. The affine transformation, a commonly used mapping between triangular patches, is rigid but not able to model perspective effects. Image transition techniques from the view interpolation community are effective in creating transitions with the correct perspective effect, however, those techniques usually require more feature points and algorithms of higher complexity. The motivation of this thesis is to enable different views of a planar surface to be interpolated with an appropriate perspective effect. The projective geometric relationship which produces the perspective effect can be specified by two quadrilaterals. This problem is equivalent to finding a perspectively appropriate interpolation for projective transformation matrices. I present two algorithms that enable smooth perspective transition between planar surfaces. The algorithms only require four point correspondences on two input images. ...The second algorithm generates transitions between shapes that lie on the same plane which exhibits a strong perspective effect. It recovers the perspective transformation which produces the perspective effect and constrains the transition so that the in-between shapes also lie on the same plane. For general image pairs with multiple quadrilateral patches, I present a novel algorithm that is transitionally symmetrical and exhibits good rigidity. The use of quadrilaterals, rather than triangles, allows an image to be represented by a small number of primitives. This algorithm uses a closed form force equilibrium scheme to correct the misalignment of the multiple transitional quadrilaterals. I also present an application for my quadrilateral interpolation algorithm in Seitz and Dyer's view morphing technique. This application automates and improves the calculation of the reprojection homography in the postwarping stage of their technique. Finally I unify different image transition research areas into a common framework, this enables analysis and comparison of the techniques and the quality of their results. I highlight that quantitative measures can greatly facilitate the comparisons among different techniques and present a quantitative measure based on epipolar geometry. This novel quantitative measure enables the quality of transitions between images of a scene from different viewpoints to be quantified by its estimated camera path.

Thesis (MSc)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: In this thesis we study the underlying mathematical principles of stationary subdivision, which can be regarded as an iterative recursion scheme for the generation of smooth curves and surfaces in computer graphics. An important tool for our work is Fourier analysis, from which we state some standard results, and give the proof of one non-standard result. Next, since cardinal spline functions have strong links with subdivision, we devote a chapter to this subject, proving also that the cardinal B-splines are refinable, and that the corresponding Euler-Frobenius polynomial has a certain zero structure which has important implications in our eventual applications. The concepts of a stationary subdivision scheme and its convergence are then introduced, with as motivating example the de Rahm-Chaikin algorithm. Standard results on convergence and regularity for the case of positive masks are quoted and graphically illustrated. Next, we introduce the concept of interpolatory stationary subdivision, in which case the limit curve contains all the original control points. We prove a certain set of sufficient conditions on the mask for convergence, at the same time also proving the existence and other salient properties of the associated refinable function. Next, we show how the analysis of a certain Bezout identity leads to the characterisation of a class of symmetric masks which satisfy the abovementioned sufficient conditions. Finally, we show that specific special cases of the Bezout identity yield convergent interpolatory symmetric subdivision schemes which are identical to choosing the corresponding mask coefficients equal to certain point evaluations of, respectively, a fundamental Lagrange interpolation polynomial and a fundamental cardinal spline interpolant. The latter procedure, which is known as the Deslauriers-Dubuc subdivision scheme in the case of a polynomial interpolant, has received attention in recent work, and our approach provides a convergence result for such schemes in a more general framework. Throughout the thesis, numerical illustrations of our results are provided by means of graphs. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die onderliggende wiskundige beginsels van stasionêre onderverdeling, wat beskou kan word as 'n iteratiewe rekursiewe skema vir die generering van gladde krommes en oppervlakke in rekenaargrafika. 'n Belangrike stuk gereedskap vir ons werk is Fourieranalise, waaruit ons sekere standaardresuJtate formuleer, en die bewys gee van een nie-standaard resultaat. Daarna, aangesien kardinale latfunksies sterk bande het met onderverdeling, wy ons 'n hoofstuk aan hierdie onderwerp, waarin ons ook bewys dat die kardinale B-Iatfunksies verfynbaar is, en dat die ooreenkomstige Euler-Frobenius polinoom 'n sekere nulpuntstruktuur het wat belangrike implikasies het in ons uiteindelike toepassings. Die konsepte van 'n stasionêre onderverdelingskema en die konvergensie daarvan word dan bekendgestel, met as motiverende voorbeeld die de Rahm-Chaikin algoritme. Standaardresultate oor konvergensie en regulariteit vir die geval van positiewe maskers word aangehaal en grafies geïllustreer. Vervolgens stelons die konsep van interpolerende stasionêre onderverdeling bekend, in welke geval die limietkromme al die oorspronklike kontrolepunte bevat. Ons bewys 'n sekere versameling van voldoende voorwaardes op die masker vir konvergensie, en bewys terselfdertyd die bestaan en ander toepaslike eienskappe van die ge-assosieerde verfynbare funksie. Daarna wys ons hoedat die analise van 'n sekere Bezout identiteit lei tot die karakterisering van 'n klas simmetriese maskers wat die bovermelde voldoende voorwaardes bevredig. Laastens wys ons dat spesifieke spesiale gevalle van die Bezout identiteit konvergente interpolerende simmetriese onderverdelingskemas lewer wat identies is daaraan om die ooreenkomstige maskerkoëffisientegelyk aan sekere puntevaluasies van, onderskeidelik, 'n fundamentele Lagrange interpolasiepolinoom en 'n kardinale latfunksie-interpolant te kies. Laasgenoemde prosedure, wat bekend staan as die Deslauriers-Dubuc onderverdelingskema in die geval van 'n polinoominterpolant, het aandag ontvang in onlangse werk, en ons benadering verskaf 'n konvergensieresultaat vir sulke skemas in 'n meer algemene raamwerk. Deurgaans in die tesis word numeriese illustrasies van ons resultate met behulp van grafieke verskaf.

