4,611 research outputs found
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
Opt: A Domain Specific Language for Non-linear Least Squares Optimization in Graphics and Imaging
Many graphics and vision problems can be expressed as non-linear least
squares optimizations of objective functions over visual data, such as images
and meshes. The mathematical descriptions of these functions are extremely
concise, but their implementation in real code is tedious, especially when
optimized for real-time performance on modern GPUs in interactive applications.
In this work, we propose a new language, Opt (available under
http://optlang.org), for writing these objective functions over image- or
graph-structured unknowns concisely and at a high level. Our compiler
automatically transforms these specifications into state-of-the-art GPU solvers
based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate
different variations of the solver, so users can easily explore tradeoffs in
numerical precision, matrix-free methods, and solver approaches. In our
results, we implement a variety of real-world graphics and vision applications.
Their energy functions are expressible in tens of lines of code, and produce
highly-optimized GPU solver implementations. These solver have performance
competitive with the best published hand-tuned, application-specific GPU
solvers, and orders of magnitude beyond a general-purpose auto-generated
solver
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
Are Estimates of Asymmetric First-Price Auction Models Credible? Semi & Nonparametric Scrutinizations
Structural first-price auction estimation methods, built upon Bayesian Nash Equilibrium (BNE), have provided prolific empirical findings. However, due to the latent nature of underlying valuations, the assumption of BNE is not feasibly testable with field data, a fact that evokes harsh criticism on the literature. To respond to skepticism regarding credibility, we provide a focused answer by scrutinizing estimates derived from experimental asymmetric auction data in which researchers observe valuations. We test the statistical equivalence between the estimated and true value distributions. The Kolmogorov-Smirnov test fails to reject the distributional equivalence, strongly supporting the credibility of structural asymmetric auction estimates
Learning to Reconstruct Shapes from Unseen Classes
From a single image, humans are able to perceive the full 3D shape of an
object by exploiting learned shape priors from everyday life. Contemporary
single-image 3D reconstruction algorithms aim to solve this task in a similar
fashion, but often end up with priors that are highly biased by training
classes. Here we present an algorithm, Generalizable Reconstruction (GenRe),
designed to capture more generic, class-agnostic shape priors. We achieve this
with an inference network and training procedure that combine 2.5D
representations of visible surfaces (depth and silhouette), spherical shape
representations of both visible and non-visible surfaces, and 3D voxel-based
representations, in a principled manner that exploits the causal structure of
how 3D shapes give rise to 2D images. Experiments demonstrate that GenRe
performs well on single-view shape reconstruction, and generalizes to diverse
novel objects from categories not seen during training.Comment: NeurIPS 2018 (Oral). The first two authors contributed equally to
this paper. Project page: http://genre.csail.mit.edu
Neutrino emission rates in highly magnetized neutron stars revisited
Magnetars are a subclass of neutron stars whose intense soft-gamma-ray bursts
and quiescent X-ray emission are believed to be powered by the decay of a
strong internal magnetic field. We reanalyze neutrino emission in such stars in
the plausibly relevant regime in which the Landau band spacing of both protons
and electrons is much larger than kT (where k is the Boltzmann constant and T
is the temperature), but still much smaller than the Fermi energies. Focusing
on the direct Urca process, we find that the emissivity oscillates as a
function of density or magnetic field, peaking when the Fermi level of the
protons or electrons lies about 3kT above the bottom of any of their Landau
bands. The oscillation amplitude is comparable to the average emissivity when
the Landau band spacing mentioned above is roughly the geometric mean of kT and
the Fermi energy (excluding mass), i. e., at fields much weaker than required
to confine all particles to the lowest Landau band. Since the density and
magnetic field strength vary continuously inside the neutron star, there will
be alternating surfaces of high and low emissivity. Globally, these
oscillations tend to average out, making it unclear whether there will be any
observable effects.Comment: 7 pages, 2 figures; accepted for publication in Astronomy &
Astrophysic
Fractal initial conditions and natural parameter values in hybrid inflation
We show that the initial field values required to produce inflation in the
two fields original hybrid model, and its supergravity F-term extension, do not
suffer from any fine-tuning problem, even when the fields are restricted to be
sub-planckian and for almost all potential parameter values. This is due to the
existence of an initial slow-roll violating evolution which has been overlooked
so far. Due to the attractor nature of the inflationary valley, these
trajectories end up producing enough accelerated expansion of the universe. By
numerically solving the full non-linear dynamics, we show that the set of such
successful initial field values is connected, of dimension two and possesses a
fractal boundary of infinite length exploring the whole field space. We then
perform a Monte-Carlo-Markov-Chain analysis of the whole parameter space
consisting of the initial field values, field velocities and potential
parameters. We give the marginalised posterior probability distributions for
each of these quantities such that the universe inflates long enough to solve
the usual cosmological problems. Inflation in the original hybrid model and its
supergravity version appears to be generic and more probable by starting
outside of the inflationary valley. Finally, the implication of our findings in
the context of the eternal inflationary scenario are discussed.Comment: 16 pages, 16 figures, uses RevTeX. Lyapunov exponents and references
added, matches published versio
A parameterization of flow separation over subaqueous dunes
Flow separation plays a key role in the development of dunes, and modeling the complicated flow behavior inside the flow separation zone requires much computational effort. To make a first step toward modeling dune development at reasonable temporal and spatial scales, a parameterization of the shape of the flow separation zone over two-dimensional dunes is proposed herein, in order to avoid modeling the complex flow inside the flow separation zone. Flow separation behind dunes, with an angle-of-repose slip face, is characterized by a large circulating leeside eddy, where a separation streamline forms the upper boundary of the recirculating eddy. Experimental data of turbulent flow over two-dimensional subaqueous bed forms are used to parameterize this separation streamline. The bed forms have various heights and height to length ratios, and a wide range of flow conditions is analyzed. This paper shows that the shape of the flow separation zone can be approximated by a third-order polynomial as a function of the distance away from the flow separation point. The coefficients of the polynomial can be estimated, independent of flow conditions, on the basis of bed form shape at the flow separation point and a constant angle of the separation streamline at the flow reattachment point. \ud
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