Analysis-by-synthesis: Pedestrian tracking with crowd simulation models in a multi-camera video network

For tracking systems consisting of multiple cameras with overlapping field-of-views, homography-based approaches are widely adopted to significantly reduce occlusions among pedestrians by sharing information among multiple views. However, in these approaches, the usage of information under real-world coordinates is only at a preliminary level. Therefore, in this paper, a multi-camera tracking system with integrated crowd simulation is proposed in order to explore the possibility to make homography information more helpful. Two crowd simulators with different simulation strategies are used to investigate the influence of the simulation strategy on the final tracking performance. The performance is evaluated by multiple object tracking precision and accuracy (MOTP and MOTA) metrics, for all the camera views and the results obtained under real-world coordinates. The experimental results demonstrate that crowd simulators boost the tracking performance significantly, especially for crowded scenes with higher density. In addition, a more realistic simulation strategy helps to further improve the overall tracking result

Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture

We consider one-dimensional quantum spin chain, which is called XX model, XX0 model or isotropic XY model in a transverse magnetic field. We study the model on the infinite lattice at zero temperature. We are interested in the entropy of a subsystem [a block of L neighboring spins]. It describes entanglement of the block with the rest of the ground state. G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev showed that for large blocks the entropy scales logarithmically. We prove the logarithmic formula for the leading term and calculate the next term. We discovered that the dependence on the magnetic field interacting with spins is very simple: the magnetic field effectively reduce the size of the subsystem. We also calculate entropy of a subsystem of a small size. We also evaluated Renyi and Tsallis entropies of the subsystem. We represented the entropy in terms of a Toeplitz determinant and calculated the asymptotic analytically.Comment: LATEX, 17 pages, 1 fi