Throughout the decades, different techniques have been proposed to improve the depth-of-focus in optical microscopy. Common techniques like optical sectioning microscopy and scanning confocal microscopy have innate problems. By simply modifying the pupil function in microscope imaging system, we can also extend the depth-of-focus. The scanning system with a thin annular pupil has a high depth-of-focus and can scan the whole object, but the output light is too dim to be detected well by a photodetector. In this thesis, we propose a scanning technique employing an optical heterodyne scanning system using a difference-of-Gaussians (DoG) pupil. The object is illuminated by the combined beam which consists of two Gaussian beams with different waists, frequencies, and amplitudes. This system does not block most light like the annular pupil system and can obtain high depth-of-focus. The main objective of the thesis is to extend the depth-of-focus using the proposed system. The depth-of-focus characteristics of the DoG pupil function are examined and compared with those of well-known functions such as the circular, annular, and Gaussian pupils. / Master of Science

Este trabalho mostra que a suavização Gaussiana pode exercer outra função além da filtração. Considerando-se imagens binárias, este processo pode funcionar como uma espécie de marcador, que modifica as feições das fronteiras entre duas regiões homogêneas contrastantes. Tais feições são pontos de concavidades, de convexidades ou de bordas em linha reta. Ou seja, toda a informação necessária para se caracterizar a forma bidimensional de uma região. A quantidade de suavização realizada em cada ponto depende da configuração preto/branco que compõe a vizinhança onde este se situa. Isto significa que cada ponto sofre uma quantidade particular de modificação, a qual reflete a interface local entre o objeto e o fundo. Então, para detectar tais feições, basta quantificar a suavização em cada ponto. No entanto, a discriminação pixel a pixel exige que a distribuição Gaussiana apresente boa localização, o que só acontece em escalas muito baixas (σ≅0,5). Assim, propõe-se uma distribuição construída a partir da soma de duas Gaussianas. Uma é bem estreita para garantir a boa localização e a outra possui abertura irrestrita para representar a escala desejada. Para confirmar a propriedade de marcação dessa distribuição, são propostos três detectores de corners de contorno, os quais são aplicados à detecção de pontos dominantes. O primeiro utiliza a entropia de Shannon para quantificar a suavização em cada ponto. O segundo utiliza as probabilidades de objeto e de fundo contidos na vizinhança observada. O terceiro utiliza a diferença entre Gaussianas (DoG) para determinar a quantidade suavizada, porém com a restrição de que uma das versões da imagem tenha suavização desprezível, para garantir a boa localização. Este trabalho se fundamenta na física da luz e na visão biológica. Os ótimos resultados apresentados sugerem que a detecção de curvaturas do sistema visual pode ocorrer na retina. / This work shows that the Gaussian smoothing can have additional function to filtration. Considering the binary images, this process can operate as a kind of marker that changes the features of the boundaries between two contrasting homogeneous regions. These features are points of concavities, convexities or straight edges, which are all the necessary information to characterize the two-dimensional shape of a region. The amount of smoothing performed at each point depends on the black/white configuration that composes the neighborhood where the point is located. This means that each point suffers a particular modification, which reflects the local interface between object and background. Thus, to detect such features, one must quantify the smoothing at each point. However, pixel-wise discrimination requires that the Gaussian distribution does not suffer flattening, which occurs in very low scales (σ≅0.5), only. Thus, it is proposed a distribution built from the sum of two Gaussians. One must be very narrow to ensure good localization, and the other is free to represent the desired scale. To confirm the property of marking, three boundary based corner detectors are proposed, which are applied to the detection of dominant points. The first uses the Shannon\'s entropy to quantify the smoothing at each point. The second uses the probabilities of object and background contained in the local neighborhood. The third uses the difference of Gaussians (DoG) to determine the amount of smoothing. This Work relies on the physics of light and biological vision. The presented results are good enough to suggest that the curvature detection, in visual system, occurs in the retina.

