Combinatorial Continuous Maximal Flows

Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching and texture synthesis. Algorithms based on the classical formulation of max-flow defined on a graph are known to exhibit metrication artefacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual min-cut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous max-flow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous max-flow problem and show that the analogous discrete formulation is different from the classical max-flow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous max-flow CCMF problem to find a null-divergence solution that exhibits no metrication artefacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the max-flow and the total variation problems are not always equivalent.Comment: 26 page

Further ALMA observations and detailed modeling of the Red Rectangle

We present new high-quality ALMA observations of the Red Rectangle (a well known post-AGB object) in C17O J=6-5 and H13CN J=4-3 line emission and results from a new reduction of already published 13CO J=3-2 data. A detailed model fitting of all the molecular line data, including previous maps and single-dish spectra, was performed using a sophisticated code. These observations and the corresponding modeling allowed us to deepen the analysis of the nebular properties. We also stress the uncertainties in the model fitting. We confirm the presence of a rotating equatorial disk and an outflow, which is mainly formed of gas leaving the disk. The mass of the disk is ~ 0.01 Mo, and that of the CO-rich outflow is ~ 10 times smaller. High temperatures of ~ 100 K are derived for most components. From comparison of the mass values, we roughly estimate the lifetime of the rotating disk, which is found to be of about 10000 yr. Taking data of a few other post-AGB composite nebulae into account, we find that the lifetimes of disks around post-AGB stars typically range between 5000 and more than 20000 yr. The angular momentum of the disk is found to be high, ~ 9 Mo AU km/s, which is comparable to that of the stellar system at present. Our observations of H13CN show a particularly wide velocity dispersion and indicate that this molecule is only abundant in the inner Keplerian disk, at ~ 60 AU from the stellar system. We suggest that HCN is formed in a dense photodissociation region (PDR) due to the UV excess known to be produced by the stellar system, following chemical mechanisms that are well established for interstellar medium PDRs and disks orbiting young stars. We further suggest that this UV excess could lead to the efficient formation and excitation of PAHs and other C-bearing macromolecules, whose emission is very intense in the optical counterpart.Comment: Astronomy & Astrohysics, in press; 17 pages, 18 figures, 1 tabl

Statistics of Magnification Perturbations by Substructure in the Cold Dark Matter Cosmological Model

We study the statistical properties of magnification perturbations by substructures in strong lensed systems using linear perturbation theory and an analytical substructure model including tidal truncation and a continuous substructure mass spectrum. We demonstrate that magnification perturbations are dominated by perturbers found within a tidal radius of an image, and that sizable magnification perturbations may arise from small, coherent contributions from several substructures within the lens halo. We find that the root-mean-square (rms) fluctuation of the magnification perturbation is 10% to 20% and both the average and rms perturbations are sensitive to the mass spectrum and density profile of the perturbers. Interestingly, we find that relative to a smooth model of the same mass, the average magnification in clumpy models is lower (higher) than that in smooth models for positive (negative) parity images. This is opposite from what is observed if one assumes that the image magnification predicted by the best-fit smooth model of a lens is a good proxy for what the observed magnification would have been if substructures were absent. While it is possible for this discrepancy to be resolved via nonlinear perturbers, we argue that a more likely explanation is that the assumption that the best-fit lens model is a good proxy for the magnification in the absence of substructure is not correct. We conclude that a better theoretical understanding of the predicted statistical properties of magnification perturbations by CDM substructure is needed in order to affirm that CDM substructures have been unambiguously detected.Comment: ApJ accepted, minor change

Geometrically Induced Force Interaction for Three-Dimensional Deformable Models

This work introduces a novel 3D deformable model that is based on a geometrically induced external force field, which can be conveniently generalised to arbitrary dimensions. This external force field is based on hypothesised interactions between the relative geometries of the deformable model and the object boundary. The relative geometrical configurations contribute to a dynamic vector force field that changes accordingly as the deformable model evolves. In addition, we show that by enhancing the geometrical interaction field with a nonlocal edge preserving algorithm, the new model can effectively overcome image noise. We provide a comprehensive comparative study and show that the proposed method achieves significant improvements against existing techniques