Learning Object-Independent Modes of Variation with Feature Flow Fields

We present a unifying framework in which "object-independent" modes of variation are learned from continuous-time data such as video sequences. These modes of variation can be used as "generators" to produce a manifold of images of a new object from a single example of that object. We develop the framework in the context of a well-known example: analyzing the modes of spatial deformations of a scene under camera movement. Our method learns a close approximation to the standard affine deformations that are expected from the geometry of the situation, and does so in a completely unsupervised (i.e. ignorant of the geometry of the situation) fashion. We stress that it is learning a "parameterization", not just the parameter values, of the data. We then demonstrate how we have used the same framework to derive a novel data-driven model of joint color change in images due to common lighting variations. The model is superior to previous models of color change in describing non-linear color changes due to lighting.

Molecular dynamics-based approach to study the anisotropic self-diffusion of molecules in porous materials with multiple cage types: Application to H-2 in losod

Van den Berg, A. W. C., Flikkema, E., Lems, S., Bromley, S. T., Jansen, J. C. (2006). Molecular dynamics-based approach to study the anisotropic self-diffusion of molecules in porous materials with multiple cage types: Application to H-2 in losod. Journal of physical chemistry b, 110 (1), 501-506. RAE2008

Search by Shape Examples: Modeling Nonrigid Deformation

We describe our work on shape-based image database search using the technique of modal matching. Modal matching employs a deformable shape decomposition that allows users to select example objects and have the computer efficiently sort the set of objects based on the similarity of their shape. Shapes are compared in terms of the types of nonrigid deformations (differences) that relate them. The modal decomposition provides deformation "control knobs" for flexible matching and thus allows for selecting weighted subsets of shape parameters that are deemed significant for a particular category or context. We demonstrate the utility of this approach for shape comparison in 2-D image databases; however, the general formulation is applicable to signals of any dimensionality.

Stochastic Mesh-Based Multiview Reconstruction

A method for reconstruction of 3D polygonal models from multiple views is presented. The method uses sampling techniques to construct a texture-mapped semi-regular polygonal mesh of the object in question. Given a set of views and segmentation of the object in each view, constructive solid geometry is used to build a visual hull from silhouette prisms. The resulting polygonal mesh is simplified and subdivided to produce a semi-regular mesh. Regions of model fit inaccuracy are found by projecting the reference images onto the mesh from different views. The resulting error images for each view are used to compute a probability density function, and several points are sampled from it. Along the epipolar lines corresponding to these sampled points, photometric consistency is evaluated. The mesh surface is then pulled towards the regions of higher photometric consistency using free-form deformations. This sampling-based approach produces a photometrically consistent solution in much less time than possible with previous multi-view algorithms given arbitrary camera placement.

Modal Matching for Correspondence and Recognition

Modal matching is a new method for establishing correspondences and computing canonical descriptions. The method is based on the idea of describing objects in terms of generalized symmetries, as defined by each object's eigenmodes. The resulting modal description is used for object recognition and categorization, where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects. In general, modes provide a global-to-local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison. In contrast to previous techniques, which required correspondence to be computed with an initial or prototype shape, modal matching utilizes a new type of finite element formulation that allows for an object's eigenmodes to be computed directly from available image information. This improved formulation provides greater generality and accuracy, and is applicable to data of any dimensionality. Correspondence results with 2-D contour and point feature data are shown, and recognition experiments with 2-D images of hand tools and airplanes are described.

Deformable Prototypes for Encoding Shape Categories in Image Databases

We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.

Active Voodoo Dolls: A Vision Based Input Device for Nonrigid Control

A vision based technique for non-rigid control is presented that can be used for animation and video game applications. The user grasps a soft, squishable object in front of a camera that can be moved and deformed in order to specify motion. Active Blobs, a non-rigid tracking technique is used to recover the position, rotation and non-rigid deformations of the object. The resulting transformations can be applied to a texture mapped mesh, thus allowing the user to control it interactively. Our use of texture mapping hardware allows us to make the system responsive enough for interactive animation and video game character control.

Deformable Shape Detection and Description via Model-Based Region Grouping

A method for deformable shape detection and recognition is described. Deformable shape templates are used to partition the image into a globally consistent interpretation, determined in part by the minimum description length principle. Statistical shape models enforce the prior probabilities on global, parametric deformations for each object class. Once trained, the system autonomously segments deformed shapes from the background, while not merging them with adjacent objects or shadows. The formulation can be used to group image regions based on any image homogeneity predicate; e.g., texture, color, or motion. The recovered shape models can be used directly in object recognition. Experiments with color imagery are reported.