Este trabalho mostra que a suavização Gaussiana pode exercer outra função além da filtração. Considerando-se imagens binárias, este processo pode funcionar como uma espécie de marcador, que modifica as feições das fronteiras entre duas regiões homogêneas contrastantes. Tais feições são pontos de concavidades, de convexidades ou de bordas em linha reta. Ou seja, toda a informação necessária para se caracterizar a forma bidimensional de uma região. A quantidade de suavização realizada em cada ponto depende da configuração preto/branco que compõe a vizinhança onde este se situa. Isto significa que cada ponto sofre uma quantidade particular de modificação, a qual reflete a interface local entre o objeto e o fundo. Então, para detectar tais feições, basta quantificar a suavização em cada ponto. No entanto, a discriminação pixel a pixel exige que a distribuição Gaussiana apresente boa localização, o que só acontece em escalas muito baixas (σ≅0,5). Assim, propõe-se uma distribuição construída a partir da soma de duas Gaussianas. Uma é bem estreita para garantir a boa localização e a outra possui abertura irrestrita para representar a escala desejada. Para confirmar a propriedade de marcação dessa distribuição, são propostos três detectores de corners de contorno, os quais são aplicados à detecção de pontos dominantes. O primeiro utiliza a entropia de Shannon para quantificar a suavização em cada ponto. O segundo utiliza as probabilidades de objeto e de fundo contidos na vizinhança observada. O terceiro utiliza a diferença entre Gaussianas (DoG) para determinar a quantidade suavizada, porém com a restrição de que uma das versões da imagem tenha suavização desprezível, para garantir a boa localização. Este trabalho se fundamenta na física da luz e na visão biológica. Os ótimos resultados apresentados sugerem que a detecção de curvaturas do sistema visual pode ocorrer na retina. / This work shows that the Gaussian smoothing can have additional function to filtration. Considering the binary images, this process can operate as a kind of marker that changes the features of the boundaries between two contrasting homogeneous regions. These features are points of concavities, convexities or straight edges, which are all the necessary information to characterize the two-dimensional shape of a region. The amount of smoothing performed at each point depends on the black/white configuration that composes the neighborhood where the point is located. This means that each point suffers a particular modification, which reflects the local interface between object and background. Thus, to detect such features, one must quantify the smoothing at each point. However, pixel-wise discrimination requires that the Gaussian distribution does not suffer flattening, which occurs in very low scales (σ≅0.5), only. Thus, it is proposed a distribution built from the sum of two Gaussians. One must be very narrow to ensure good localization, and the other is free to represent the desired scale. To confirm the property of marking, three boundary based corner detectors are proposed, which are applied to the detection of dominant points. The first uses the Shannon\'s entropy to quantify the smoothing at each point. The second uses the probabilities of object and background contained in the local neighborhood. The third uses the difference of Gaussians (DoG) to determine the amount of smoothing. This Work relies on the physics of light and biological vision. The presented results are good enough to suggest that the curvature detection, in visual system, occurs in the retina.

Correspondance de forme est un problème fondamental dans de nombreuses disciplines de recherche, tels que la géométrie algorithmique, vision par ordinateur et l'infographie. Communément définie comme un problème de trouver injective/ multivaluée correspondance entre une source et une cible, il constitue une tâche centrale dans de nombreuses applications y compris le transfert de attributes, récupération des formes etc. Dans récupération des formes, on peut d'abord calculer la correspondance entre la forme de requête et les formes dans une base de données, puis obtenir le meilleure correspondance en utilisant une mesure de qualité de correspondance prédéfini. Il est également particulièrement avantageuse dans les applications basées sur la modélisation statistique des formes. En encapsulant les propriétés statistiques de l'anatomie du sujet dans le model de forme, comme variations géométriques, des variations de densité, etc., il est utile non seulement pour l'analyse des structures anatomiques telles que des organes ou des os et leur variations valides, mais aussi pour apprendre les modèle de déformation de la classe d'objets. Dans cette thèse, nous nous intéressons à une enquête sur une nouvelle méthode d'appariement de forme qui exploite grande redondance de l'information à partir des ensembles de données dynamiques, variables dans le temps. Récemment, une grande quantité de recherches ont été effectuées en infographie sur l'établissement de correspondances entre les mailles statiques (Anguelov, Srinivasan et al. 2005, Aiger, Mitra et al. 2008, Castellani, Cristani et al. 2008). Ces méthodes reposent sur les caractéristiques géométriques ou les propriétés extrinsèques/intrinsèques des surfaces statiques (Lipman et Funkhouser 2009, Sun, Ovsjanikov et al. 2009, Ovsjanikov, Mérigot et al. 2010, Kim, Lipman et al., 2011) pour élaguer efficacement les paires. Bien que l'utilisation de la caractéristique géométrique est encore un standard d'or, les méthodes reposant uniquement sur l'information statique de formes peuvent générer dans les résultats de correspondance grossièrement trompeurs lorsque les formes sont radicalement différentes ou ne contiennent pas suffisamment de caractéristiques géométriques. [...] / 3D geometry modelling tools and 3D scanners become more enhanced and to a greater degree affordable today. Thus, development of the new algorithms in geometry processing, shape analysis and shape correspondence gather momentum in computer graphics. Those algorithms steadily extend and increasingly replace prevailing methods based on images and videos. Non-rigid shape correspondence or deformable shape matching has been a long-studied subject in computer graphics and related research fields. Not to forget, shape correspondence is of wide use in many applications such as statistical shape analysis, motion cloning, texture transfer, medical applications and many more. However, robust and efficient non-rigid shape correspondence still remains a challenging task due to fundamental variations between individual subjects, acquisition noise and the number of degrees of freedom involved in correspondence search. Although dynamic 2D/3D intra-subject shape correspondence problem has been addressed in the rich set of previous methods, dynamic inter-subject shape correspondence received much less attention. The primary purpose of our research is to develop a novel, efficient, robust deforming shape analysis and correspondence framework for animated meshes based on their dynamic and motion properties. We elaborate our method by exploiting a profitable set of motion data exhibited by deforming meshes with time-varying embedding. Our approach is based on an observation that a dynamic, deforming shape of a given subject contains much more information rather than a single static posture of it. That is different from the existing methods that rely on static shape information for shape correspondence and analysis.Our framework of deforming shape analysis and correspondence of animated meshes is comprised of several major contributions: a new dynamic feature detection technique based on multi-scale animated mesh’s deformation characteristics, novel dynamic feature descriptor, and an adaptation of a robust graph-based feature correspondence approach followed by the fine matching of the animated meshes. [...]

