Background Subtraction via Generalized Fused Lasso Foreground Modeling

Background Subtraction (BS) is one of the key steps in video analysis. Many background models have been proposed and achieved promising performance on public data sets. However, due to challenges such as illumination change, dynamic background etc. the resulted foreground segmentation often consists of holes as well as background noise. In this regard, we consider generalized fused lasso regularization to quest for intact structured foregrounds. Together with certain assumptions about the background, such as the low-rank assumption or the sparse-composition assumption (depending on whether pure background frames are provided), we formulate BS as a matrix decomposition problem using regularization terms for both the foreground and background matrices. Moreover, under the proposed formulation, the two generally distinctive background assumptions can be solved in a unified manner. The optimization was carried out via applying the augmented Lagrange multiplier (ALM) method in such a way that a fast parametric-flow algorithm is used for updating the foreground matrix. Experimental results on several popular BS data sets demonstrate the advantage of the proposed model compared to state-of-the-arts

Gradient flow approach to an exponential thin film equation: global existence and latent singularity

In this work, we study a fourth order exponential equation, $u_t=\Delta e^{-\Delta u},$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.Comment: latent singularity, curve of maximal slope. arXiv admin note: text overlap with arXiv:1711.07405 by other author

Temperature-dependent contact of weakly interacting single-component Fermi gases and loss rate of degenerate polar molecules

Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state KRb molecules with intrinsic two-body losses [L. De Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate Fermi gas of polar molecules, Science 363, 853 (2019)], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the $p$-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using $p$-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally -- in agreement with the Bethe-Wigner threshold law -- linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular $p$-wave gases but also to atomic single-component Fermi gases, such as 40K and 6Li