Combinations of Deformable Shape Prototypes

We propose to investigate a model-based technique for encoding non-rigid object classes in terms of object prototypes. Objects from the same class can be parameterized by identifying shape and appearance invariants of the class to devise low-level representations. The approach presented here creates a flexible model for an object class from a set of prototypes. This model is then used to estimate the parameters of low-level representation of novel objects as combinations of the prototype parameters. Variations in the object shape are modeled as non-rigid deformations. Appearance variations are modeled as intensity variations. In the training phase, the system is presented with several example prototype images. These prototype images are registered to a reference image by a finite element-based technique called Active Blobs. The deformations of the finite element model to register a prototype image with the reference image provide the shape description or shape vector for the prototype. The shape vector for each prototype, is then used to warp the prototype image onto the reference image and obtain the corresponding texture vector. The prototype texture vectors, being warped onto the same reference image have a pixel by pixel correspondence with each other and hence are "shape normalized". Given sufficient number of prototypes that exhibit appropriate in-class variations, the shape and the texture vectors define a linear prototype subspace that spans the object class. Each prototype is a vector in this subspace. The matching phase involves the estimation of a set of combination parameters for synthesis of the novel object by combining the prototype shape and texture vectors. The strengths of this technique lie in the combined estimation of both shape and appearance parameters. This is in contrast with the previous approaches where shape and appearance parameters were estimated separately.

Preparation and characterisation of ceria particles

Cerium dioxide (ceria) nanoparticles have been the subject of intense academic and industrial interest. Ceria has a host of applications but academic interest largely stems from their use in the modern automotive catalyst but it is also of interest because of many other application areas notably as the abrasive in chemical-mechanical planarisation of silicon substrates. Recently, ceria has been the focus of research investigating health effects of nanoparticles. Importantly, the role of non-stoichiometry in ceria nanoparticles is implicated in their biochemistry. Ceria has well understood non-stoichiometry based around the ease of formation of anion vacancies and these can form ordered superstructures based around the fluorite lattice structure exhibited by ceria. The anion vacancies are associated with localised or small polaron states formed by the electrons that remain after oxygen desorption. In simple terms these electrons combine with Ce4+ states to form Ce3+ states whose larger ionic radii is associated with a lattice expansion compared to stoichiometric CeO2. This is a very simplistic explanation and greater defect chemistry complexity is suggested by more recent work. Various authors have shown that vacancies are mobile and may result in vacancy clustering. Ceria nanoparticles are of particular interest because of the high activity and surface area of small particulates. The sensitivity of the cerium electronic band structure to environment would suggest that changes in the properties of ceria particles at nanoscale dimensions might be expected. Notably many authors report a lattice expansion with reducing particle size (largely confined to sub-10 nm particles). Most authors assign increased lattice dimensions to the presence of a surface stable Ce2O3 type layer at low nanoparticle dimensions. However, our understanding of oxide nanoparticles is limited and their full and quantitative characterisation offers serious challenges. In a series of chemical preparations by ourselves we see little evidence of a consistent model emerging to explain lattice parameter changes with nanoparticle size. Based on these results and a review of the literature it is worthwhile asking if a model of surface enhanced defect concentration is consistent with known cerium/cerium oxide chemistries, whether this is applicable to a range of different synthesis methods and if a more consistent description is possible. In Chapter one the science of cerium oxide is outlined including the crystal structure, defect chemistry and different oxidation states available. The uses and applications of cerium oxide are also discussed as well as modelling of the lattice parameter and the doping of the ceria lattice. Chapter two describes both the synthesis techniques and the analytical methods employed to execute this research. Chapter three focuses on high surface area ceria nano-particles and how these have been prepared using a citrate sol-gel precipitation method. Changes to the particle size have been made by calcining the ceria powders at different temperatures. X-ray diffraction methods were used to determine their lattice parameters. The particles sizes were also assessed using transmission electron microscopy (TEM), scanning electron microscopy (SEM), and BET, and, the lattice parameter was found to decrease with decreasing particle size. The results are discussed in light of the role played by surface tension effects. Chapter four describes the morphological and structural characterization of crystalline CeO2 nanoparticles prepared by forward and reverse precipitation techniques and compares these by powder x-ray diffraction (PXRD), nitrogen adsorption (BET) and high resolution transmission electron microscopy (HRTEM) analysis. The two routes give quite different materials although in both cases the products are essentially highly crystalline, dense particulates. It was found that the reverse precipitation technique gave the smallest crystallites with the narrowest size dispersion. This route also gave as-synthesised materials with higher surface areas. HRTEM confirmed the observations made from PXRD data and showed that the two methods resulted in quite different morphologies and surface chemistries. The forward route gives products with significantly greater densities of Ce3+ species compared to the reverse route. Data are explained using known precipitation chemistry and kinetic effects. Chapter five centres on the addition of terbia to ceria and has been investigated using XRD, XRF, XPS and TEM. Good solid solutions were formed across the entire composition range and there was no evidence for the formation of mixed phases or surface segregation over either the composition or temperature range investigated. Both Tb3+ and Tb4+ ions exist within the solution and the ratios of these cations are consistent with the addition of Tb8O15 to the fluorite ceria structure across a wide range of compositions. Local regions of anion vacancy ordering may be visible for small crystallites. There is no evidence of significant Ce3+ ion concentrations formed at the surface or in the bulk by the addition of terbia. The lattice parameter of these materials was seen to decrease with decreasing crystallite size. This is consistent with increased surface tension effects at small dimension. Chapter six reviews size related lattice parameter changes and surface defects in ceria nanocrystals. Ceria (CeO2) has many important applications, notably in catalysis. Many of its uses rely on generating nanodimensioned particles. Ceria has important redox chemistry where Ce4+ cations can be reversibly reduced to Ce3+ cations and associated anion vacancies. The significantly larger size of Ce3+ (compared with Ce4+) has been shown to result in lattice expansion. Many authors have observed lattice expansion in nanodimensioned crystals (nanocrystals), and these have been attributed to the presence of stabilized Ce3+ -anion vacancy combinations in these systems. Experimental results presented here show (i) that significant, but complex changes in the lattice parameter with size can occur in 2-500 nm crystallites, (ii) that there is a definitive relationship between defect chemistry and the lattice parameter in ceria nanocrystals, and (iii) that the stabilizing mechanism for the Ce3+ -anion vacancy defects at the surface of ceria nanocrystals is determined by the size, the surface status, and the analysis conditions. In this work, both lattice expansion and a more unusual lattice contraction in ultrafine nanocrystals are observed. The lattice deformations seen can be defined as a function of both the anion vacancy (hydroxyl) concentration in the nanocrystal and the intensity of the additional pressure imposed by the surface tension on the crystal. The expansion of lattice parameters in ceria nanocrystals is attributed to a number of factors, most notably, the presence of any hydroxyl moieties in the materials. Thus, a very careful understanding of the synthesis combined with characterization is required to understand the surface chemistry of ceria nanocrystals.

