The shapes of naturally occurring objects characteristically involve spatial events occurring at many scales. This paper offers a symbolic approach to constructing a primitive shape description across scales for 2D binary (silhouette) shape images: grouping operations are performed over collections of tokens residing on a Scale-Space Blackboard. Two types of grouping operations are identified that, respectively: (1) aggregate edge primitives at one scale into edge primitives at a coarser scale and (2) group edge primitives into partial-region assertions, including curved- contours, primitive-corners, and bars. This approach avoids several drawbacks of numerical smoothing methods.

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits.

Methods for fusing two computer vision methods are discussed and several example algorithms are presented to illustrate the variational method of fusing algorithms. The example algorithms seek to determine planet topography given two images taken from two different locations with two different lighting conditions. The algorithms each employ assingle cost function that combines the computer vision methods of shape-from-shading and stereo in different ways. The algorithms are closely coupled and take into account all the constraints of the photo-topography problem. The algorithms are run on four synthetic test image sets of varying difficulty.

How the visual system extracts shape information from a single grey-level image can be approached by examining how the information about shape is contained in the image. This technical report considers the characteristic equations derived by Horn as a dynamical system. Certain image critical points generate dynamical system critical points. The stable and unstable manifolds of these critical points correspond to convex and concave solution surfaces, giving more general existence and uniqueness results. A new kind of highly parallel, robust shape from shading algorithm is suggested on neighborhoods of these critical points. The information at bounding contours in the image is also analyzed.

This report shows how knowledge about the visual world can be built into a shape representation in the form of a descriptive vocabulary making explicit the important geometrical relationships comprising objects' shapes. Two computational tools are offered: (1) Shapestokens are placed on a Scale-Space Blackboard, (2) Dimensionality-reduction captures deformation classes in configurations of tokens. Knowledge lies in the token types and deformation classes tailored to the constraints and regularities ofparticular shape worlds. A hierarchical shape vocabulary has been implemented supporting several later visual tasks in the two-dimensional shape domain of the dorsal fins of fishes.

We present a statistical image-based shape + structure model for Bayesian visual hull reconstruction and 3D structure inference. The 3D shape of a class of objects is represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes are then estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We show how the use of a class-specific prior in a visual hull reconstruction can reduce the effect of segmentation errors from the silhouette extraction process. The proposed method is applied to a data set of pedestrian images, and improvements in the approximate 3D models under various noise conditions are shown. We further augment the shape model to incorporate structural features of interest; unknown structural parameters for a novel set of contours are then inferred via the Bayesian reconstruction process. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and works even with only a single input view. Using a data set of thousands of pedestrian images generated from a synthetic model, we can accurately infer the 3D locations of 19 joints on the body based on observed silhouette contours from real images.

La mise en forme de l'alliage d'aluminium de corroyage 7075 de pièces fonctionnelles à géométrie complexe se fait la plupart du temps par usinage. Pour un nombre de pièces important, le coût peut être réduit en réalisant une ébauche par forgeage. Il est cependant plus intéressant de réaliser une ébauche proche des dimensions finales pour limiter l'usinage (aspect near-net-shape). Pour mettre en forme une pièce à géométrie complexe en une seule étape, la résistance à la déformation de la matière doit être suffisamment faible. Cette faible déformation nécessite la génération d'une phase liquide, ce qui introduit des défauts dans l'alliage de corroyage tels que la fissuration à chaud, porosité, retassure, retrait important, macroségrégation solide-liquide. L'apparition de ces défauts peut être réduite en limitant la fraction volumique de la phase liquide à 0.1. AA 7075 étant particulièrement sensible à la fissuration à chaud, un faible retrait est un atout. Nous choisirons le procédé RAP pour obtenir une matière globulaire semi-solide. Ce procédé utilise la recristallisation d'une matière extrudée pour réaliser une matière qui a un comportement rhéofluidifiant-thixotrope. Le procédé de mise en forme de cette matière semi-solide globulaire à faible phase liquide est le thixoforgeage. Des essais de chauffage de la matière extrudée et de filage permettront d'étudier l'influence des divers paramètres du procédé sur l'effort de mise en forme et sur la qualité des pièces produites. Nous adapterons les paramètres de chauffage et de mise en forme sur un outillage spécialement conçu pour le thixoforgeage pour des pièces à géométrie simple et pour des pièces à géométrie complexe. Une étude de l'influence des paramètres sur les caractéristiques mécaniques et sur la qualité des pièces a montré le très bon potentiel de mise en forme de AA 7075 par thixoforgeage.

