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Rotation, Scale And Translation Invariant Automatic Target Recognition Using Template Matching For Satellite ImageryErturk, Alp 01 January 2010 (has links) (PDF)
In this thesis, rotation, scale and translation (RST) invariant automatic target recognition (ATR) for satellite imagery is presented. Template matching is used to realize the target recognition. However, unlike most of the studies of template matching in the literature, RST invariance is required in our problem, since most of the time we will have only a small number of templates of each target, while the targets to be recognized in the scenes will have various orientations, scaling and translations. RST invariance is studied in detail and implemented with some of the competing methods in the literature, such as Fourier-Mellin transform and bipectrum combined with log-polar mapping. Phase correlation and normalized cross-correlation are used as similarity metrics. Encountered drawbacks were overcome with additional operations and modifications of the algorithms. ATR using reconstruction of the target image with respect to the template, based on bispectrum, log-polar mapping and phase correlation outperformed the other methods and successful recognition was realized for various target types, especially for targets on relatively simpler backgrounds, i.e. containing little or no other objects.
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Dirichlė L funkcijų Melino transformacijos / Mellin transforms of Dirichlet L- functionsBalčiūnas, Aidas 09 December 2014 (has links)
Disertacijoje gautas Dirichlė L funkcijų modifikuotosios Melino transformacijos pratęsimas į visą kompleksinę plokštumą. / In the thesis a meremorphic continuation of Dirichlet L- functions to the whole complex plane have been obtained.
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Mellin transforms of Dirichlet L-functions / Dirichlė L funkcijų Melino transformacijosBalčiūnas, Aidas 09 December 2014 (has links)
In the thesis moromorphic continuation of modified Mellin transforms of Dirichlet L-functions to the whole complex plane have been obtained. / Disertacijoje gauta modifikuotosios Melino transformacijos L- funkcijai meromorfinis pratęsimas į visą kompleksinę plokštumą.
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The Rare Decay of the Neutral Pion into a DielectronGhaderi, Hazhar January 2013 (has links)
We give a rather self-contained introduction to the rare pion to dielectron decay which in nontrivial leading order is given by a QED triangle loop. We work within the dispersive framework where the imaginary part of the amplitude is obtained via the Cutkosky rules. We derive these rules in detail. Using the twofold Mellin-Barnes representation for the pion transition form factor, we derive a simple expression for the branching ratio B(π0 <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Crightarrow" /> e+e-) which we then test for various models. In particular a more recent form factor derived from a Lagrangian for light pseudoscalars and vector mesons inspired by effective field theories. Comparison with the KTeV experiment at Fermilab is made and we find that we are more than 3σ below the KTeV experiment for some of the form factors. This is in agreement with other theoretical models, such as the Vector Meson Dominance model and the quark-loop model within the constituent-quark framework. But we also find that we can be in agreement with KTeV if we explore some freedom of the form factor not fixed by the low-energy Lagrangian.
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Moments des fonctions thêta / Moments of theta functionsMunsch, Marc 12 December 2013 (has links)
On s’intéresse dans cette thèse à l’étude des fonctions thêta intervenant dans la preuve de l’équation fonctionnelle des fonctions L de Dirichlet. En particulier, on adapte certains résultats obtenus dans le cadre des fonctions L au cas des fonctions thêta. S. Chowla a conjecturé que les fonctions L de Dirichlet associées à des caractères χ primitifs ne doivent pas s’annuler au point central de leur équation fonctionnelle. De façon analogue, il est conjecturé que les fonctions thêta ne s'annulent pas au point 1. Dans le but de prouver cette conjecture pour beaucoup de caractères, on étudie les moments de fonctions thêta dans plusieurs familles. On se focalise sur deux familles importantes. La première considérée est l’ensemble des caractères de Dirichlet modulo p où p est un nombre premier. On prouve des formules asymptotiques pour les moments d'ordre 2 et 4 en se ramenant à des problèmes de nature diophantienne. La seconde famille considérée est celle des caractères primitifs et quadratiques associés à des discriminants fondamentaux d inférieurs à une certaine borne fixée. On donne une formule asymptotique pour le premier moment et une majoration pour le moment d'ordre 2 en utilisant des techniques de transformée de Mellin ainsi que des estimations sur les sommes de caractères. Dans les deux cas, on en déduit des résultats de non-annulation des fonctions thêta. On propose également un algorithme qui, pour beaucoup de caractères, se révèle en pratique efficace pour prouver la non-annulation sur l'axe réel positif des fonctions thêta ce qui entraîne la non-annulation sur le même axe des fonctions L associées. / In this thesis, we focus on the study of theta functions involved in the proof of the functional equation of Dirichlet L- functions. In particular, we adapt some results obtained for L-functions to the case of theta functions. S. Chowla conjectured that Dirichlet L- functions associated to primitive characters χ don’t vanish at the central point of their functional equation. In a similar way to Chowla’s conjecture, it is conjectured that theta functions don't vanish at the central point of their functional equation for each primitive character. With the aim of proving this conjecture for a lot of characters, we study moments of theta functions in various families. We concentrate on two important families. The first one which we consider is the family of all Dirichlet characters modulo p where p is a prime number. In this case, we prove asymptotic formulae for the second and fourth moment of theta functions using diophantine techniques. The second family which we consider is the set of primitive quadratic characters associated to a fundamental discriminant less than a fixed bound. We give an asymptotic formula for the first moment and an upper bound for the second moment using techniques of Mellin transforms and estimation of character sums. In both cases, we deduce some results of non-vanishing. We also give an algorithm which, in practice, works well for a lot of characters to prove the non-vanishing of theta functions on the positive real axis. In this case, this implies in particular that the associated L-functions don’t vanish on the same axis.