On stable non supersymmetric vacua at the bottom of cascading theories

We consider a wide class of cascading gauge theories which usually lead to runaway behaviour in the IR, and discuss possible deformations of the superpotential at the bottom of the cascade which stabilize the runaway direction and provide stable non-supersymmetric vacua. The models we find may allow for a weakly coupled supergravity analysis of dynamical supersymmetric breaking in the context of the gauge/string correspondence. © SISSA 2006.

Measurement of intracellular strain on deformable substrates with texture correlation.

Mechanical stimuli are important factors that regulate cell proliferation, survival, metabolism and motility in a variety of cell types. The relationship between mechanical deformation of the extracellular matrix and intracellular deformation of cellular sub-regions and organelles has not been fully elucidated, but may provide new insight into the mechanisms involved in transducing mechanical stimuli to biological responses. In this study, a novel fluorescence microscopy and image analysis method was applied to examine the hypothesis that mechanical strains are fully transferred from a planar, deformable substrate to cytoplasmic and intranuclear regions within attached cells. Intracellular strains were measured in cells derived from the anulus fibrosus of the intervertebral disc when attached to an elastic silicone membrane that was subjected to tensile stretch. Measurements indicated cytoplasmic strains were similar to those of the underlying substrate, with a strain transfer ratio (STR) of 0.79. In contrast, nuclear strains were much smaller than those of the substrate, with an STR of 0.17. These findings are consistent with previous studies indicating nuclear stiffness is significantly greater than cytoplasmic stiffness, as measured using other methods. This study provides a novel method for the study of cellular mechanics, including a new technique for measuring intranuclear deformations, with evidence of differential magnitudes and patterns of strain transferred from the substrate to cell cytoplasm and nucleus.

Spanning the scales of granular materials through microscopic force imaging.

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. Here we describe experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the observed nontrivial mechanical response of the packing, revealing a surprising microscopic particle deformation enhancement mechanism.

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension 3$">n>3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions 4$">n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed. © SISSA 2006.

Parity-violating vertices for spin-3 gauge fields

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincaré invariance, and parity noninvariance, we classify all the nontrivial perturbative deformations of the Abelian gauge algebra. In space-time dimensions n=3 and n=5, deformations of the free theory are obtained which make the gauge algebra non-Abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first order in the deformation parameter g. At second order in g, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the n=3 candidate. Moreover, in the five-dimensional first-order deformation case, the gauge transformations are modified by a new term which involves the second de Wit-Freedman connection in a simple and suggestive way. © 2006 The American Physical Society.