STV-based Video Feature Processing for Action Recognition

In comparison to still image-based processes, video features can provide rich and intuitive information about dynamic events occurred over a period of time, such as human actions, crowd behaviours, and other subject pattern changes. Although substantial progresses have been made in the last decade on image processing and seen its successful applications in face matching and object recognition, video-based event detection still remains one of the most difficult challenges in computer vision research due to its complex continuous or discrete input signals, arbitrary dynamic feature definitions, and the often ambiguous analytical methods. In this paper, a Spatio-Temporal Volume (STV) and region intersection (RI) based 3D shape-matching method has been proposed to facilitate the definition and recognition of human actions recorded in videos. The distinctive characteristics and the performance gain of the devised approach stemmed from a coefficient factor-boosted 3D region intersection and matching mechanism developed in this research. This paper also reported the investigation into techniques for efficient STV data filtering to reduce the amount of voxels (volumetric-pixels) that need to be processed in each operational cycle in the implemented system. The encouraging features and improvements on the operational performance registered in the experiments have been discussed at the end

Fast human detection for video event recognition

Human body detection, which has become a research hotspot during the last two years, can be used in many video content analysis applications. This paper investigates a fast human detection method for volume based video event detection. Compared with other object detection systems, human body detection brings more challenge due to threshold problems coming from a wide range of dynamic properties. Motivated by approaches successfully introduced in facial recognition applications, it adapts and adopts feature extraction and machine learning mechanism to classify certain areas from video frames. This method starts from the extraction of Haar-like features from large numbers of sample images for well-regulated feature distribution and is followed by AdaBoost learning and detection algorithm for pattern classification. Experiment on the classifier proves the Haar-like feature based machine learning mechanism can provide a fast and steady result for human body detection and can be further applied to reduce negative aspects in human modelling and analysis for volume based event detection

Maximum entropy distributions of dark matter in Λ\LambdaCDM cosmology

Small-scale challenges to $\Lambda$CDM cosmology require a deeper understanding of dark matter physics.This paper aims to develop maximum entropy distributions for dark matter particle velocity (denoted by $X$), speed (denoted by $Z$), and energy (denoted by $E$) that are especially relevant on small scales where system approaches full virialization. For systems involving long-range interactions, a spectrum of halos of different sizes is required to form to maximize system entropy. While velocity in halos can be Gaussian, the velocity distribution throughout entire system, involving all halos of different sizes, is non-Gaussian. With the virial theorem for mechanical equilibrium, we applied maximum entropy principle to the statistical equilibrium of entire system, such that maximum entropy distribution of velocity (the $X$ distribution) could be analytically derived. The halo mass function was not required in this formulation, but it did indeed result from the maximum entropy. The predicted $X$ distribution involves a shape parameter $\alpha$ and a velocity scale, $v_0$. The shape parameter $\alpha$ reflects the nature of force ($\alpha\rightarrow0$ for long-range force or $\alpha\rightarrow\infty$ for short-range force). Therefore, the distribution approaches Laplacian with $\alpha\rightarrow0$ and Gaussian with $\alpha\rightarrow\infty$. For an intermediate value of $\alpha$, the distribution naturally exhibits a Gaussian core for $v\ll v_0$ and exponential wings for $v\gg v_0$, as confirmed by N-body simulations. From this distribution, the mean particle energy of all dark matter particles with a given speed, $v$, follows a parabolic scaling for low speeds ($\propto v^2$ for $v\ll v_0$ in halo core region, i.e., "Newtonian") and a linear scaling for high speeds ($\propto v$ for $v\gg v_0$ in halo outskirt, i.e., exhibiting "non-Newtonian" behavior in MOND due to long-range gravity).Comment: Published version, 8 pages, 7 figure

Cold dark matter particle mass and properties and axion-like dark radiation in Λ\LambdaCDM cosmology

