Chemnitz, Techn. Univ., Diplomarb., 2008.

The silhouette score is a widely used technique to evaluate the quality of a clustering result. One of the current issues with the silhouette score is its sensitivity to outliers, which can lead to misleading interpretations. This problem is caused by the silhouette score using the arithmetic mean to calculate the average intra and inter-cluster distances. To address this issue, three modified silhouette scores are presented: GenSil, TrimSil, and extended TrimSil, which replace the arithmetic mean with the generalized mean, the trimmed mean and a modified trimmed mean, respectively. Experiments on both simulated and real-world datasets show that GenSil is the most effective method, significantly reducing the impact of outliers and achieving high silhouette scores with negative parameter values. TrimSil also improves silhouette scores but performs worse than GenSil, while the extended TrimSil outperforms TrimSil but is still less effective than GenSil. To further aid in selecting the optimal number of clusters with these modified silhouette scores, a more straightforward visualization technique, the silhouette-parameter plot, is also introduced. / Thesis / Master of Science (MSc)

Two types of problems are studied in this thesis: reconstruction and visualization of polygons and polyhedra. <br /><br /> Three problems are considered in reconstruction of polygons and polyhedra, given a set of projection characteristics. The first problem is to reconstruct a closed convex polygon (polyhedron) given the number of visible edges (faces) from each of a set of directions <em>S</em>. The main results for this problem include the necessary and sufficient conditions for the existence of a polygon that realizes the projections. This characterization gives an algorithm to construct a feasible polygon when it exists. The other main result is an algorithm to find the maximum and minimum size of a feasible polygon for the given set <em>S</em>. Some special cases for non-convex polygons and for perspective projections are also studied. <br /><br /> For reconstruction of polyhedra, it is shown that when the projection directions are co-planar, a feasible polyhedron (i. e. a polyhedron satisfying the projection properties) can be constructed from a feasible polygon and vice versa. When the directions are covered by two planes, if the number of visible faces from each of the directions is at least four, then an algorithm is presented to decide the existence of a feasible polyhedron and to construct one, when it exists. When the directions see arbitrary number of faces, the same algorithm works, except for a particular sub-case. <br /><br /> A polyhedron is, in general, called equiprojective, if from any direction the size of the projection or the projection boundary is fixed, where the "size" means the number of vertices, edge, or faces. A special problem on reconstruction of polyhedra is to find all equiprojective polyhedra. For the case when the size is the number of vertices in the projection boundary, main results include the characterization of all equiprojective polyhedra and an algorithm to recognize them, and finding the minimum equiprojective polyhedra. Other measures of equiprojectivity are also studied. <br /><br /> Finally, the problem of efficient visualization of polyhedra under given constraints is considered. A user might wish to find a projection that highlights certain properties of a polyhedron. In particular, the problem considered is given a set of vertices, edges, and/or faces of a convex polyhedron, how to determine all projections of the polyhedron such that the elements of the given set are on the projection boundary. The results include efficient algorithms for both perspective and orthogonal projections, and improved adaptive algorithm when only edges are given and they form disjoint paths. A related problem of finding all projections where the given edges, faces, and/or vertices are not on the projection boundary is also studied.

A intenção do presente trabalho é conceituar roupa interior feminina com foco no século XIX. A partir da conceituação de roupa interior, e da pesquisa da roupa exterior, as peças internas serão identificadas e analisadas para compreender seu conceito como suporte do corpo. Com o estudo de imagens, catálogos, fotografias, revistas, livros, periódicos e manuais de construção de roupas, o trabalho destina-se ao entendimento do corpo modelado pela roupa interior, formadora das silhuetas do século XIX, analisando os suportes internos como influenciadores da forma do corpo e do comportamento no período / Conceptualizing underclothing for women is the main intention of this paper and such concept is focused in the Nineteenth Century. Based upon the conceptualization of underclothing and the research involving the usual outer clothing of the time, under pieces are identified and analyzed. Thus, it\'s possible to understand the role these pieces play as a concept for bodily support. Through the study of images, catalogs, photographies, magazines, books, journals and guides of garment manufacturing, this paper looks forward to understanding the body as modeled by underclothing (which helped shape the body in the Nineteenth Century) and to analyzing the inner supports as major influences in the social conduct and bodily shapes of that era

This work presents a novel technique for 2D human motion capture using a single non calibrated camera. The user's five extremities (head, hands and feet) are extracted, labelled and tracked after silhouette segmentation. As they are the minimal number of points that can be used in order to enable whole body gestural interaction, we will henceforth refer to these features as crucial points. The crucial point candidates are defined as the local maxima of the geodesic distance with respect to the center of gravity of the actor region which lie on the silhouette boundary. In order to disambiguate the selected crucial points into head, left and right foot, left and right hand classes, we propose a Bayesian method that combines a prior human model and the intensities of the tracked crucial points. Due to its low computational complexity, the system can run at real-time paces on standard Personal Computers, with an average error rate range between 2% and 7% in realistic situations, depending on the context and segmentation quality.

