Geometry-Aware Network for Non-Rigid Shape Prediction from a Single View

We propose a method for predicting the 3D shape of a deformable surface from a single view. By contrast with previous approaches, we do not need a pre-registered template of the surface, and our method is robust to the lack of texture and partial occlusions. At the core of our approach is a {\it geometry-aware} deep architecture that tackles the problem as usually done in analytic solutions: first perform 2D detection of the mesh and then estimate a 3D shape that is geometrically consistent with the image. We train this architecture in an end-to-end manner using a large dataset of synthetic renderings of shapes under different levels of deformation, material properties, textures and lighting conditions. We evaluate our approach on a test split of this dataset and available real benchmarks, consistently improving state-of-the-art solutions with a significantly lower computational time.Comment: Accepted at CVPR 201

Shape from Shading through Shape Evolution

In this paper, we address the shape-from-shading problem by training deep networks with synthetic images. Unlike conventional approaches that combine deep learning and synthetic imagery, we propose an approach that does not need any external shape dataset to render synthetic images. Our approach consists of two synergistic processes: the evolution of complex shapes from simple primitives, and the training of a deep network for shape-from-shading. The evolution generates better shapes guided by the network training, while the training improves by using the evolved shapes. We show that our approach achieves state-of-the-art performance on a shape-from-shading benchmark

Natural age dispersion arising from the analysis of broken crystals, part II. Practical application to apatite (U-Th)/He thermochronometry

We describe a new numerical inversion approach to deriving thermal history information from a range of naturally dispersed single grain apatite (U-Th)/He ages. The approach explicitly exploits the information about the shape of the 4He diffusion profile within individual grains that is inherent in the pattern of dispersion that arises from the common and routine practice of analysing broken crystals. Additional dispersion arising from differences in grain size and in U and Th concentration of grains, and the resultant changes to helium diffusivity caused by differential accumulation and annealing of radiation damage, is explicitly included. In this approach we calculate the ingrowth and loss, due to both thermal diffusion and the effects of α-ejection, of helium over time using a finite cylinder geometry. Broken grains are treated explicitly as fragments of an initially larger crystal. The initial grain lengths, L0, can be treated as unknown parameters to be estimated, although this is computationally demanding. A practical solution to the problem of solving for the unknown initial grain lengths is to simply apply a constant and sufficiently long L0 value to each fragment. We found that a good value for L0 was given by the maximum fragment length plus two times the maximum radius of a given set of fragments. Currently whole crystals and fragments with one termination are taken into account. A set of numerical experiments using synthetic fragment ages generated for increasingly complex thermal histories, and including realistic amounts of random noise (5-15%), are presented and show that useful thermal history information can be extracted from datasets showing very large dispersion. These include experiments where dispersion arises only from fragmentation of a single grain (length 400μm and radius 75μm, c. 6-50% dispersion), including the effects of grain size variation (for spherical equivalent grain radii between 74-122 μm, c. 10-70% dispersion) and the combined effects of fragmentation, grain size and radiation damage (for eU between 5-150 ppm, c.10-107% dispersion). Additionally we show that if the spherical equivalent radius of a broken grain is used as a measure of the effective diffusion domain for thermal history inversions then this will likely lead to erroneous thermal histories being obtained in many cases. The viability of the new technique is demonstrated for a real data set of 25 single grain (U-Th)/He apatite ages obtained for a gabbro sample from the BK-1 (Bierkraal) borehole drilled through the Bushveld Complex in South Africa. The inversion produces a well constrained thermal history consistent with both the (U-Th)/He data and available fission track analysis data. The advantage of the new approach is that it can explicitly accommodate all the details of conventional schemes, such as the effects of temporally variable diffusivity, zonation of U and Th and arbitrary grain size variations, and it works equally effectively for whole or broken crystals, and for the most common situation where a mixture of both are analysed. For the routine application of the apatite (U-Th)/He thermochronometry technique with samples where whole apatite grains are rare our experiments indicate that 15-20 single grain analyses are typically required to characterise the age dispersion pattern of a sample. The experiments also suggest that picking very short crystal fragments as well as long fragments, or even deliberately breaking long crystals to maximise the age dispersion in some cases, would ensure the best constraints on the thermal history models. The inversion strategy described in this paper is likely also directly applicable to other thermochronometers, such as the apatite, rutile and titanite U-Pb systems, where the diffusion domain is approximated by the physical grain size

Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces

The reconstruction of a 3D object or a scene is a classical inverse problem in Computer Vision. In the case of a single image this is called the Shape-from-Shading (SfS) problem and it is known to be ill-posed even in a simplified version like the vertical light source case. A huge number of works deals with the orthographic SfS problem based on the Lambertian reflectance model, the most common and simplest model which leads to an eikonal type equation when the light source is on the vertical axis. In this paper we want to study non-Lambertian models since they are more realistic and suitable whenever one has to deal with different kind of surfaces, rough or specular. We will present a unified mathematical formulation of some popular orthographic non-Lambertian models, considering vertical and oblique light directions as well as different viewer positions. These models lead to more complex stationary nonlinear partial differential equations of Hamilton-Jacobi type which can be regarded as the generalization of the classical eikonal equation corresponding to the Lambertian case. However, all the equations corresponding to the models considered here (Oren-Nayar and Phong) have a similar structure so we can look for weak solutions to this class in the viscosity solution framework. Via this unified approach, we are able to develop a semi-Lagrangian approximation scheme for the Oren-Nayar and the Phong model and to prove a general convergence result. Numerical simulations on synthetic and real images will illustrate the effectiveness of this approach and the main features of the scheme, also comparing the results with previous results in the literature.Comment: Accepted version to Journal of Mathematical Imaging and Vision, 57 page

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom

Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data

Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the electric and magnetic parts of the Weyl curvature tensor, form the basis of a recently developed approach to visualizing spacetime curvature. In particular, this method has been proposed as a tool for interpreting results from numerical binary black hole simulations, providing a deeper insight into the physical processes governing the merger of black holes and the emission of gravitational radiation. Here we apply this approach to approximate but analytical initial data for both single boosted and binary black holes. These perturbative data become exact in the limit of small boost or large binary separation. We hope that these calculations will provide additional insight into the properties of tendex and vortex fields, and will form a useful test for future numerical calculations.Comment: 18 pages, 8 figures, submitted to PR

Droplet migration: quantitative comparisons with experiment

An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H, of a thin energetically stable wetting layer, or precursor lm, over the entire substrate. The necessity that H be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H near wetting lines, increases the computational demands signicantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly ecient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the eect of H and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet ows down an inclined plane

A New Methodology for Building-Up a Robust Model for Heliostat Field Flux Characterization

The heliostat field of solar central receiver systems (SCRS) is formed by hundreds, even thousands, of working heliostats. Their adequate configuration and control define a currently active research line. For instance, automatic aiming methodologies of existing heliostat fields are being widely studied. In general, control techniques require a model of the system to be controlled in order to obtain an estimation of its states. However, this kind of information may not be available or may be hard to obtain for every plant to be studied. In this work, an innovative methodology for data-based analytical heliostat field characterization is proposed and described. It formalizes the way in which the behavior of a whole field can be derived from the study of its more descriptive parts. By successfully applying this procedure, the instantaneous behavior of a field could be expressed by a reduced set of expressions that can be seen as a field descriptor. It is not intended to replace real experimentation but to enhance researchers’ autonomy to build their own reliable and portable synthetic datasets at preliminary stages of their work. The methodology proposed in this paper is successfully applied to a virtual field. Only 30 heliostats out of 541 were studied to characterize the whole field. For the validation set, the average difference in power between the flux maps directly fitted from the measured information and the estimated ones is only of 0.67% (just 0.10946 kW/m2 of root-mean-square error, on average, between them). According to these results, a consistent field descriptor can be built by applying the proposed methodology, which is hence ready for use