Resolver um problema de processamento de imagens pode ser uma tarefa bastante complexa. Em geral, isto depende de diversos fatores, como o conhecimento, experiência e intuição de um especialista, e o conhecimento do domínio da aplicação em questão. Motivados por tal complexidade, alguns grupos de pesquisa têm trabalhado na criação de técnicas para projetar operadores de imagens automaticamente, a partir de uma coleção de exemplos de entrada e saída do operador desejado. A abordagem multirresolução tem sido empregada com sucesso no projeto estatístico de W-operadores de janelas grandes. Esta metodologia usa uma estrutura piramidal de janelas para auxiliar na estimação das distribuições de probabilidade condicional para padrões não observados no conjunto de treinamento. No entanto, a qualidade do operador projetado depende diretamente da pirâmide escolhida. Tal escolha é feita pelo projetista a partir de sua intuição e de seu conhecimento prévio sobre o problema. Neste trabalho, investigamos o uso da entropia condicional como um critério para determinar automaticamente uma boa pirâmide a ser usada no projeto do W-operador. Para isto, desenvolvemos uma técnica que utiliza o arcabouço piramidal multirresolução como um modelo na estimação da distribuição conjunta de probabilidades. Experimentos com o problema de reconhecimento de dígitos manuscritos foram realizados para avaliar o desempenho do método. Utilizamos duas bases de dados diferentes, com bons resultados. Além disso, outra contribuição deste trabalho foi a experimentação com mapeamentos de resolução da teoria de pirâmides de imagens no contexto do projeto de W-operadores multirresolução. / The task of finding a good solution for an image processing problem is often very complex. It usually depends on the knowledge, experience and intuition of an image processing specialist. This complexity has served as a motivation for some research groups to create techniques for automatically designing image operators based on a collection of input and output examples of a desired operator. The multiresolution approach has been successfully used to statistically design W-operators for large windows. However, the success of this method directly depends on the adequate choice of a pyramidal window structure, which is used to aid in the estimation of the conditional probability distributions for patterns that do not appear in the training set. The choice is made by the designer, based on his intuition and previous knowledge of the problem domain. In this work, we investigate the use of the conditional entropy criterion for automatically determining a good pyramid. In order to compute the entropy, we have developed a technique that uses the multiresolution pyramidal framework as a model in the estimation of the joint probability distribution. The performance of the method is evaluated on the problem of handwritten digits recognition. Two different databases are used, with good practical results. Another important contribution of this work is the experimentation with resolution mappings from image pyramids theory in the context of multiresolution W-operator design.

Dans ce travail, nous étudions la répartition des chiffres des nombres premiers. Bourgain (2015) a obtenu une formule asymptotique pour le nombre de nombres premiers avec une proportion$c > 0$ de chiffres préassignés en base 2 ($c$ est une constante absolue non précisée).Nous généralisons ce résultat à toute base $g \geq 2$ et nousdonnons des valeurs explicites pour la proportion $c$ en fonction de $g$. En adaptant, développant et précisant la stratégie introduite par Bourgain dans le cas $g=2$, nous présentons une démonstration détaillée du cas général.La preuve est fondée sur la méthode du cercle et combine des techniques d’analyse harmonique avec des résultats sur les zéros des fonctions $L$ de Dirichlet, notamment une région sans zérotrès fine due à Iwaniec.Ce travail s'inscrit aussi dans l'étude des nombres premiers dans des ensembles << rares >>.Nous étudions également la répartition des << chiffres >> (au sens de Dartyge et S\'ark\"ozy) de quelques suites remarquables dans le contexte des corps finis. Ce concept de << chiffre >> est à la base de la représentation des corps finis dans les logiciels de calcul formel.Nous étudions des suites variées comme les suites polynomiales, les générateurs ou encore les produits d'éléments de deux ensembles assez grands. Les méthodes développées permettent d'obtenir des estimations explicites très précises voire optimales dans certains cas. Les sommes d'exponentielles sur les corps finis jouent un rôle essentiel dans les démonstrations.Les résultats obtenus peuvent être reformulés d'un point de vue plus algébrique avec la fonction trace qui est très importante dans l'étude des corps finis. / In this work, we study the distribution of prime numbers' digits. Bourgain (2015) obtained an asymptotic formula for the number of prime numbers with a proportion $c > 0$ of preassigned digits in base 2 ($c$ is an absolute constant not specified). We generalize this result in any base $g \geq 2$ and we provide explicit admissible values for the proportion $c$ depending on $g$.By adapting, developing and refining Bourgain's strategy in the case $g=2$, we present a detailed proof for the general case.The proof is based onthe circle method and combines techniques from harmonic analysis together with results onzeros of Dirichlet $L$-functions, notably a very sharp zero-free region due to Iwaniec.This work also falls within the study of prime numbers in sparse ``sets''.In addition, we study the distribution of the ``digits'' (in the sense of Dartyge and S\'ark\"ozy) of some sequences of interest in the context of finite fields. This concept of ``digits'' is fundamental in the representation of finite fields in computer algebra systems. We study various sequences such as polynomial sequences, generators as well as products of elements of two large enough sets.Our methods provide very sharp explicit estimates which are even optimal in some cases.Exponential sums over finite fields play an essential role in the proofs.Our results can be reformulated from a more algebraic point of view with the trace function which is of basic importance in the study of finite fields.