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Asymptotic Analysis of the kth Subword ComplexityLida Ahmadi (6858680) 02 August 2019 (has links)
<div>The Subword Complexity of a character string refers to the number of distinct substrings of any length that occur as contiguous patterns in the string. The kth Subword Complexity in particular, refers to the number of distinct substrings of length k in a string of length n. In this work, we evaluate the expected value and the second factorial moment of the kth Subword Complexity for the binary strings over memory-less sources. We first take a combinatorial approach to derive a probability generating function for the number of occurrences of patterns in strings of finite length. This enables us to have an exact expression for the two moments in terms of patterns' auto-correlation and correlation polynomials. We then investigate the asymptotic behavior for values of k=a log n. In the proof, we compare the distribution of the kth Subword Complexity of binary strings to the distribution of distinct prefixes of independent strings stored in a trie. </div><div>The methodology that we use involves complex analysis, analytical poissonization and depoissonization, the Mellin transform, and saddle point analysis.</div>
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[en] EXPLORATION AND VISUAL MAPPING ALGORITHMS DEVELOPMENT FOR LOW COST MOBILE ROBOTS / [pt] DESENVOLVIMENTO DE ALGORITMOS DE EXPLORAÇÃO E MAPEAMENTO VISUAL PARA ROBÔS MÓVEIS DE BAIXO CUSTOFELIPE AUGUSTO WEILEMANN BELO 16 October 2006 (has links)
[pt] Ao mesmo tempo em que a autonomia de robôs pessoais e
domésticos
aumenta, cresce a necessidade de interação dos mesmos com
o ambiente. A
interação mais básica de um robô com o ambiente é feita
pela percepção deste e
sua navegação. Para uma série de aplicações não é prático
prover modelos
geométricos válidos do ambiente a um robô antes de seu
uso. O robô necessita,
então, criar estes modelos enquanto se movimenta e percebe
o meio em que está
inserido através de sensores. Ao mesmo tempo é necessário
minimizar a
complexidade requerida quanto a hardware e sensores
utilizados. No presente
trabalho, um algoritmo iterativo baseado em entropia é
proposto para planejar
uma estratégia de exploração visual, permitindo a
construção eficaz de um modelo
em grafo do ambiente. O algoritmo se baseia na
determinação da informação
presente em sub-regiões de uma imagem panorâmica 2-D da
localização atual do
robô obtida com uma câmera fixa sobre o mesmo. Utilizando
a métrica de
entropia baseada na Teoria da Informação de Shannon, o
algoritmo determina nós
potenciais para os quais deve se prosseguir a exploração.
