Foreground Detection in Camouflaged Scenes

Foreground detection has been widely studied for decades due to its importance in many practical applications. Most of the existing methods assume foreground and background show visually distinct characteristics and thus the foreground can be detected once a good background model is obtained. However, there are many situations where this is not the case. Of particular interest in video surveillance is the camouflage case. For example, an active attacker camouflages by intentionally wearing clothes that are visually similar to the background. In such cases, even given a decent background model, it is not trivial to detect foreground objects. This paper proposes a texture guided weighted voting (TGWV) method which can efficiently detect foreground objects in camouflaged scenes. The proposed method employs the stationary wavelet transform to decompose the image into frequency bands. We show that the small and hardly noticeable differences between foreground and background in the image domain can be effectively captured in certain wavelet frequency bands. To make the final foreground decision, a weighted voting scheme is developed based on intensity and texture of all the wavelet bands with weights carefully designed. Experimental results demonstrate that the proposed method achieves superior performance compared to the current state-of-the-art results.Comment: IEEE International Conference on Image Processing, 201

On the Global Convergence of Continuous-Time Stochastic Heavy-Ball Method for Nonconvex Optimization

We study the convergence behavior of the stochastic heavy-ball method with a small stepsize. Under a change of time scale, we approximate the discrete method by a stochastic differential equation that models small random perturbations of a coupled system of nonlinear oscillators. We rigorously show that the perturbed system converges to a local minimum in a logarithmic time. This indicates that for the diffusion process that approximates the stochastic heavy-ball method, it takes (up to a logarithmic factor) only a linear time of the square root of the inverse stepsize to escape from all saddle points. This results may suggest a fast convergence of its discrete-time counterpart. Our theoretical results are validated by numerical experiments.Comment: accepted at IEEE International Conference on Big Data in 201

A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain

Detecting camouflaged moving foreground objects has been known to be difficult due to the similarity between the foreground objects and the background. Conventional methods cannot distinguish the foreground from background due to the small differences between them and thus suffer from under-detection of the camouflaged foreground objects. In this paper, we present a fusion framework to address this problem in the wavelet domain. We first show that the small differences in the image domain can be highlighted in certain wavelet bands. Then the likelihood of each wavelet coefficient being foreground is estimated by formulating foreground and background models for each wavelet band. The proposed framework effectively aggregates the likelihoods from different wavelet bands based on the characteristics of the wavelet transform. Experimental results demonstrated that the proposed method significantly outperformed existing methods in detecting camouflaged foreground objects. Specifically, the average F-measure for the proposed algorithm was 0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI

On the fast convergence of random perturbations of the gradient flow

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in $O(\ln (\varepsilon^{-1}))$ time on the average, where $\varepsilon$ is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points. This can be regarded as a manifestation of fast convergence of the discrete-time stochastic gradient method, the latter being used heavily in modern statistical machine learning.Comment: Revise and Resubmit at Asymptotic Analysi