Consider a polyhedral surface in three-space that has the property that it can change its shape while keeping all its polygonal faces congruent. Adjacent faces are allowed to rotate along common edges. Mathematically exact flexible surfaces were found by Connelly in 1978. But the question remained as to whether the volume bounded by such surfaces was necessarily constant during the flex. In other words, is there a mathematically perfect bellows that actually will exhale and inhale as it flexes? For the known examples, the volume did remain constant. Following an idea of Sabitov, but using the theory of places in algebraic geometry (suggested by Steve Chase), Connelly et al. showed that there is no perfect mathematical bellows. All flexible surfaces must flex with constant volume. We built several models to illustrate the above theory, in particular, we built a model of the cubeoctahedron after a suggestion by Walser. This model is cut at a line of symmetry, pops up to minimize its energy stored by 4 rubber bands in its interior, and in doing so also maximizes its volume. Three MATLAB programs were written to illustrate how the cuboctahedron is obtained by truncation, how the physical cuboctahedron moves and how the motion of the cubeoctahedron can be described if self-intersection is possible.

Current two dimensional face recognition methods rely on visible photometric or geometric attributes that are present in the intensity image. In many of these approaches a technique called Principal Component Analysis (PCA) is extensively used. PCA extracts the maximum intensity variations from the set of input images in the form of "eigen" faces which are used as a feature vector. In these approaches the intensity images used were mostly that of the subject's frontal face, which yielded promising results after doing PCA. These approaches however fail in the presence of facial expression, unstable lighting conditions and artifacts such as make-up, glasses etc. Thus, it is desirable to establish a new biometric source that will be least affected bythe afore mentioned factors. This study describes a face recognition method that is designed based on the consideration of anatomical and biomechanical characteristics of facial tissues. During facial expressions such as smile, frown, anger etc, various muscles get activated in tandem. A strain pattern inferred from a face expression can reveal an individual's signature associated with the underlying anatomical structure, and thus has the potential for face recognition. In this study, the strain is computed by measuring the displacement of a point on the face that results from a facial expression such as opening the mouth. The information provided by the change in the depth value for the face across the open and close mouth frames does not provide any information required for computing the strain maps, because the strain map depends on the relative displacements of two points on the face, which remains same with rigid motions of the face such as rotation and translation. Hence the information in the 2D spaceis sufficient to compute strain since the depth is assumed constant. The approach used to calculate strain computes the strain distribution directly using the mathematical definition of strain as the derivative of displacement in 2D space (XY plane). The strain values obtained are converted to gray scale intensity images, which are used as inputs for the intensity based PCA analysis. Experiments were conducted using 62 subjects. The data set comprised of two pairs of images for a subject: closed mouth and open mouth under bright and low light. Analysis of CMC and ROC curves indicate that the proposed strain map biometric is a promising new biometric that has the potential to improve the performance of current face recognition method. In summary, the contribution of this thesis is twofold: 1. Facial strain map proves to be promising new biometric. 2. Strain map helps increase the identification rate when used in conjunction with intensity based biometric as a multi-classifier.

Research on video-based face recognition has started getting increased attention in the past few years. Algorithms developed for video have an advantage from the availability of plentitude of frames in videos to extract information from. Despite this fact, most research in this direction has limited the scope of the problem to the application of still image-based approaches to some selected frames on which 2D algorithms are expected to perform well. It can be realized that such an approach only uses the spatial information contained in video and does not incorporate the temporal structure.Only recently has the intelligence community begun to approach the problem in this direction. Video-based face recognition algorithms in the last couple of years attempt to simultaneously use the spatial and temporal information for the recognition of moving faces. A new face recognition method that falls into the category of algorithms that adopt spatio-temporal representation and utilizes dynamic information extracted from video is presented. The method was designed based on the hypothesis that the strain pattern exhibited during facial expression provides a unique "fingerprint" for recognition. First, a dense motion field is obtained with an optical flow algorithm. A strain pattern is then derived from the motion field. In experiments with 30 subjects, results indicate that strain pattern is an useful biometric, especially when dealing with extreme conditions such as shadow light and face camouflage, for which conventional face recognition methods are expected to fail. The ability to characterize the face using the elastic properties of facial skin opens up newer avenues to the face recognition community in the context of modeling a face using features beyond visible cues.

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L'analyse quantitative de la fonction contractile myocardique constitue un enjeu majeur pour le dépistage, le traitement et le suivi des maladies cardio-vasculaires, première cause de mortalité dans les pays développés. Dans ce contexte, l'Imagerie par Résonance Magnétique (IRM) s'impose comme une modalité privilégiée pour l'exploration dynamique du coeur, renseignant, d'une part, sur l'évolution des parois (ciné IRM), et permettant, d'autre part, d'accéder à des informations cinématiques au sein du myocarde (IRM de marquage). L'exploitation quantitative de ces données est néanmoins actuellement limitée par la quasi-absence de méthodologies fiables, robustes et reproductibles d'estimation de mouvement non rigide à partir de séquences d'images acquises dans cette modalité.<br /><br />Cette thèse se propose de démontrer que les techniques de recalage non rigide statistique constituent un cadre approprié pour l'estimation des déformations myocardiques en IRM, leur quantification à des fins diagnostiques, et leur modélisation en vue d'établir une référence numérique de normalité. Ses contributions concernent :<br /><br /> 1. l'élaboration d'une méthode robuste non supervisée d'estimation des déplacements myocardiques à partir de séquences d'IRM de marquage. Elle permet l'obtention de mesures de mouvement fiables en tout point du myocarde, à tout instant du cycle cardiaque et sous incidence de coupe arbitraire.<br /><br /> 2. le développement d'un outil de quantification dynamique des déformations à l'échelle du pixel et du segment myocardique, intégrant un étape de segmentation automatique du coeur par recalage d'images ciné IRM acquises conjointement aux données de marquage. Pour le coeur sain, la comparaison des mesures obtenues à des valeurs de référence issues d'une synthèse approfondie de la littérature médicale démontre une excellente corrélation. Pour des coeurs pathologiques, les expériences menées ont montré la pertinence d'une analyse quantitative multiparamétrique pour localiser et caractériser les zones atteintes.<br /><br /> 3. la construction d'un modèle statistique (atlas) de contraction d'un coeur sain. Cet atlas fournit des modèles quantitatifs de référence locaux et segmentaires pour les paramètres de déformation. Son intégration, en tant que modèle de mouvement, au processus de recalage des données d'IRM de marquage conduit en outre à une description très compacte des déplacements myocardiques sans perte de précision notable.