In computer vision, object recognition involves segmentation of the image into separate components. One way to do this is to detect the edges of the components. Several algorithms for edge detection exist and one of the most sophisticated is the Canny edge detector.Canny [2] designed an optimal edge detector for images which are corrupted with noise. He suggested that a Gaussian filter be applied to the image and edges be sought in the smoothed image. The directional derivative of the Gaussian is obtained, then convolved with the image. The direction, n, involved is normal to the edge direction. Edges are assumed to exist where the result is a local extreme, i.e., where∂2 (g * f) = 0.(0.1)_____∂n2In the above, g(x, y) is the Gaussian, f (x, y) is the image function and The direction of n is an estimate of the direction of the gradient of the true edge. In this thesis, we discuss the computational algorithm of the Canny edge detector and its implementation. Our experimental results show that the Canny edge detection scheme is robust enough to perform well over a wide range of signal-to-noise ratios. In most cases the Canny edge detector performs much better than the other edge detectors. / Department of Mathematical Sciences

Proefschrift--Utrecht. / "Stellingen": [2] p. laid in.

Proefschrift--Utrecht. / "Stellingen": [2] p. laid in.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 61).

L'instabilité du drapeau et la nage des poissons sont deux des problèmes d'interaction entièrement couplés fluide-structure. Ils peuvent être considérés comme l’ interaction entre la structure déformable (plaque) et un écoulement de grand nombre de Reynolds. Si la plaque est allongée (petit rapport d’aspect), la théorie du corps élancé (Lighthill 1960) applique pour calculer la force de pression exercée sur la plaque par le fluide. Alors que pour une plaque avec une très grande envergure (grand rapport d’aspect), la théorie bidimensionnelle de l’aile instationnaire (Wu 1961) est utilisée pour modéliser la dynamique de l'écoulement. Cependant, aucun de ces deux modèles donne la force de pression précise agissant sur une plaque avec un rapport d'aspect intermédiaire. Généralement, l'écoulement entourant peut être modélisé par l'équation de Laplace (en termes de potentiel de vitesse) avec une condition aux limites de Neumann. Par la méthode de Green, le problème se réduit à une équation intégrale de surface portante (mathématiquement appelée l’équation intégrale de Fredholm de première espèce avec un noyau singulier). Le saut de potentiel peut être trouvé en inversant l'équation de surface portante, et la distribution de saut de pression peut être par conséquent obtenue en appliquant l'équation de Bernoulli instationnaire.Dans cette thèse, l'équation de surface portante est résolue numériquement par la méthode de surface portante à fréquence fixée. La méthode numérique proposée est validée par les modèles théoriques (théorie du corps élancé et 2D théorie de l’aile instationnaire). L'équation de surface portante est également résolue analytiquement dans la limite du petit rapport d’aspect, par la méthode de raccordement de développement asymptotique (Matched Asymptotic Expansion) ou encore la technique asymptotique proposée. La méthode analytique proposée donne la force de pression plus précise sur une surface avec un rapport d’aspect intermédiaire (de 0 à 0.5), par rapport à la théorie du corps élancé. Cela en fait est un bon candidat pour l'optimisation et le contrôle. Le modèle de fluide analytique proposée est ensuite couplé avec l'équation d’Euler-Bernoulli de poutre pour étudier l’ instabilité du drapeau. Nous étudions l'influence du rapport d'aspect et le ratio de masse sur la vitesse d'écoulement critique. Les résultats montrent de très bons accords à ceux de Eloy et al. 2007. Le modèle de fluide d'analyse proposée est également appliqué au problème de la nage des poissons. Une nouvelle formule de la moyenne de poussée est proposée, et une analyse qualitative sur la morphologie du poisson est effectuée. De ces études, nous pouvons conclure que le modèle proposé fluide peut être considéré comme la théorie du corps élancé corrigée pour l'effet de rapport d'aspect. Ainsi, l'écoulement autour d'une surface de rapport d’aspect intermédiaire peut être inclus par ce modèle. / The flapping flag instability and fish swimming are two fully-coupled fluid-structure interaction problems. They can be considered as the interaction between a deformable structure (plate) and a high Reynolds number flow. If the plate is elongated (small aspect ratio), Slender-body theory (Lighthill 1960) applies to calculate the pressure force exerted on the plate by the surrounding flow. While for a plate with very large span (large aspect ratio), 2D unsteady airfoil theory (Wu 1961) is used to model the dynamics of the surrounding flow. However, none of these two models gives accurate pressure force acting on a plate with intermediate aspect ratio. Generally, the surrounding flow can be modeled by the Laplace equation (in terms of velocity potential) with a Neumann boundary condition. By means of Green representation theorem, the problem reduces to a lifting-surface integral equation (mathematically called Fredholm integral equation of first kind with a singular kernel). The potential jump can be found by inverting this lifting-surface equation, and the pressure jump distribution can be therefore obtained by applying unsteady Bernoulli equation. In this thesis, the lifting-surface equation is solved numerically through the fixed-frequency lifting-surface method. The proposed numerical method is validated by the theoretical models (Slender-body theory and 2D unsteady airfoil theory). The lifting-surface equation is also solved analytically in the limit of small aspect ratio, by the Matched Asymptotic Expansion method or alternatively the proposed asymptotic technique. The proposed analytical method gives more accurate pressure force on a surface with intermediate aspect ratio (ranging from 0 to 0.5), comparing to Slender-body theory. This makes it a good candidate for the optimization and control. The proposed analytical fluid model is then coupled with Euler-Bernoulli beam equation to study the flapping flag instability. We investigate the influence of plate aspect ratio and mass ratio on the critical flow velocity. The results show very good agreements to those of Eloy et al. 2007. The proposed analytical fluid model is also applied to the fish swimming problem. A new formula of mean thrust is proposed, and a qualitative analysis on the fish morphology is performed. From these studies, we can conclude that the proposed fluid model can viewed as Slender-body theory corrected for the aspect ratio effect. Thus, the flow surrounding a lifting-surface with intermediate aspect ratio can be included by this model

