Global optimisation techniques for image segmentation with higher order models

Energy minimisation methods are one of the most successful approaches to image segmentation. Typically used energy functions are limited to pairwise interactions due to the increased complexity when working with higher-order functions. However, some important assumptions about objects are not translatable to pairwise interactions. The goal of this thesis is to explore higher order models for segmentation that are applicable to a wide range of objects. We consider: (1) a connectivity constraint, (2) a joint model over the segmentation and the appearance, and (3) a model for segmenting the same object in multiple images. We start by investigating a connectivity prior, which is a natural assumption about objects. We show how this prior can be formulated in the energy minimisation framework and explore the complexity of the underlying optimisation problem, introducing two different algorithms for optimisation. This connectivity prior is useful to overcome the “shrinking bias” of the pairwise model, in particular in interactive segmentation systems. Secondly, we consider an existing model that treats the appearance of the image segments as variables. We show how to globally optimise this model using a Dual Decomposition technique and show that this optimisation method outperforms existing ones. Finally, we explore the current limits of the energy minimisation framework. We consider the cosegmentation task and show that a preference for object-like segmentations is an important addition to cosegmentation. This preference is, however, not easily encoded in the energy minimisation framework. Instead, we use a practical proposal generation approach that allows not only the inclusion of a preference for object-like segmentations, but also to learn the similarity measure needed to define the cosegmentation task. We conclude that higher order models are useful for different object segmentation tasks. We show how some of these models can be formulated in the energy minimisation framework. Furthermore, we introduce global optimisation methods for these energies and make extensive use of the Dual Decomposition optimisation approach that proves to be suitable for this type of models

Time-dependent reliability analyses of prestressed concrete girders strengthened with CFRP laminates

This paper presents a time-dependent reliability analysis of prestressed concrete girders subjected to degradation caused by pitting corrosion. The procedure presented includes the effects of both spatial and temporal pitting corrosions on prestressing steel, as well as the degradation of the strengthening CFRP laminate used for the rehabilitation of the member. Results indicate that the correlation of corrosion in different segments of the prestressing tendons impacts on the computed safety index for the deteriorated structure. Ditlevsen bounds are proposed for a better approximation of the correlation between failure modes in the spatial discretisation. Results show that such approach produces adequate estimates of the reliability index over the full range of analysis in comparison with other tested models. It is also observed that the degradation of the CFRP laminates does not affect the reliability as significantly as corrosion, and that traffic loads, models uncertainties, corrosion error and corrosion rate are the most relevant variables in the analysis, followed by prestressing strength and concrete cover. The significance of the variables changes with time: the corrosion rate, corrosion model error and concrete cover increase in importance with the development of corrosion, whereas traffic loads become gradually less important

Introduction to Holographic Superconductors

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the end.Comment: 34 pages, 10 figures, to appear in the proceedings of the 5th Aegean Summer School, "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence"; v2: references adde

Nucleation and growth of biomimetic apatite layers on 3D plotted biodegradable polymeric scaffolds : effect of static and dynamic coating conditions

Apatite layers were grown on the surface of newly developed starch/polycaprolactone (SPCL)-based scaffolds by a 3D plotting technology. To produce the biomimetic coatings, a sodium silicate gel was used as nucleating agent, followed by immersion in a simulated body fluid (SBF) solution. After growing a stable apatite layer for 7 days, the scaffolds were placed in SBF under static, agitated (80 strokes min!1) and circulating flow perfusion (Q = 4 ml min!1; tR = 15 s) for up to 14 days. The materials were characterized by scanning electron microscopy/energy dispersive X-ray spectroscopy, Fourier transform infrared spectroscopy and thin-film X-ray diffraction. Cross-sections were obtained and the coating thickness was measured. The elemental composition of solution and coatings was monitored by inductively coupled plasma spectroscopy. After only 6 h of immersion in SBF it was possible to observe the formation of small nuclei of an amorphous calcium phosphate (ACP) layer. After subsequent SBF immersion from 7 to 14 days under static, agitated and circulating flow perfusion conditions, these layers grew into bone-like nanocrystalline carbonated apatites covering each scaffold fiber without compromising its initial morphology. No differences in the apatite composition/chemical structure were detectable between the coating conditions. In case of flow perfusion, the coating thickness was significantly higher. This condition, besides mimicking better the biological milieu, allowed for the coating of complex architectures at higher rates, which can greatly reduce the coating step.The authors acknowledge the Portuguese Foundation for Science and Technology (PhD grant to A.L.O., SFRH/BD/10956/2002 and post-doctoral Grant to R.A.S., SFRH/BPD/17151/2004, under the POCTI Program). This work was partially supported by FCT through POCTI and/or FEDER programmes and also partially supported by the EU Project HIPPOCRATES (NMP3-CT-2003-505758) and EXPERTISSUES (NMP-CT-2004-500283)

BF models, Duality and Bosonization on higher genus surfaces

The generating functional of two dimensional $BF$ field theories coupled to fermionic fields and conserved currents is computed in the general case when the base manifold is a genus g compact Riemann surface. The lagrangian density $L=dB{\wedge}A$ is written in terms of a globally defined 1-form $A$ and a multi-valued scalar field $B$. Consistency conditions on the periods of $dB$ have to be imposed. It is shown that there exist a non-trivial dependence of the generating functional on the topological restrictions imposed to $B$. In particular if the periods of the $B$ field are constrained to take values $4\pi n$, with $n$ any integer, then the partition function is independent of the chosen spin structure and may be written as a sum over all the spin structures associated to the fermions even when one started with a fixed spin structure. These results are then applied to the functional bosonization of fermionic fields on higher genus surfaces. A bosonized form of the partition function which takes care of the chosen spin structure is obtainedComment: 17 page

Probabilistic-based characterisation of the mechanical properties of CFRP laminates

Fibre reinforced polymer (FRP) composites have been increasingly used worldwide in the strengthening of civil engineering structures. As FRP becomes more common in structural strengthening, the development of probability-based limit state design codes will require accurate models for the prediction of the mechanical properties of the FRPs. Existing models, however, are based on small sample sizes and ignore the importance of the tail region for analyses and design. Addressing these limitations, this paper presents a probabilistic-based characterisation of the mechanical properties of carbon FRP (CFRP) laminates using a large batch of tension tests. The analysed specimens were pre-cured laminates of carbon fibres embedded in epoxy matrices, which is the most commonly used laminate for the strengthening concrete beams and slabs. Based on the existing data, probabilistic models and correlations were established for the Young's modulus, ultimate strain and tensile strength. Analyses demonstrate the suitability of the Weibull distribution for the estimation of CFRP properties. Results also show that the statistical characterisation of the mechanical properties should be performed with a focus on the tail region. The proposed distributions constitute a set of validated probabilistic models that can be used for performing reliability analyses of structures strengthened with CFRP laminates

The Relativistic Factor in the Orbital Dynamics of Point Masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations