A variational approach to 3D cylindrical geometry reconstruction from multiple views

[EN] In this paper we present a variational technique for the reconstruction of 3D cylindrical surfaces. Roughly speaking by a cylindrical surface we mean a surface that can be parameterized using the projection on a cylinder in terms of two coordinates, representing the displacement and angle in a cylindrical coordinate system respectively. The starting point for our method is a set of different views of a cylindrical surface, as well as a precomputed disparity map estimation between pair of images. The proposed variational technique is based on an energy minimization where we balance on the one hand the regularity of the cylindrical function given by the distance of the surface points to cylinder axis, and on the other hand, the distance between the projection of the surface points on the images and the expected location following the precomputed disparity map estimation between pair of images. One interesting advantage of this approach is that we regularize the 3D surface by means of a bi-dimensio al minimization problem. We show some experimental results for large stereo sequences.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.

People semantic description and re-identification from point cloud geometry

The automatic extraction of biometric descriptors of anonymous people is a challenging scenario in camera networks. This task is typically accomplished making use of visual information. Calibrated RGBD sensors make possible the extraction of point cloud information. We present a novel approach for people semantic description and re-identification using the individual point cloud information. The proposal combines the use of simple geometric features with point cloud features based on surface normals.

Influence of reservoir geometry and conditions on the seismic response of arch dams

[EN]An analysis of the influence that reservoir levels and bottom sediment properties (especially on the degree of saturation) have on the dynamic response of arch dams is caried out. For this purpose, a Boundary Element Model developed by the authors that allows the direct dynamic study of problems that incorporate scalar, viscoelastic and poroelastic media is used.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

A LES study of a modified Ahmed body geometry

A numerical study using Large Eddy Simulation Coherent Structure Model (LES-CSM), of the flow around a simplified Ahmed body, has been done in this work of thesis. The models used are two salient geometries from the experimental investigation performed in [1], and consist, in particular, in two notch-back body geometries. Six simulation are carried out in total, changing Reynolds number and back-light angle of the model’s rear part. The Reynolds numbers used, based on the height of the models and the free stream velocity, are Re = 10000, Re = 30000 and Re = 50000. The back-light angles of the slanted surface with respect to the horizontal roof surface, that characterizes the vehicle, are taken as B = 31.8◦ and B = 42◦ respectively. The experimental results in [1] have shown that, depending on the parameter B, asymmetric and symmetric averaged flow over the back-light and in the wake for a symmetric geometry can be observed. The aims of the present work of master thesis are principally two. The first aim is to investigate and confirm the influence of the parameter B on the presence of the asymmetry of the averaged flow, and confirm the features described in the experimental results. The second important aspect is to investigate and observe the influence of the second variable, the Reynolds number, in the developing of the asymmetric flow itself. The results have shown the presence of the mentioned asymmetry as well as an influence of the Reynolds number on it.

Deep geometry of subduction below the Andean belt of Colombia as revealed by seismic tomography

In this study new tomographic models of Colombia were calculated. I used the seismicity recorded by the Colombian seismic network during the period 2006-2009. In this time period, the improvement of the seismic network yields more stable hypocentral results with respect to older data set and allows to compute new 3D Vp and Vp/Vs models. The final dataset consists of 10813 P- and 8614 S-arrival times associated to 1405 earthquakes. Tests with synthetic data and resolution analysis indicate that velocity models are well constrained in central, western and southwestern Colombia to a depth of 160 km; the resolution is poor in the northern Colombia and close to Venezuela due to a lack of seismic stations and seismicity. The tomographic models and the relocated seismicity indicate the existence of E-SE subducting Nazca lithosphere beneath central and southern Colombia. The North-South changes in Wadati-Benioff zone, Vp & Vp/Vs pattern and volcanism, show that the downgoing plate is segmented by slab tears E-W directed, suggesting the presence of three sectors. Earthquakes in the northernmost sector represent most of the Colombian seimicity and concentrated on 100-170 km depth interval, beneath the Eastern Cordillera. Here a massive dehydration is inferred, resulting from a delay in the eclogitization of a thickened oceanic crust in a flat-subduction geometry. In this sector a cluster of intermediate-depth seismicity (Bucaramanga Nest) is present beneath the elbow of the Eastern Cordillera, interpreted as the result of massive and highly localized dehydration phenomenon caused by a hyper-hydrous oceanic crust. The central and southern sectors, although different in Vp pattern show, conversely, a continuous, steep and more homogeneous Wadati-Benioff zone with overlying volcanic areas. Here a "normalthickened" oceanic crust is inferred, allowing for a gradual and continuous metamorphic reactions to take place with depth, enabling the fluid migration towards the mantle wedge.