In chapter I known asymptotic forms and expansions of the hypergeometric function obtained by Erdélyi [5], Hapaev [10,11], Knottnerus [15L Sommerfeld [25] and Watson [28] are discussed. Also the asymptotic expansions of the hypergeometric function occurring in gas-flow theory will be discussed. These expansions were obtained by Cherry [1,2], Lighthill [17] and Seifert [2J]. Moreover, using a paper by Thorne [28] asymptotic expansions of ₂F₁(p+1, -p; 1-m; (1-t)/2), -1 < t < 1, and ₂P₁( (p+m+2)/2, (p+m+1)/2; p+ 3/2-, t⁻² ), t > 1, are obtained as p-»» and m = -(p+ 1/2)a, where a is fixed and 0 < a < 1. The : expansions are in terms of Airy functions of the first kind. The hypergeometric equation is normalized in chapter II. It readily yields the two turning points t₁, i = 1,2. If we consider,the case the a=b is a large real parameter of the hypergeometric function ₂F₁(a,b; c; t), then the turning points coalesce with the regular singularities t = 0 and t = ∞ of the hypergeometric equation as | a | →∞. In chapter III new asymptotic forms are found for this particular case; that is, for ₂F₁ (a, a; c;t) , 0 < T₁ ≤ t < 1, and ₂F₁ (a,a+1-c; 1; t⁻¹), 1 < t ≤ T₂ < ∞ , as –a → ∞ . The asymptotic form is in terms of modified Bessel functions of order 1/2. Asymptotic expansions can be obtained in a similar manner. Furthermore, a new asymptotic form is derived for ₂F₁ (c-a, c-a; c; t), 0 < T₁ ≤ t < 1, as –a → ∞, this result then leads to a sharper estimate on the modulus of n-th order derivatives of holomorphic functions as n becomes large. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis deals with two topics in asymptotic statistics. A concept of asymptotic optimality for sequential tests of statistical hypotheses is introduced. Sequential Probability Ratio Tests are shown to have asymptotic optimality properties corresponding to their usual optimality properties. Secondly, the asymptotic power of Pearson's chi-square test for goodness of fit is derived in a new way. The main tool for evaluating asymptotic performance of tests is the likelihood ratio of two hypotheses. In situations examined here the likelihood ratio based on a sample of size ⁿ has a limiting distribution as ⁿ → ∞ and the limit is also a likelihood ratio. To calculate limiting values of various performance criteria of statistical tests the calculations can be made using the limiting likelihood ratio. / Science, Faculty of / Statistics, Department of / Graduate

<p> This thesis is concerned with investigating point processes and the numerous methods available for obtaining information about them. </p> / Thesis / Master of Science (MSc)

No description available.

The asymptotic behaviour of nonoscillatory solutions of second order nonlinear ordinary differential equations is studied. Necessary and sufficient conditions are given for the existence of positive solutions with specified asymptotic behaviour at infinity. Existence of nonoscillatory solutions is established using the Schauder-Tychonoff fixed point theorem. Techniques such as factorization of linear disconjugate operators are employed to reveal the similar nature of asymptotic solutions of nonlinear differential equations to that of linear equations. Some examples illustrating the asymptotic theory of ordinary differential equations are given. / Science, Faculty of / Mathematics, Department of / Graduate