Two types of problems are studied in this thesis: reconstruction and visualization of polygons and polyhedra. <br /><br /> Three problems are considered in reconstruction of polygons and polyhedra, given a set of projection characteristics. The first problem is to reconstruct a closed convex polygon (polyhedron) given the number of visible edges (faces) from each of a set of directions <em>S</em>. The main results for this problem include the necessary and sufficient conditions for the existence of a polygon that realizes the projections. This characterization gives an algorithm to construct a feasible polygon when it exists. The other main result is an algorithm to find the maximum and minimum size of a feasible polygon for the given set <em>S</em>. Some special cases for non-convex polygons and for perspective projections are also studied. <br /><br /> For reconstruction of polyhedra, it is shown that when the projection directions are co-planar, a feasible polyhedron (i. e. a polyhedron satisfying the projection properties) can be constructed from a feasible polygon and vice versa. When the directions are covered by two planes, if the number of visible faces from each of the directions is at least four, then an algorithm is presented to decide the existence of a feasible polyhedron and to construct one, when it exists. When the directions see arbitrary number of faces, the same algorithm works, except for a particular sub-case. <br /><br /> A polyhedron is, in general, called equiprojective, if from any direction the size of the projection or the projection boundary is fixed, where the "size" means the number of vertices, edge, or faces. A special problem on reconstruction of polyhedra is to find all equiprojective polyhedra. For the case when the size is the number of vertices in the projection boundary, main results include the characterization of all equiprojective polyhedra and an algorithm to recognize them, and finding the minimum equiprojective polyhedra. Other measures of equiprojectivity are also studied. <br /><br /> Finally, the problem of efficient visualization of polyhedra under given constraints is considered. A user might wish to find a projection that highlights certain properties of a polyhedron. In particular, the problem considered is given a set of vertices, edges, and/or faces of a convex polyhedron, how to determine all projections of the polyhedron such that the elements of the given set are on the projection boundary. The results include efficient algorithms for both perspective and orthogonal projections, and improved adaptive algorithm when only edges are given and they form disjoint paths. A related problem of finding all projections where the given edges, faces, and/or vertices are not on the projection boundary is also studied.

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Cette thèse présente principalement des résultats sur la combinatoire des droites et segments qui apparaissent naturellement dans l'étude des problèmes de visibilité en trois dimensions. Nous exposons en premier lieu des résultats sur la taille de la silhouette d'un objet vu d'un point, c'est à dire sur la complexite de l'ensemble des droites ou segments tangents à l'objet et passant par le point. Nous présentons en particulier les premières bornes théoriques non triviales pour des polyèdres non-convexes, à savoir que, sous des hypothèses raisonnables, la complexité moyenne de la silhouette est au plus la racine carrée de la complexité du polyèdre, phénomène largement observé en infographie. Nous présentons aussi des bornes, en moyenne et dans le cas le pire, sur le nombre de droites et segments tangents à quatre objets dans une scène composée d'objets polyédriques ou sphériques. Ces bornes donnent en particulier l'espoir que la complexité des structures de données globales comme le complexe de visibilité ne soit pas nécessairement prohibitive. Les bornes sur les polytopes sont également les premières à tirer parti des propriétés structurelles des scènes composées de triangles organisés en polytopes de facon réaliste, c'est à dire non nécessairement disjoints. Ces bornes induisent enfin les premières bornes non triviales sur la complexité des ombres induites par des sources lumineuses non ponctuelles. Les résultats presentés dans cette thèse améliorent significativement l'état de l'art sur les propriétés combinatoires des structures de visibilité en trois dimensions et devraient favoriser les développements algorithmiques futurs pour ces problèmes.

In der Archäologie ist das Zeichnen von Fundobjekten ein zeitaufwändiger und daher kostenintensiver Prozess. Die Abbildungen sind wegen fehlender Standards sowie den unterschiedlichen persönlichen Stilen und Fähigkeiten der Zeichner subjektiv und stark inhomogen. Es gibt deswegen erste Ansätze, mithilfe von 3D-Scannern virtuelle Modelle zu erzeugen, von denen dann objektive, standardisierte Abbildungen extrahiert werden sollen. Von den zahlreichen Verfahren aus dem Bereich des Non-Photorealistic Rendering (NPR) kommen dafür insbesondere solche in Betracht, die Verzierungen und Oberflächeneigenschaften betonen. Auf Interaktion soll dabei nach Möglichkeit verzichtet werden.

<p>This dissertation presents a method capable of smoothing the silhouette of a 3D model using interpolation to find smooth edges. The method has as goal to be used with normal mapping to improve the performance and give a better result with a low polygonal count. To do this the lines located on the silhouette of a model is interpolated to find a curve that is used as clipping frame in the stencil buffer. This method is able to modify the silhouette for the better. The amount of interpolation is rather limited.</p>