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Numerical methods for the dispersion analysis of Guided Waves

The use of guided ultrasonic waves (GUW) has increased considerably in the fields of non-destructive (NDE) testing and structural health monitoring (SHM) due to their ability to perform long range inspections, to probe hidden areas as well as to provide a complete monitoring of the entire waveguide. Guided waves can be fully exploited only once their dispersive properties are known for the given waveguide. In this context, well stated analytical and numerical methods are represented by the Matrix family methods and the Semi Analytical Finite Element (SAFE) methods. However, while the former are limited to simple geometries of finite or infinite extent, the latter can model arbitrary cross-section waveguides of finite domain only. This thesis is aimed at developing three different numerical methods for modelling wave propagation in complex translational invariant systems. First, a classical SAFE formulation for viscoelastic waveguides is extended to account for a three dimensional translational invariant static prestress state. The effect of prestress, residual stress and applied loads on the dispersion properties of the guided waves is shown. Next, a two-and-a-half Boundary Element Method (2.5D BEM) for the dispersion analysis of damped guided waves in waveguides and cavities of arbitrary cross-section is proposed. The attenuation dispersive spectrum due to material damping and geometrical spreading of cavities with arbitrary shape is shown for the first time. Finally, a coupled SAFE-2.5D BEM framework is developed to study the dispersion characteristics of waves in viscoelastic waveguides of arbitrary geometry embedded in infinite solid or liquid media. Dispersion of leaky and non-leaky guided waves in terms of speed and attenuation, as well as the radiated wavefields, can be computed. The results obtained in this thesis can be helpful for the design of both actuation and sensing systems in practical application, as well as to tune experimental setup.

A biomimetic model membrane system on oxidic surfaces designed for the investigation of cytochrome c oxidase and other membrane proteins by fluorescence and waveguide spectroscopy

Die transmembrane Potenzialdifferenz Δφm ist direkt mit der katalytischen Aktivität der Cytochrom c Oxidase (CcO) verknüpft. Die CcO ist das terminale Enzym (Komplex IV) in der Atmungskette der Mitochondrien. Das Enzym katalysiert die Reduktion von O2 zu 2 H2O. Dabei werden Elektronen vom natürlichen Substrat Cytochrom c zur CcO übertragen. Der Eleltronentransfer innerhalb der CcO ist an die Protonentranslokation über die Membran gekoppelt. Folglich bildet sich über der inneren Membrane der Mitochondrien eine Differenz in der Protonenkonzentration. Zusätzlich wird eine Potenzialdifferenz Δφm generiert.rnrnDas Transmembranpotenzial Δφm kann mit Hilfe der Fluoreszenzspektroskopie unter Einsatz eines potenzialemfindlichen Farbstoffs gemessen werden. Um quantitative Aussagen aus solchen Untersuchungen ableiten zu können, müssen zuvor Kalibrierungsmessungen am Membransystem durchgeführt werden.rnrnIn dieser Arbeit werden Kalibrierungsmessungen von Δφm in einer Modellmembrane mit inkorporiertem CcO vorgestellt. Dazu wurde ein biomimetisches Membransystem, die Proteinverankerte Doppelschicht (protein-tethered Bilayer Lipid Membrane, ptBLM), auf einem transparenten, leitfähigem Substrat (Indiumzinnoxid, ITO) entwickelt. ITO ermöglicht den simultanen Einsatz von elektrochemischen und Fluoreszenz- oder optischen wellenleiterspektroskopischen Methoden. Das Δφm in der ptBLM wurde durch extern angelegte, definierte elektrische Spannungen induziert. rnrnEine dünne Hydrogelschicht wurde als "soft cushion" für die ptBLM auf ITO eingesetzt. Das Polymernetzwerk enthält die NTA Funktionsgruppen zur orientierten Immobilisierung der CcO auf der Oberfläche der Hydrogels mit Hilfe der Ni-NTA Technik. Die ptBLM wurde nach der Immobilisierung der CcO mittels in-situ Dialyse gebildet. Elektrochemische Impedanzmessungen zeigten einen hohen elektrischen Widerstand (≈ 1 MΩ) der ptBLM. Optische Wellenleiterspektren (SPR / OWS) zeigten eine erhöhte Anisotropie des Systems nach der Bildung der Doppellipidschicht. Cyklovoltammetriemessungen von reduziertem Cytochrom c bestätigten die Aktivität der CcO in der Hydrogel-gestützten ptBLM. Das Membranpotenzial in der Hydrogel-gestützten ptBLM, induziert durch definierte elektrische Spannungen, wurde mit Hilfe der ratiometrischen Fluoreszenzspektroskopie gemessen. Referenzmessungen mit einer einfach verankerten Dopplellipidschicht (tBLM) lieferten einen Umrechnungsfaktor zwischen dem ratiometrischen Parameter Rn und dem Membranpotenzial (0,05 / 100 mV). Die Nachweisgrenze für das Membranpotenzial in einer Hydrogel-gestützten ptBLM lag bei ≈ 80 mV. Diese Daten dienen als gute Grundlage für künftige Untersuchungen des selbstgenerierten Δφm der CcO in einer ptBLM.