Radon is a radioactive gas that is the leading cause of lung cancer in non-smokers. While radon is natural and ubiquitous, higher concentrations greatly increase cancer risk. As such, understanding the spatial distribution of radon potential is key to planning and public health efforts. This project tests a method of determining radon potential using in situ measurements of gamma radiation. The in situ measurements were used to create a raster of gamma emissions in the study region using kriging. The resulting model showed that the operational scale of gamma radiation in the study region was 4.5 km. Indoor radon concentrations were then assigned gamma emission rates from the raster and the two were compared. While there was evidence of an association between higher gamma and high radon, the gamma readings were not quantitatively predictive. As such only categorical predictions of radon potential and risk could be made.

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No description available.

Creation of accurate and coherent surface models is vital to the effective planning and construction of flood control and hurricane protection projects. Typically, topographic surface models are synthesized from Delaunay triangulations or interpolated raster grids. Although these techniques are adequate in most general situations, they do not effectively address the specific case where topographic data is available only as cross-section and profile centerline data, such as the elevation sampling produced by traditional hydrographic surveys. The hydraulic spline algorithm was developed to generate irregular two-dimensional channel grids from hydrographic cross-sections at any desired resolution. Hydraulic spline output grids can be easily merged with datasets of higher resolution, such as LIDAR data, to build a complete model of channel geometry and overbank topography. In testing, the hydraulic spline algorithm faithfully reproduces elevations of known input cross-section points where they exist, while generating a smooth transition between known cross-sections. The algorithm performs particularly well compared to traditional techniques with respect to aesthetics and accuracy when input data is sparse. These qualities make the hydraulic spline an ideal choice for practical applications where available data may be limited due to historic or budgetary reasons.

SuperNEC is a method of moments (MoM) electromagnetic eld solver based on the Numerical Electromagnetics Code (NEC). Much of the simulation time can be attributed to the lling of the impedance matrix, which is performed at each frequency point of interest. Impedance matrix interpolation methods have been implemented in SuperNEC to reduce the computational time required to ll the impedance matrix [Z]. Elements in [Z] vary predictably over frequency and can be approximated by a second order polynomial. A second improved method is implemented where the dominant frequency variation term is removed prior to calculating the tting function. A method of determining the optimum sample range relative to simulation range and maximum interaction distance has been developed. Given the correct choice of sample range the mean error in the MoM solution is less than 10% over the frequency range and the input impedance can be reproduced with good agreement over a wide bandwith. Improvement in the simulation e ciency of 1.7 times can be expected if su cient frequency points are of interest to account for the computational time required to sample the matrix and determine tting function coe cients. This method has been applied to a dipole antenna, an LPDA and a horn antenna. To increase the simulation bandwidth and retain an acceptable level of accuracy, the bandwidth is split into multiple sub-bands.

La thèse est consacrée à une étude d'interpolation complexe "semi-libre" dans le sens suivant: étant donné un ensemble "sigma" dans le disque unité D et une fonction f holomorphe dans D appartenant à une certaine classe X, on cherche g dans une autre classe Y (plus petite que X) qui minimise la norme de g dans Y parmi toutes les fonctions g satisfaisant g=f sur l'ensemble "sigma". Plus précisément, nous nous intéressons aux estimations de la constante d'interpolation suivante: c(sigma, X, Y ) = sup{ inf{||g||_Y: g=f sur sigma}: ||f||_X<=1} Dans la thèse, nous étudions le cas où Y = H^infini et où l'espace des contraintes X est choisi parmi les espaces suivants: les espaces de Hardy, les espaces de Bergman pondérés à poids radial ou encore les espaces de fonctions holomorphes ayant leurs coefficients de Taylor dans lp(w) (w étant un poids). La thèse contient également certaines applications aux nombres conditionnés des matrices de Toeplitz. / The thesis is devoted to a "semi-free" interpolation problem in the following way. Let sigma be a finite set of the unit disc D and f an holomorphic function in D which belongs to a certain class X, we search for g in another class Y (smaller than X) which minimize the norm of g in Y among all the functions g such that g=f on the set "sigma". More precisely, we are interested in the following interpolation constant : c(sigma, X, Y ) = sup{ inf{||g||_Y: g=f sur sigma}: ||f||_X<=1}. We study in the thesis the case where Y=H^\infinity and the space of constrains X is chosen among the following spaces: Hardy spaces, weighted Bergman spaces (with radial waights), and holomorphic functions which Taylor coefficients are in lp(w) (w being a weight). The thesis also contains an application to the condition numbers of Toeplitz matrices.

Os objetivos deste trabalho são: i) Fixado um inteiro positivo n, estudar dois métodos "construtivos" para aproximar-se uma função real contínua definida na esfera unitária S ^{r-1} de R^r, por polinômios esféricos de grau <=n; ii) Obter estimativas para as normas dos operadores de interpolação e hiperinterpolação, comparando-as com a norma da projeção ortogonal de C(S^{r-1}) sobre o espaço de polinômios onde as aproximações residem. / This work addresses two issues: i) To study two constructive methods to approximate a real continuous function on the unit sphere S^{r-1} of R^r by spherical polynomials of degree <=n (n fixed); ii) To estimate the norms of the interpolation and hyperinterpolation operators, comparing them with the norm of the orthogonal projection of C(S^{r-1}) over the polynomial space where the approximations live.