Através de procedimento
de Visual Tracking, em conjunto com a técnica SIFT (Scale
Invariant Feature
Transform), o algoritmo auxilia a navegação do robô para
cada nó novo, onde o
processo é repetido. Um procedimento baseado em
transformações invariáveis a
determinadas variações espaciais (desenvolvidas a partir
de Fourier e Mellin) é
utilizado para auxiliar o processo de guiar o robô para
nós já conhecidos. Também
é proposto um método baseado na técnica SIFT. Os processos
relativos à obtenção
de imagens, avaliação, criação do grafo, e prosseguimento
dos passos citados
continua até que o robô tenha mapeado o ambiente com nível
pré-especificado de
detalhes. O conjunto de nós e imagens obtidos são
combinados de modo a se criar
um modelo em grafo do ambiente. Seguindo os caminhos, nó a
nó, um robô pode
navegar pelo ambiente já explorado. O método é
particularmente adequado para
ambientes planos. As componentes do algoritmo proposto
foram desenvolvidas e
testadas no presente trabalho. Resultados experimentais
mostrando a eficácia dos
métodos propostos são apresentados. / [en] As the autonomy of personal service robotic systems
increases so has their
need to interact with their environment. The most basic
interaction a robotic agent
may have with its environment is to sense and navigate
through it. For many
applications it is not usually practical to provide robots
in advance with valid
geometric models of their environment. The robot will need
to create these models
by moving around and sensing the environment, while
minimizing the complexity
of the required sensing hardware. This work proposes an
entropy-based iterative
algorithm to plan the robot´s visual exploration strategy,
enabling it to most
efficiently build a graph model of its environment. The
algorithm is based on
determining the information present in sub-regions of a 2-
D panoramic image of
the environment from the robot´s current location using a
single camera fixed on
the mobile robot. Using a metric based on Shannon s
information theory, the
algorithm determines potential locations of nodes from
which to further image the
environment. Using a Visual Tracking process based on SIFT
(Scale Invariant
Feature Transform), the algorithm helps navigate the robot
to each new node,
where the imaging process is repeated. An invariant
transform (based on Fourier
and Mellin) and tracking process is used to guide the
robot back to a previous
node. Also, an SIFT based method is proposed to accomplish
such task. This
imaging, evaluation, branching and retracing its steps
continues until the robot has
mapped the environment to a pre-specified level of detail.
The set of nodes and
the images taken at each node are combined into a graph to
model the
environment. By tracing its path from node to node, a
service robot can navigate
around its environment. This method is particularly well
suited for flat-floored
environments. The components of the proposed algorithm
were developed and
tested. Experimental results show the effectiveness of the
proposed methods.
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Fast Registration of Tabular Document Images Using the Fourier-Mellin TransformHutchison, Luke Alexander Daysh 24 March 2004 (has links)
Image registration, the process of finding the transformation that best maps one image to another, is an important tool in document image processing. Having properly-aligned microfilm images can help in manual and automated content extraction, zoning, and batch compression of images. An image registration algorithm is presented that quickly identifies the global affine transformation (rotation, scale, translation and/or shear) that maps one tabular document image to another, using the Fourier-Mellin Transform. Each component of the affine transform is recovered independantly from the others, dramatically reducing the parameter space of the problem, and improving upon standard Fourier-Mellin Image Registration (FMIR), which only directly separates translation from the other components. FMIR is also extended to handle shear, as well as different scale factors for each document axis. This registration method deals with all transform components in a uniform way, by working in the frequency domain. Registration is limited to foreground pixels (the document form and printed text) through the introduction of a novel, locally adaptive foreground-background segmentation algorithm, based on the median filter. The background removal algorithm is also demonstrated as a useful tool to remove ambient signal noise during correlation. Common problems with FMIR are eliminated by background removal, meaning that apodization (tapering down to zero at the edge of the image) is not needed for accurate recovery of the rotation parameter, allowing the entire image to be used for registration. An effective new optimization to the median filter is presented. Rotation and scale parameter detection is less susceptible to problems arising from the non-commutativity of rotation and "tiling" (periodicity) than for standard FMIR, because only the regions of the frequency domain directly corresponding to tabular features are used in registration. An original method is also presented for automatically obtaining blank document templates from a set of registered document images, by computing the "pointwise median" of a set of registered documents. Finally, registration is demonstrated as an effective tool for predictive image compression. The presented registration algorithm is reliable and robust, and handles a wider range of transformation types than most document image registration systems (which typically only perform deskewing).