The functional properties of nanoparticles highly depend on the surface morphology of the particles, so precise measurements of a particle's morphology enable reliable characterizing of the nanoparticle's properties. Obtaining the measurements requires image analysis of electron microscopic pictures of nanoparticles. Today's labor-intensive image analysis of electron micrographs of nanoparticles is a significant bottleneck for efficient material characterization. The objective of this dissertation is to develop automated morphology analysis methods. Morphology analysis is comprised of three tasks: separate individual particles from an agglomerate of overlapping nano-objects (image segmentation); infer the particle's missing contours (shape inference); and ultimately, classify the particles by shape based on their complete contours (shape classification). Two approaches are proposed in this dissertation: the divide-and-conquer approach and the convex shape analysis approach. The divide-and-conquer approach solves each task separately, taking less than one minute to complete the required analysis, even for the largest-sized micrograph. However, its separating capability of particle overlaps is limited, meaning that it is able to split only touching particles. The convex shape analysis approach solves shape inference and classification simultaneously for better accuracy, but it requires more computation time, ten minutes for the biggest-sized electron micrograph. However, with a little sacrifice of time efficiency, the second approach achieves far superior separation than the divide-and-conquer approach, and it handles the chain-linked structure of particle overlaps well. The capabilities of the two proposed methods cannot be substituted by generic image processing and bio-imaging methods. This is due to the unique features that the electron microscopic pictures of nanoparticles have, including special particle overlap structures, and large number of particles to be processed. The application of the proposed methods to real electron microscopic pictures showed that the two proposed methods were more capable of extracting the morphology information than the state-of-the-art methods. When nanoparticles do not have many overlaps, the divide-and-conquer approach performed adequately. When nanoparticles have many overlaps, forming chain-linked clusters, the convex shape analysis approach performed much better than the state-of-the-art alternatives in bio-imaging. The author believes that the capabilities of the proposed methods expedite the morphology characterization process of nanoparticles. The author further conjectures that the technical generality of the proposed methods could even be a competent alternative to the current methods analyzing general overlapping convex-shaped objects other than nanoparticles.

Hydrogen fuel cells are devices used to generate electricity from the electrochemical reaction between air and hydrogen gas. An attractive advantage of these devices is that their byproduct is water, which is very safe to the environment. However, hydrogen fuel cells still lack some improvements in terms of increasing their life time and electricity production, decreasing power losses, and optimizing their operating conditions. In this thesis, the cathode part of the hydrogen fuel cell will be considered. This part mainly consists of an air gas channel and a gas diffusion layer. To simulate the fluid dynamics taking place in the cathode, we present two models, a general model and a simple model both based on a set of conservation laws governing the fluid dynamics and chemical reactions. A numerical method to solve these models is presented and verified in terms of accuracy. We also show that both models give similar results and validate the simple model by recovering a polarization curve obtained experimentally. Next, a shape optimization problem is introduced to find an optimal design of the air gas channel. This problem is defined from the simple model and a cost functional, $E$, that measures efficiency factors. The objective of this functional is to maximize the electricity production, uniformize the reaction rate in the catalytic layer and minimize the pressure drop in the gas channel. The impact of the gas channel shape optimization is investigated with a series of test cases in long and short fuel cell geometries. In most instances, the optimal design improves efficiency in on- and off-design operating conditions by shifting the polarization curve vertically and to the right. The second primary goal of the thesis is to analyze mathematical issues related to the introduced shape optimization problem. This involves existence and uniqueness of the solution for the presented model and differentiability of the state variables with respect to the domain of the air channel. The optimization problem is solved using the gradient method, and hence the gradient of $E$ must be found. The gradient of $E$ is obtained by introducing an adjoint system of equations, which is coupled with the state problem, namely the simple model of the fuel cell. The existence and uniqueness of the solution for the adjoint system is shown, and the shape differentiability of the cost functional $E$ is proved.

Eighteen splice specimens were tested under four-point loading as part of a larger experimental investigation to study the behaviour of lap spliced plain steel bars in reinforced concrete specimens. Three of the specimens were instrumented with strain gauges adhered to the reinforcement and the concrete side face. Three lap splice lengths, two bar sizes for square bars, and one bar size for round bars were investigated. The principal reinforcement was either cast in the bottom or top position. The results of maximum loads, crack patterns, load versus deflection behaviour, and deflected profiles are presented for all specimens. The analysis of specimens with strain gauge instrumentation is also presented, and includes results of strain compatibility, bond stress distribution, and flexural section analysis. All specimens failed by bond, caused by a sudden pullout of the reinforcement within the splice region. An equivalent round diameter based upon the cross-section area of the square bars allowed for a single predictive equation between the maximum normalized load as a function of splice length, casting position and bar size. A top cast factor of 0.4 and 0.6 captures the reduction in the maximum normalized load for specimens cast with round and square bars, respectively, in the top position. The CEB-FIP Model Code (1993) predictive equations are reasonably conservative in capturing the behaviour of specimens reinforced with round bars cast in the bottom position, and square bars with side dimension of 25 mm cast in the bottom position. However, the CEB-FIP Model Code (1993) predictive equation is unconservative when predicting the behaviour of specimens reinforced with either square or round bars cast in the top position. On the other hand, the draft CEB-FIP Model Code (2010) provisions showed an overly conservative prediction for all specimens reinforced with either round or square bars cast in the top or bottom position. Instrumented specimens showed that strain compatibility between the longitudinal reinforcement and the surrounding concrete did not exist for much of the loading range due to bond loss. The evaluation of the neutral axis location within the shear span showed that shear is first transferred by beam action, followed by arch action. The use of three strain gauges adhered to the concrete side face provided flexural moments similar to that predicted theoretically.