In the early days of computer graphics, research was mainly driven by the goal to create realistic synthetic imagery. By contrast, non-photorealistic computer graphics, established as its own branch of computer graphics in the early 1990s, is mainly motivated by concepts and principles found in traditional art forms, such as painting, illustration, and graphic design, and it investigates concepts and techniques that abstract from reality using expressive, stylized, or illustrative rendering techniques. This thesis focuses on the artistic stylization of two-dimensional content and presents several novel automatic techniques for the creation of simplified stylistic illustrations from color images, video, and 3D renderings. Primary innovation of these novel techniques is that they utilize the smooth structure tensor as a simple and efficient way to obtain information about the local structure of an image. More specifically, this thesis contributes to knowledge in this field in the following ways. First, a comprehensive review of the structure tensor is provided. In particular, different methods for integrating the minor eigenvector field of the smoothed structure tensor are developed, and the superiority of the smoothed structure tensor over the popular edge tangent flow is demonstrated. Second, separable implementations of the popular bilateral and difference of Gaussians filters that adapt to the local structure are presented. These filters avoid artifacts while being computationally highly efficient. Taken together, both provide an effective way to create a cartoon-style effect. Third, a generalization of the Kuwahara filter is presented that avoids artifacts by adapting the shape, scale, and orientation of the filter to the local structure. This causes directional image features to be better preserved and emphasized, resulting in overall sharper edges and a more feature-abiding painterly effect. In addition to the single-scale variant, a multi-scale variant is presented, which is capable of performing a highly aggressive abstraction. Fourth, a technique that builds upon the idea of combining flow-guided smoothing with shock filtering is presented, allowing for an aggressive exaggeration and an emphasis of directional image features. All presented techniques are suitable for temporally coherent per-frame filtering of video or dynamic 3D renderings, without requiring expensive extra processing, such as optical flow. Moreover, they can be efficiently implemented to process content in real-time on a GPU. / In den Anfängen der Computergrafik war die Forschung hauptsächlich von dem Anspruch getragen, realistisch aussehende synthetische Bilder zu erstellen. Im Gegensatz dazu ist die nicht-photorealistische Computergraphik, ein Untergebiet der Computergrafik, welches in den frühen 1990er Jahren gegründet wurde, vor allem motiviert durch Konzepte und Prinzipien der traditionellen Kunst wie Malerei, Illustration und Grafikdesign. Diese Arbeit beschäftigt sich mit der künstlerischen Verarbeitung von zweidimensionalen Bildinhalten und präsentiert mehrere neue automatische Verfahren für die Erstellung von vereinfachten künstlerischen Darstellungen von Farbbildern, Videos und 3D- Renderings. Wichtigste Neuerung dieser Techniken ist die Verwendung des Strukturtensors als eine einfache und effiziente Möglichkeit, Informationen über die lokale Struktur eines Bildes zu erhalten. Konkret werden die folgenden Beiträge gemacht. Erstens wird eine umfassende übersicht über den Strukturtensor gegeben. Insbesondere werden verschiedene Methoden für die Integration des kleineren Eigenvektorfeldes des geglätteten Strukturtensors entwickelt, und die Überlegenheit des geglätteten Strukturtensors gegenüber dem populären Edge-Tangent-Flow demonstriert. Zweitens werden separable Implementierungen des bilateralen Filters und des Difference of Gaussians Filters vorgestellt. Durch die Anpassung der Filter an die lokale Struktur des Bildes werden Bildfehler vermieden, wobei der Vorgang rechnerisch effizient bleibt. Zusammengenommen bieten beide Techniken eine effektive Möglichkeit, um einen Cartoon-ähnlichen Effekt zu erzielen. Drittens wird eine Verallgemeinerung des Kuwahara-Filters vorgestellt. Durch die Anpassung von Form, Umfang und Orientierung der Filter an die lokale Struktur werden Bildfehler verhindert. Außerdem werden direktionale Bildmerkmale besser berücksichtigt und betont, was zu schärferen Kanten und einem malerischen Effekt führt. Neben der single-scale Variante wird auch eine multi-scale Variante vorgestellt, welche im Stande ist, eine höhere Abstraktion zu erzielen. Viertens wird eine Technik vorgestellt, die auf der Kombination von flussgesteuerter Glättung und Schock-Filterung beruht, was zu einer intensiven Verstärkung und Betonung der direktionalen Bildmerkmale führt. Alle vorgestellten Techniken erlauben die zeitlich kohärente Verarbeitung von Einzelbildern eines Videos oder einer dynamischen 3D-Szene, ohne dass andere aufwendige Verfahren wie zum Beispiel die Berechnung des optischen Flusses, benötigt werden. Darüberhinaus können die Techniken effizient implementiert werden und ermöglichen die Verarbeitung in Echtzeit auf einem Grafikprozessor (GPU).