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Fast and deep deformation approximations
Character rigs are procedural systems that compute the shape of an animated character for a given pose. They can be highly complex and must account for bulges, wrinkles, and other aspects of a character's appearance. When comparing film-quality character rigs with those designed for real-time applications, there is typically a substantial and readily apparent difference in the quality of the mesh deformations. Real-time rigs are limited by a computational budget and often trade realism for performance. Rigs for film do not have this same limitation, and character riggers can make the rig as complicated as necessary to achieve realistic deformations. However, increasing the rig complexity slows rig evaluation, and the animators working with it can become less efficient and may experience frustration. In this paper, we present a method to reduce the time required to compute mesh deformations for film-quality rigs, allowing better interactivity during animation authoring and use in real-time games and applications. Our approach learns the deformations from an existing rig by splitting the mesh deformation into linear and nonlinear portions. The linear deformations are computed directly from the transformations of the rig's underlying skeleton. We use deep learning methods to approximate the remaining nonlinear portion. In the examples we show from production rigs used to animate lead characters, our approach reduces the computational time spent on evaluating deformations by a factor of 5Ă—-10Ă—. This significant savings allows us to run the complex, film-quality rigs in real-time even when using a CPU-only implementation on a mobile device
Fast Predictive Image Registration
We present a method to predict image deformations based on patch-wise image
appearance. Specifically, we design a patch-based deep encoder-decoder network
which learns the pixel/voxel-wise mapping between image appearance and
registration parameters. Our approach can predict general deformation
parameterizations, however, we focus on the large deformation diffeomorphic
metric mapping (LDDMM) registration model. By predicting the LDDMM
momentum-parameterization we retain the desirable theoretical properties of
LDDMM, while reducing computation time by orders of magnitude: combined with
patch pruning, we achieve a 1500x/66x speed up compared to GPU-based
optimization for 2D/3D image registration. Our approach has better prediction
accuracy than predicting deformation or velocity fields and results in
diffeomorphic transformations. Additionally, we create a Bayesian probabilistic
version of our network, which allows evaluation of deformation field
uncertainty through Monte Carlo sampling using dropout at test time. We show
that deformation uncertainty highlights areas of ambiguous deformations. We
test our method on the OASIS brain image dataset in 2D and 3D
A Lagrangian Dynamical Theory for the Mass Function of Cosmic Structures: I Dynamics
A new theory for determining the mass function of cosmic structures is
presented. It relies on a realistic treatment of collapse dynamics.
Gravitational collapse is analyzed in the Lagrangian perturbative framework.
Lagrangian perturbations provide an approximation of truncated type, i.e.
small-scale structure is filtered out. The collapse time is suitably defined as
the instant at which orbit crossing takes place. The convergence of the
Lagrangian series in predicting the collapse time of a homogeneous ellipsoid is
demonstrated; it is also shown that third-order calculations are necessary in
predicting collapse. Then, the Lagrangian prediction, with a correction for
quasi-spherical perturbations, can be used to determine the collapse time of a
homogeneous ellipsoid in a fast and precise way. Furthermore, ellipsoidal
collapse can be considered as a particular truncation of the Lagrangian series.
Gaussian fields with scale-free power spectra are then considered. The
Lagrangian series for the collapse time is found to converge when the collapse
time is not large. In this case, ellipsoidal collapse gives a fast and accurate
approximation of the collapse time; spherical collapse is found to poorly
reproduce the collapse time, even in a statistical sense. Analytical fits of
the distribution functions of the inverse collapse times, as predicted by the
ellipsoid model and by third-order Lagrangian theory, are given. These will be
necessary for a determination of the mass function, which will be given in
paper II.Comment: 18 pages, Latex, uses mn.sty and psfig, 7 postscript figures (fig. 2
and 3 not complete). Revised version, stylistic changes. MNRAS, in pres
Naturally light dilatons from nearly marginal deformations
We discuss the presence of a light dilaton in CFTs deformed by a
nearly-marginal operator O, in the holographic realizations consisting of
confining RG flows that end on a soft wall. Generically, the deformations
induce a condensate , and the dilaton mode can be identified as the
fluctuation of . We obtain a mass formula for the dilaton as a certain
average along the RG flow. The dilaton is naturally light whenever i)
confinement is reached fast enough (such as via the condensation of O) and ii)
the beta function is small (walking) at the condensation scale. These
conditions are satisfied for a class of models with a bulk pseudo-Goldstone
boson whose potential is nearly flat at small field and exponential at large
field values. Thus, the recent observation by Contino, Pomarol and Rattazzi
holds in CFTs with a single nearly-marginal operator. We also discuss the