A theory is presented for the mass, size, lifetime, and other properties of cold dark matter particles within the $\Lambda$CDM cosmology. Using Illustris simulations, we demonstrate the mass and energy cascade in self-gravitating collisionless dark matter that facilitates the hierarchical structure formation of dark matter haloes. A scale-independent rate of energy cascade $\varepsilon_u \approx 10^{-7}m^2/s^3$ can be identified. Energy cascade leads to universal scaling laws on relevant scales $r$, i.e. a two-thirds law for kinetic energy ($v_r^2\propto \varepsilon_u^{2/3}r^{2/3}$) and a four-thirds law for halo density ($\rho_r\propto\varepsilon_u^{2/3}G^{-1}r^{-4/3}$), where $G$ is the gravitational constant. Both scaling laws can be confirmed by simulations and galaxy rotation curves. For cold and collisionless dark matter interacting via gravity only and because of the scale independence of $\varepsilon_u$, these scaling laws can be extended down to the smallest scale where quantum effect is important. Combined with the uncertainty principle and virial theorem on that scale, we estimate a mass $m_X=(\varepsilon_u\hbar^5G^{-4})^{1/9}=10^{12}$GeV, size $l_X=(\varepsilon_u^{-1}\hbar G)^{1/3}=10^{-13}$m, and lifetime $\tau_X=c^2/\varepsilon_u=10^{16}$years for cold dark matter particles. Here $\hbar$ is Planck constant, and $c$ is the speed of light. The energy scale $E_X=(\varepsilon_u^5\hbar^7G^{-2})^{1/9}=10^{-9}$eV strongly suggests a dark radiation to provide a viable mechanism for energy dissipation. The axion-like dark radiation should be produced at an early time $t_X=(\varepsilon_u^{-5}\hbar^2G^2)^{1/9}=10^{-6}$s (quark epoch) with a mass of $10^{-9}$eV, a GUT scale decay constant $10^{16}$GeV, an axion-photon coupling constant $10^{-18}$GeV$^{-1}$, and energy density 1$\%$ of the photon energy in CMB. Potential extension to self-interacting dark matter is also presented.Comment: 9 pages, 10 figure

Universal scaling laws and density slope for dark matter halos from rotation curves and energy cascade

Smalls scale challenges suggest some missing pieces in our current understandings of dark matter. A cascade theory for dark matter flow is proposed to provide extra insights, similar to the cascade in hydrodynamic turbulence. The energy cascade from small to large scales with a constant rate $\varepsilon_u$ ($\approx -4.6\times 10^{-7}m^2/s^3$) is a fundamental feature of dark matter flow. Energy cascade leads to a two-thirds law for kinetic energy $v_r^2$ on scale $r$ such that $v_r^2 \propto (\varepsilon_u r)^{2/3}$, as confirmed by N-body simulations. This is equivalent to a four-thirds law for mean halo density $\rho_s$ enclosed in the scale radius $r_s$ such that $\rho_s \propto \varepsilon_u^{2/3}G^{-1}r_s^{-4/3}$, as confirmed by data from galaxy rotation curves. By identifying relevant key constants, critical scales of dark matter might be obtained. The largest halo scale $r_l$ can be determined by $-u_0^3/\varepsilon_u$, where $u_0$ is the velocity dispersion. The smallest scale $r_{\eta}$ is dependent on the nature of dark matter. For collisionless dark matter, $r_{\eta} \propto (-{G\hbar/\varepsilon_{u}}) ^{1/3}\approx 10^{-13}m$, where $\hbar$ is the Planck constant. A uncertainty principle for momentum and acceleration fluctuations is also postulated. For self-interacting dark matter, $r_{\eta} \propto \varepsilon_{u}^2 G^{-3}(\sigma/m)^3$, where $\sigma/m$ is the cross-section. On halo scale, the energy cascade leads to an asymptotic slope $\gamma=-4/3$ for fully virialized halos with a vanishing radial flow, which might explain the nearly universal halo density. Based on the continuity equation, halo density is analytically shown to be closely dependent on the radial flow and mass accretion such that simulated halos can have different limiting slopes. A modified Einasto density profile is proposed accordingly.Comment: 7 pages, 7 figure