Efficient Linear Programming for Dense CRFs

The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear programming (LP) relaxation, the state-of-the-art algorithm is too slow to be useful in practice. To alleviate this deficiency, we introduce an efficient LP minimization algorithm for dense CRFs. To this end, we develop a proximal minimization framework, where the dual of each proximal problem is optimized via block coordinate descent. We show that each block of variables can be efficiently optimized. Specifically, for one block, the problem decomposes into significantly smaller subproblems, each of which is defined over a single pixel. For the other block, the problem is optimized via conditional gradient descent. This has two advantages: 1) the conditional gradient can be computed in a time linear in the number of pixels and labels; and 2) the optimal step size can be computed analytically. Our experiments on standard datasets provide compelling evidence that our approach outperforms all existing baselines including the previous LP based approach for dense CRFs.Comment: 24 pages, 10 figures and 4 table

Efficient Relaxations for Dense CRFs with Sparse Higher Order Potentials

Dense conditional random fields (CRFs) have become a popular framework for modelling several problems in computer vision such as stereo correspondence and multi-class semantic segmentation. By modelling long-range interactions, dense CRFs provide a labelling that captures finer detail than their sparse counterparts. Currently, the state-of-the-art algorithm performs mean-field inference using a filter-based method but fails to provide a strong theoretical guarantee on the quality of the solution. A question naturally arises as to whether it is possible to obtain a maximum a posteriori (MAP) estimate of a dense CRF using a principled method. Within this paper, we show that this is indeed possible. We will show that, by using a filter-based method, continuous relaxations of the MAP problem can be optimised efficiently using state-of-the-art algorithms. Specifically, we will solve a quadratic programming (QP) relaxation using the Frank-Wolfe algorithm and a linear programming (LP) relaxation by developing a proximal minimisation framework. By exploiting labelling consistency in the higher-order potentials and utilising the filter-based method, we are able to formulate the above algorithms such that each iteration has a complexity linear in the number of classes and random variables. The presented algorithms can be applied to any labelling problem using a dense CRF with sparse higher-order potentials. In this paper, we use semantic segmentation as an example application as it demonstrates the ability of the algorithm to scale to dense CRFs with large dimensions. We perform experiments on the Pascal dataset to indicate that the presented algorithms are able to attain lower energies than the mean-field inference method

Human Detection and Segmentation via Multi-View Consensus

Self-supervised detection and segmentation of foreground objects aims for accuracy without annotated training data. However, existing approaches predominantly rely on restrictive assumptions on appearance and motion. For scenes with dynamic activities and camera motion, we propose a multi-camera framework in which geometric constraints are embedded in the form of multi-view consistency during training via coarse 3D localization in a voxel grid and fine-grained offset regression. In this manner, we learn a joint distribution of proposals over multiple views. At inference time, our method operates on single RGB images. We outperform state-of-the-art techniques both on images that visually depart from those of standard benchmarks and on those of the classical Human3.6M dataset

Photoelectron spin polarization approaching unity: photoionization of TI

Böwering N, Salzmann M, Müller M, Klausing H-W, Heinzmann U. Photoelectron spin polarization approaching unity: photoionization of TI. Physica Scripta. 1990;41(4):429-432.It is shown that a complete photoelectron-spin polarization occurs independent of emission angle for two special sets of values of the dynamical photoionization parameters. In spin- and angle-resolved photoelectron spectroscopy of thallium the dynamical parameters were measured near the autoionization resonances at 149 nm and 82 nm. A pronounced angular variation of the polarization component A[Theta] was observed at 83 nm. For both resonances the parameters were found to approach different limiting values such that the length of the spin-polarization vector assumes values close to unity at all emission angles. The implications of these results for the corresponding dipole transition matrix elements are discussed

Influence of autoionisation and predissociation on the photoelectron parameters in HBr

Lefebvre-Brion H, Salzmann M, Klausing H-W, Müller M, Böwering N, Heinzmann U. Influence of autoionisation and predissociation on the photoelectron parameters in HBr. Journal of Physics B: Atomic, Molecular and Optical Physics. 1989;22(23):3891-3900

Microfield distributions in strongly coupled two-component plasmas

The electric microfield distribution at charged particles is studied for two-component electron-ion plasmas using molecular dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using an electron-ion Coulomb potential regularized at distances less than the de Broglie length to take into account the quantum-diffraction effects. The potential-of-mean-force (PMF) approximation is deduced from a canonical ensemble formulation. The resulting probability density of the electric microfield satisfies exactly the second-moment sum rule without the use of adjustable parameters. The correlation functions between the charged radiator and the plasma ions and electrons are calculated using molecular dynamics simulations and the hypernetted-chain approximation for a two-component plasma. It is shown that the agreement between the theoretical models for the microfield distributions and the simulations is quite good in general.Comment: 18 figures. Submitted to Phys. Rev.