holographic method to compute the condensate , based on solving the
first-order nonlinear differential equation that the beta function satisfies.Comment: 37 pages, 7 figures; v2 typos corrected, references added; v3
comments added in sec. 2.2, footnote 9 adde
Towards Efficient Modelling Of Macro And Micro Tool Deformations In Sheet Metal Forming
During forming, the deep drawing press and tools undergo large loads, and even though they are extremely sturdy\ud
structures, deformations occur. This causes changes in the geometry of the tool surface and the gap width between the tools.\ud
The deep drawing process can be very sensitive to these deformations. Tool and press deformations can be split into two\ud
categories. The deflection of the press bed-plate or slide and global deformation in the deep drawing tools are referred to as\ud
macro press deformation. Micro-deformation occurs directly at the surfaces of the forming tools and is one or two orders\ud
lower in magnitude.\ud
The goal is to include tool deformation in a FE forming simulation. This is not principally problematic, however, the FE\ud
meshes become very large, causing an extremely large increase in numerical effort. In this paper, various methods are\ud
discussed to include tool elasticity phenomena with acceptable cost. For macro deformation, modal methods or ’deformable\ud
rigid bodies’ provide interesting possibilities. Static condensation is also a well known method to reduce the number of DOFs,\ud
however the increasing bandwidth of the stiffness matrix limits this method severely, and decreased calculation times are not\ud
expected. At the moment, modeling Micro-deformation remains unfeasible. Theoretically, it can be taken into account, but\ud
the results may not be reliable due to the limited size of the tool meshes and due to approximations in the contact algorithms
Surface Networks
We study data-driven representations for three-dimensional triangle meshes,
which are one of the prevalent objects used to represent 3D geometry. Recent
works have developed models that exploit the intrinsic geometry of manifolds
and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants,
which learn from the local metric tensor via the Laplacian operator. Despite
offering excellent sample complexity and built-in invariances, intrinsic
geometry alone is invariant to isometric deformations, making it unsuitable for
many applications. To overcome this limitation, we propose several upgrades to
GNNs to leverage extrinsic differential geometry properties of
three-dimensional surfaces, increasing its modeling power.
In particular, we propose to exploit the Dirac operator, whose spectrum
detects principal curvature directions --- this is in stark contrast with the
classical Laplace operator, which directly measures mean curvature. We coin the
resulting models \emph{Surface Networks (SN)}. We prove that these models
define shape representations that are stable to deformation and to
discretization, and we demonstrate the efficiency and versatility of SNs on two
challenging tasks: temporal prediction of mesh deformations under non-linear
dynamics and generative models using a variational autoencoder framework with
encoders/decoders given by SNs
Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach
This paper introduces Quicksilver, a fast deformable image registration
method. Quicksilver registration for image-pairs works by patch-wise prediction
of a deformation model based directly on image appearance. A deep
encoder-decoder network is used as the prediction model. While the prediction
strategy is general, we focus on predictions for the Large Deformation
Diffeomorphic Metric Mapping (LDDMM) model. Specifically, we predict the
momentum-parameterization of LDDMM, which facilitates a patch-wise prediction
strategy while maintaining the theoretical properties of LDDMM, such as
guaranteed diffeomorphic mappings for sufficiently strong regularization. We
also provide a probabilistic version of our prediction network which can be
sampled during the testing time to calculate uncertainties in the predicted
deformations. Finally, we introduce a new correction network which greatly
increases the prediction accuracy of an already existing prediction network. We
show experimental results for uni-modal atlas-to-image as well as uni- / multi-
modal image-to-image registrations. These experiments demonstrate that our
method accurately predicts registrations obtained by numerical optimization, is
very fast, achieves state-of-the-art registration results on four standard
validation datasets, and can jointly learn an image similarity measure.
Quicksilver is freely available as an open-source software.Comment: Add new discussion
Universality of soft and collinear factors in hard-scattering factorization
Universality in QCD factorization of parton densities, fragmentation
functions, and soft factors is endangered by the process dependence of the
directions of Wilson lines in their definitions. We find a choice of directions
that is consistent with factorization and that gives universality between
e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the
Drell-Yan process. Universality is only modified by a time-reversal
transformation of the soft function and parton densities between Drell-Yan and
the other processes, whose only effect is the known reversal of sign for T-odd
parton densities like the Sivers function. The modifications of the definitions
needed to remove rapidity divergences with light-like Wilson lines do not
affect the results.Comment: 4 pages. Extra references. Text and references as in published
versio
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