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Un théorème de Gallagher pour la fonction de Möbius / A Gallagher theorem for the Moebius functionBetah, Mohamed Haye 29 November 2018 (has links)
La fonction de Möbius est définie par$$\mu(n)= \begin{cases} 1 & \textit{si $n=1$},\\ (-1)^k& \textit{si n est le produit de k nombres premiers distincts,}\\ 0 & \textit{si n contient un facteur carré. } \end{cases}$$Nous avons démontré que pour $x \ge \exp( 10^9) $ et $h=x^{1-\frac{1}{16000}}$, il existe dans chaque intervalle $[x-h,x]$ des entiers $n_1$ avec $\mu(n_1)=1$ et des entiers $n_2$ avec $\mu(n_2)=-1$.\\Ce résultat est une conséquence d'un résultat plus général.\\Pour $x \ge \exp(4\times 10^6)$, $\frac{1}{\sqrt{\log x}} \le \theta \le \frac{1}{2000}$, $h=x^{1-\theta}$ et $Q=(x/h)^{\frac{1}{20}}$, nous avons \\$$\sum_{q \leq Q} \log(Q/q)\sum_{\chi mod q}^*\left| \sum_{x.-h\le n \le x} \mu(n) \chi(n) \right| \leq 10^{20} h \theta \log(x) \exp( \frac{-1}{300 \theta}); $$la somme $\sum^*$ portant sur les caractères primitifs sauf l'éventuel caractère exceptionnel.\\Et en particulier pour $x \ge \exp( 10^9)$,$$ \left | \sum_{x.-x^{1-\frac{1}{16000}}\le n \le x} \mu(n) \right | \le \frac{1}{100} x^{1-\frac{1}{16000}}.\\$$ / The Möbius function is defined by$$\mu(n)= \begin{cases} 1 & \textit{if $n=1$},\\ (-1)^k& \textit{if n is a product of k distinct prime numbers,}\\ 0 & \textit{if n contains a square factor. } \end{cases}$$We demonstrate that for $x \ge \exp( 10^9) $ and $h=x^{1-\frac{1}{16000}}$, it exists in each interval $[x-h,x]$ integers $n_1$ with $\mu(n_1)=1$ and integers $n_2$ with $\mu(n_2)=-1$.\\This result is a consequence of a more general result. \\For $x \ge \exp(4\times 10^6)$, $\frac{1}{\sqrt{\log x}} \le \theta \le \frac{1}{2000}$, $h=x^{1-\theta}$ et $Q=(x/h)^{\frac{1}{20}}$, we have \\ $$\sum_{q \leq Q} \log(Q/q)\sum_{\chi mod q}^*\left| \sum_{x-h \le n \le x} \mu(n) \chi(n) \right| \leq 10^{20} h \theta \log(x) \exp( \frac{-1}{300 \theta}); $$the sum $\sum^*$ relating to primitive characters except for possible exceptional character.\\And in particular for $x \ge \exp( 10^9)$,$$\left | \sum_{x-.x^{1-\frac{1}{16000}}\le n \le x} \mu(n) \right | \le \frac{1}{100} x^{1-\frac{1}{16000}}.$$
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Contributions à l'amélioration de la performance des conditions aux limites approchées pour des problèmes de couche mince en domaines non réguliers / Contributions to the performance’s improvement of approximate boundary conditions for problems with thin layer in corner domainAuvray, Alexis 02 July 2018 (has links)
Les problèmes de transmission avec couche mince sont délicats à approcher numériquement, en raison de la nécessité de construire des maillages à l’échelle de la couche mince. Il est courant d’éviter ces difficultés en usant de problèmes avec conditions aux limites approchées — dites d’impédance. Si l’approximation des problèmes de transmission par des problèmes d’impédance s’avère performante dans le cas de domaines réguliers, elle l’est beaucoup moins lorsque ceux-ci comportent des coins ou arêtes. L’objet de cette thèse est de proposer de nouvelles conditions d’impédance, plus performantes, afin de corriger cette perte de performance. Pour cela, les développements asymptotiques des différents problèmes-modèles sont construits et étudiés afin de localiser avec précision l’origine de la perte, en lien avec les profils singuliers associés aux coins et arêtes. De nouvelles conditions d’impédance sont construites, de type Robin multi-échelle ou Venctel. D’abord étudiées en dimension 2, elles sont ensuite généralisées à certaines situations en dimension 3. Des simulations viennent confirmer l’efficience des méthodes théoriques. / Transmission problems with thin layer are delicate to approximate numerically, because of the necessity to build meshes on the scale of the thin layer. It is common to avoid these difficulties by using problems with approximate boundary conditions — also called impedance conditions. Whereas the approximation of transmission problems by impedance problems turns out to be successful in the case of smooth domains, the situation is less satisfactory in the presence of corners and edges. The goal of this thesis is to propose new impedance conditions, more efficient, to correct this lack of performance. For that purpose, the asymptotic expansions of the various models -problems are built and studied to locate exactly the origin of the loss, in connection with the singular profiles associated to corners and edges. New impedance conditions are built, of multi-scale Robin or Venctel types. At first studied in dimension 2, they are then generalized in certain situations in dimension 3. Simulations have been carried out to confirm the efficiency of the theoretical methods to some.
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