An acht isolierten Hinterbeinen gliedmaßengesunder Rinder wurden röntgen- und querschnittsanatomische Untersuchungen des Tarsus, Metatarsus und der Phalangen durchgeführt. Im Gegensatz zu anderen Tierarten gab es bisher für das Rind noch keine Erkenntnisse zur Interpretation von MRT-Befunden. Zur besseren Orientierung werden magnetresonanztomographische und anatomische Schnitte gegenübergestellt und bewertet. Es sind 23 transversale Ebenen in T1-gewichteten Sequenzen beschrieben worden. Die röntgenanatomischen Untersuchungen erfolgten immer in den beiden Standardebenen und für Sprunggelenk und Zehe zusätzlich in zwei schrägen Aufnahmerichtungen. Mit den Untersuchungen wurde nachgewiesen, dass die verwendeten Röntgenrichtungen für eine umfassende Darstellung von Knochen und Gelenken geeignet sind. Durch die verschiedenen Aufnahmerichtungen konnten die meisten Bereiche überlagerungsfrei herausprojiziert und der Beurteilung zugänglich gemacht werden. Fast alle anatomischen Strukturen wurden in der MRT-Untersuchung dargestellt und voneinander differenziert. Über den direkten Vergleich zum anatomischen Sägeschnitt zeichneten sich die MRT-Befunde durch einen sehr hohen Informationsgehalt aus. Das Magic Angle Phänomen konnte im Bereich von Sehnen und Bändern nachgewiesen werden. Die Aufzweigungen des Ramus profundus des N. plantaris lateralis konnten im Rahmen dieser Untersuchung bis in den mittleren Metatarsusbereich nachgewiesen werden. Sie sind bei anderen Tierarten als Nn. metatarsei plantares in der Nomenklatur zu finden. Ausgehend von einer sehr umfangreichen Literaturauswertung erfolgte eine umfassende Zusammenstellung des Erkenntnisstandes unter anatomischen und orthopädischen Gesichtspunkten. Die dabei zusammengetragenen Ergebnisse bilden eine entscheidende Grundlage für die Auswertung und Interpretation von Befunden der Hintergliedmaße des Rindes mit Hilfe der bildgebenden Diagnostik. / The study was based on the evaluation of eight hindlimbs from animals free from orthopedic disease. The tarsus, metatarsus and phalanges were examined radiographically and by MRI to characterize anatomical structures. Twenty-three transverse MRI sections of each limb were collected using T1 weighted images. Corresponding MRI and cross-section anatomical preparations were compared to optimize understanding of structural features. In addition to standard 0° and 90° views of the hindlimbs, oblique views of the tarsus and phalanges were made. Comparison of photographs and images was satifactory for the evaluation of bony structures without superimposition in most cases. MRI examination resulted in visualization and differentiation of tissues in almost every situation. The magic angle phenomenon was observed in areas of tendons and ligaments. The terminal branches of the R. profundus of the N. plantaris lateralis were discernable to the level of the middle of the metatarsus. These branches are described in other species as the Nn. metatarsei plantares. This work was undertaken to document anatomical findings and relationships which may be used as a resource for interpretation of images obtained from the hindlimbs of cattle using various diagnostic imaging modalities.

The hand has the highest surface area-to-volume ratio of any body part. This property offers the potential for the hand to serve an important function in thermoregulation through radiative heat loss. Theoretically, the capacity for heat loss may be influenced by hand and digit proportions, but the extent to which these proportions influence the hand's radiative properties remains under-investigated. Although hand morphology is highly constrained by both integration and functional dexterity, phenotypic variation in hand and digit proportions across human populations shows broad ecogeographic patterns. These patterns have been associated with climate adaptation. However, the theory linking climate adaptation to such ecogeographic patterns is based on underlying assumptions relating to thermodynamic principles, which have not been tested in vivo. This study sought to determine the influence of hand and digit proportions on heat loss from the hands directly, the additional anthropometric factors that may affect this relationship, and the impact of variation in hand proportions on dexterity in the cold. The relationship between hand proportions and thermoregulation was tested through both laboratory-based investigation and a field study. The laboratory investigation assessed the relationship between hand proportions and heat loss, the influence of body size and composition on this relationship, and the effect of morphological variation on manual dexterity. Participants (N=114; 18-50 years of age), underwent a 3-minute ice-water hand-immersion. Thermal imaging analysis was used to quantify heat loss. Hand and digit proportions were quantified using 2D and 3D scanning techniques; body size and composition were measured using established anthropometric methods and bio-impedance analysis. After accounting for body size, hand width, digit-to-palm length ratio, and skeletal muscle mass were significant predictors of heat loss from the hand, whilsthand length and fat mass were not. A separate set of participants (N=40) performed a Purdue pegboard dexterity test before and after the immersion test, which demonstrated that digit width alone negatively correlated with dexterity. The field study tested whether phenotypic variation in upper limb proportions could be attributed to cold adaptation or selection for dexterity in living populations exposed to significant energetic stress. Upper limb segment lengths were obtained from participants (N=254; 18-59 years of age), from highland and lowland regions of the Nepalese Himalayas using established anthropometric methods, and relative hand proportions were assessed in relation to severe energetic stress associated with life at high altitude. Relative to height, hand length and hand width were not reduced with altitude stress, whilst ulna length was. This indicates that cold adaptation is not shaping hand proportions in this case, although phenotypic variation in other limb segments may be attributed to cold adaptation or a thrifty phenotype mechanism. The current study provides empirical evidence to support the link between surface area-to-volume ratio, thermodynamic principles and ecogeographical patterns in human hand morphology. However, this research also demonstrates the complexity of the hand's role in thermoregulation; not only do other factors such as muscularity affect heat loss from the hand, but hand morphology is also highly constrained by integration and dexterity.