An advancing front Delaunay triangulation algorithm designed for robustness

A new algorithm is described for generating an unstructured mesh about an arbitrary two-dimensional configuration. Mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements, and the resulting triangulation constitutes the Delaunay triangulation of these points. The algorithm combines the mathematical elegance and efficiency of Delaunay triangulation algorithms with the desirable point placement features, boundary integrity, and robustness traditionally associated with advancing-front-type mesh generation strategies. The method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow-field

High-speed Video from Asynchronous Camera Array

This paper presents a method for capturing high-speed video using an asynchronous camera array. Our method sequentially fires each sensor in a camera array with a small time offset and assembles captured frames into a high-speed video according to the time stamps. The resulting video, however, suffers from parallax jittering caused by the viewpoint difference among sensors in the camera array. To address this problem, we develop a dedicated novel view synthesis algorithm that transforms the video frames as if they were captured by a single reference sensor. Specifically, for any frame from a non-reference sensor, we find the two temporally neighboring frames captured by the reference sensor. Using these three frames, we render a new frame with the same time stamp as the non-reference frame but from the viewpoint of the reference sensor. Specifically, we segment these frames into super-pixels and then apply local content-preserving warping to warp them to form the new frame. We employ a multi-label Markov Random Field method to blend these warped frames. Our experiments show that our method can produce high-quality and high-speed video of a wide variety of scenes with large parallax, scene dynamics, and camera motion and outperforms several baseline and state-of-the-art approaches.Comment: 10 pages, 82 figures, Published at IEEE WACV 201

An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling

A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in- Cell (PIC) simulation method, is explored. In the two dimensional (2d) electrostatic version of our method, called the Arbitrary Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are carried out in 2d on a uniform grid on the unit square logical domain, and mapped to a nonuniform boundary-fitted grid on the physical domain. As the resulting logical grid equations of motion are not separable, we have developed an extension of the semi-implicit Modified Leapfrog (ML) integration technique to preserve the symplectic nature of the logical grid particle mover. A generalized, curvilinear coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid is also developed. By our formulation, we compute the plasma charge density on the logical grid based on the particles' positions on the logical domain. That is, the plasma particles are weighted to the uniform logical grid and the self-consistent mean electrostatic fields obtained from the solution of the logical grid Poisson equation are interpolated to the particle positions on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid and allows us to run the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201

General Dynamic Scene Reconstruction from Multiple View Video

This paper introduces a general approach to dynamic scene reconstruction from multiple moving cameras without prior knowledge or limiting constraints on the scene structure, appearance, or illumination. Existing techniques for dynamic scene reconstruction from multiple wide-baseline camera views primarily focus on accurate reconstruction in controlled environments, where the cameras are fixed and calibrated and background is known. These approaches are not robust for general dynamic scenes captured with sparse moving cameras. Previous approaches for outdoor dynamic scene reconstruction assume prior knowledge of the static background appearance and structure. The primary contributions of this paper are twofold: an automatic method for initial coarse dynamic scene segmentation and reconstruction without prior knowledge of background appearance or structure; and a general robust approach for joint segmentation refinement and dense reconstruction of dynamic scenes from multiple wide-baseline static or moving cameras. Evaluation is performed on a variety of indoor and outdoor scenes with cluttered backgrounds and multiple dynamic non-rigid objects such as people. Comparison with state-of-the-art approaches demonstrates improved accuracy in both multiple view segmentation and dense reconstruction. The proposed approach also eliminates the requirement for prior knowledge of scene structure and appearance

The persistent cosmic web and its filamentary structure II: Illustrations

The recently introduced discrete persistent structure extractor (DisPerSE, Soubie 2010, paper I) is implemented on realistic 3D cosmological simulations and observed redshift catalogues (SDSS); it is found that DisPerSE traces equally well the observed filaments, walls, and voids in both cases. In either setting, filaments are shown to connect onto halos, outskirt walls, which circumvent voids. Indeed this algorithm operates directly on the particles without assuming anything about the distribution, and yields a natural (topologically motivated) self-consistent criterion for selecting the significance level of the identified structures. It is shown that this extraction is possible even for very sparsely sampled point processes, as a function of the persistence ratio. Hence astrophysicists should be in a position to trace and measure precisely the filaments, walls and voids from such samples and assess the confidence of the post-processed sets as a function of this threshold, which can be expressed relative to the expected amplitude of shot noise. In a cosmic framework, this criterion is comparable to friend of friend for the identifications of peaks, while it also identifies the connected filaments and walls, and quantitatively recovers the full set of topological invariants (Betti numbers) {\sl directly from the particles} as a function of the persistence threshold. This criterion is found to be sufficient even if one particle out of two is noise, when the persistence ratio is set to 3-sigma or more. The algorithm is also implemented on the SDSS catalogue and used to locat interesting configurations of the filamentary structure. In this context we carried the identification of an ``optically faint'' cluster at the intersection of filaments through the recent observation of its X-ray counterpart by SUZAKU. The corresponding filament catalogue will be made available online.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material (movie and data). Submitted to MNRA

An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle

Mantle convection is the fundamental physical process within earth's interior responsible for the thermal and geological evolution of the planet, including plate tectonics. The mantle is modeled as a viscous, incompressible, non-Newtonian fluid. The wide range of spatial scales, extreme variability and anisotropy in material properties, and severely nonlinear rheology have made global mantle convection modeling with realistic parameters prohibitive. Here we present a new implicit solver that exhibits optimal algorithmic performance and is capable of extreme scaling for hard PDE problems, such as mantle convection. To maximize accuracy and minimize runtime, the solver incorporates a number of advances, including aggressive multi-octree adaptivity, mixed continuous-discontinuous discretization, arbitrarily-high-order accuracy, hybrid spectral/geometric/algebraic multigrid, and novel Schur-complement preconditioning. These features present enormous challenges for extreme scalability. We demonstrate that---contrary to conventional wisdom---algorithmically optimal implicit solvers can be designed that scale out to 1.5 million cores for severely nonlinear, ill-conditioned, heterogeneous, and anisotropic PDEs