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Vehicle counting and traffic volume estimation on traffic videos has gained extensive attention from multimedia and computer vision communities. Recent vehicle counting and volume estimation methods, including detection based and time-spatial image (TSI) based methods have achieved significant improvements. However, how to balance the accuracy and speed is still a challenge to this task. In this paper, we design a fast and accurate vehicle counting and traffic volume estimation method. Firstly, traffic videos are converted to TSIs and we annotate the vehicle locations in TSIs manually. Then, we design a simple TSI density map estimation network which utilizes attention mechanism to strengthen the features in the traffic locations for vehicle counting. Finally, we use the parameters obtained from the vehicle counting network to further estimate the traffic volume. Experiments on UA-DETRAC dataset demonstrate that the vehicle counting network not only takes a balance between counting accuracy and speed, but also well estimates the traffic volume when the video data is insufficient.

The linear phase is a major characteristic of digital differentiators in many signal processing applications. This study presents a sequential partial optimization method for designing a fullband infinite impulse response digital differentiator with a near linear phase. To achieve a near linear phase, the group delay is treated as an optimization variable, and the maximum phase error is minimized within a constrained domain. During each iteration of the algorithm, in addition to the whole numerator and group delay, only one secondorder denominator factor is optimized. The necessary and sufficient stability triangles are applied to insure the stability of the differentiators, and the Gauss-Newton strategy is used to handle the nonconvexity of the design problems. Design examples show that the proposed method outperforms several state-of-the-art methods in terms of the maximum phase deviation from the desired linear phase.

A sequential partial optimization method is presented in this paper for the minimax design of two-dimensional infinite impulse response filters with separable denominator. The method converts the minimax design problem into a sequence of smaller subproblems, each updating only one pair of second-order denominator factors. The necessary and sufficient stability triangles for one-dimensional filters are used as the stability constraints on the two-dimensional filters. The first-order Taylor expansion and a trust-region method are used to deal with the nonconvexity of the subproblems and guarantee the convergence of the solution algorithm. By comparing with a corresponding joint optimization method, the sequential partial optimization algorithm is shown to converge faster for filters with relatively high denominator order. This is mainly due to the observation that the trust region to assure the convergence is usually much smaller for the joint optimization method. Moreover, the limit solution of the sequential partial optimization algorithm has been proved to be a Karush–Kuhn–Tucker point of the design problem. Design examples demonstrate that the proposed algorithm has obtained smaller maximum frequency response errors than the competing methods both for filters with separable denominator of the same order and for filters with nonseparable denominator of about the same implementation complexity.