New biosensor applications of surface plasmon and hydrogel optical waveguide spectroscopy

Rapid and sensitive detection of chemical and biological analytes becomes increasingly important in areas such as medical diagnostics, food control and environmental monitoring. Optical biosensors based on surface plasmon resonance (SPR) and optical waveguide spectroscopy have been extensively pushed forward in these fields. In this study, we combine SPR, surface plasmon-enhanced fluorescence spectroscopy (SPFS) and optical waveguide spectroscopy with hydrogel thin film for highly sensitive detection of molecular analytes.rnrnA novel biosensor based on SPFS which was advanced through the excitation of long range surface plasmons (LRSPs) is reported in this study. LRSPs are special surface plasmon waves propagating along thin metal films with orders of magnitude higher electromagnetic field intensity and lower damping than conventional SPs. Therefore, their excitation on the sensor surface provides further increased fluorescence signal. An inhibition immunoassay based on LRSP-enhanced fluorescence spectroscopy (LRSP-FS) was developed for the detection of aflatoxin M1 (AFM1) in milk. The biosensor allowed for the detection of AFM1 in milk at concentrations as low as 0.6 pg mL-1, which is about two orders of magnitude lower than the maximum AFM1 residue level in milk stipulated by the European Commission legislation.rnrnIn addition, LRSPs probe the medium adjacent to the metallic surface with more extended evanescent field than regular SPs. Therefore, three-dimensional binding matrices with up to micrometer thickness have been proposed for the immobilization of biomolecular recognition elements with large surface density that allows to exploit the whole evanescent field of LRSP. A photocrosslinkable carboxymethyl dextran (PCDM) hydrogel thin film is used as a binding matrix, and it is applied for the detection of free prostate specific antigen (f-PSA) based on the LRSP-FS and sandwich immunoassay. We show that this approach allows for the detection of f-PSA at low femto-molar range, which is approximately four orders of magnitude lower than that for direct detection of f-PSA based on the monitoring of binding-induced refractive index changes.rnrnHowever, a three dimensional hydrogel binding matrix with micrometer thickness can also serve as an optical waveguide. Based on the measurement of binding-induced refractive index changes, a hydrogel optical waveguide spectroscopy (HOWS) is reported for a label-free biosensor. This biosensor is implemented by using a SPR optical setup in which a carboxylated poly(N-isoproprylacrylamide) (PNIPAAm) hydrogel film is attached on a metallic surface and modified by protein catcher molecules. Compared to regular SPR biosensor with thiol self-assembled monolayer (SAM), HOWS provides an order of magnitude improved resolution in the refractive index measurements and enlarged binding capacity owing to its low damping and large swelling ratio, respectively. A model immunoassay experiment revealed that HOWS allowed detection of IgG molecules with a 10 pM limit of detection (LOD) that was five-fold lower than that achieved for SPR with thiol SAM. For the high capacity hydrogel matrix, the affinity binding was mass transport limited.rnrnThe mass transport of target molecules to the sensor surface can play as critical a role as the chemical reaction itself. In order to overcome the diffusion-limited mass transfer, magnetic iron oxide nanoparticles were employed. The magnetic nanoparticles (MNPs) can serve both as labels providing enhancement of the refractive index changes, and “vehicles” for rapidly delivering the analytes from sample solution to an SPR sensor surface with a gradient magnetic field. A model sandwich assay for the detection of β human chorionic gonadotropin (βhCG) has been utilized on a gold sensor surface with metallic diffraction grating structure supporting the excitation of SPs. Various detection formats including a) direct detection, b) sandwich assay, c) MNPs immunoassay without and d) with applied magnetic field were compared. The results show that the highly-sensitive MNPs immunoassay improves the LOD on the detection of βhCG by a factor of 5 orders of magnitude with respect to the direct detection.rn