15,064 research outputs found
Deep Fluids: A Generative Network for Parameterized Fluid Simulations
This paper presents a novel generative model to synthesize fluid simulations
from a set of reduced parameters. A convolutional neural network is trained on
a collection of discrete, parameterizable fluid simulation velocity fields. Due
to the capability of deep learning architectures to learn representative
features of the data, our generative model is able to accurately approximate
the training data set, while providing plausible interpolated in-betweens. The
proposed generative model is optimized for fluids by a novel loss function that
guarantees divergence-free velocity fields at all times. In addition, we
demonstrate that we can handle complex parameterizations in reduced spaces, and
advance simulations in time by integrating in the latent space with a second
network. Our method models a wide variety of fluid behaviors, thus enabling
applications such as fast construction of simulations, interpolation of fluids
with different parameters, time re-sampling, latent space simulations, and
compression of fluid simulation data. Reconstructed velocity fields are
generated up to 700x faster than re-simulating the data with the underlying CPU
solver, while achieving compression rates of up to 1300x.Comment: Computer Graphics Forum (Proceedings of EUROGRAPHICS 2019),
additional materials: http://www.byungsoo.me/project/deep-fluids
Discrete Geometric Structures in Homogenization and Inverse Homogenization with application to EIT
We introduce a new geometric approach for the homogenization and inverse
homogenization of the divergence form elliptic operator with rough conductivity
coefficients in dimension two. We show that conductivity
coefficients are in one-to-one correspondence with divergence-free matrices and
convex functions over the domain . Although homogenization is a
non-linear and non-injective operator when applied directly to conductivity
coefficients, homogenization becomes a linear interpolation operator over
triangulations of when re-expressed using convex functions, and is a
volume averaging operator when re-expressed with divergence-free matrices.
Using optimal weighted Delaunay triangulations for linearly interpolating
convex functions, we obtain an optimally robust homogenization algorithm for
arbitrary rough coefficients. Next, we consider inverse homogenization and show
how to decompose it into a linear ill-posed problem and a well-posed non-linear
problem. We apply this new geometric approach to Electrical Impedance
Tomography (EIT). It is known that the EIT problem admits at most one isotropic
solution. If an isotropic solution exists, we show how to compute it from any
conductivity having the same boundary Dirichlet-to-Neumann map. It is known
that the EIT problem admits a unique (stable with respect to -convergence)
solution in the space of divergence-free matrices. As such we suggest that the
space of convex functions is the natural space in which to parameterize
solutions of the EIT problem
On the coupling between an ideal fluid and immersed particles
In this paper we use Lagrange-Poincare reduction to understand the coupling
between a fluid and a set of Lagrangian particles that are supposed to simulate
it. In particular, we reinterpret the work of Cendra et al. by substituting
velocity interpolation from particle velocities for their principal connection.
The consequence of writing evolution equations in terms of interpolation is
two-fold. First, it gives estimates on the error incurred when interpolation is
used to derive the evolution of the system. Second, this form of the equations
of motion can inspire a family of particle and hybrid particle-spectral methods
where the error analysis is "built-in". We also discuss the influence of other
parameters attached to the particles, such as shape, orientation, or
higher-order deformations, and how they can help with conservation of momenta
in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom
Correcting curvature-density effects in the Hamilton-Jacobi skeleton
The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method
Information-Theoretic Registration with Explicit Reorientation of Diffusion-Weighted Images
We present an information-theoretic approach to the registration of images
with directional information, and especially for diffusion-Weighted Images
(DWI), with explicit optimization over the directional scale. We call it
Locally Orderless Registration with Directions (LORD). We focus on normalized
mutual information as a robust information-theoretic similarity measure for
DWI. The framework is an extension of the LOR-DWI density-based hierarchical
scale-space model that varies and optimizes the integration, spatial,
directional, and intensity scales. As affine transformations are insufficient
for inter-subject registration, we extend the model to non-rigid deformations.
We illustrate that the proposed model deforms orientation distribution
functions (ODFs) correctly and is capable of handling the classic complex
challenges in DWI-registrations, such as the registration of fiber-crossings
along with kissing, fanning, and interleaving fibers. Our experimental results
clearly illustrate a novel promising regularizing effect, that comes from the
nonlinear orientation-based cost function. We show the properties of the
different image scales and, we show that including orientational information in
our model makes the model better at retrieving deformations in contrast to
standard scalar-based registration.Comment: 16 pages, 19 figure
An Image Morphing Technique Based on Optimal Mass Preserving Mapping
©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.896637Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The 2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods
- …