Camera network optimization is an important problem in computer vision and has been explored by many researchers. Most of the early works were based on a single camera focused on a static object, and the problem was to find the best position for the camera that maximize the quality of features on the object [1, 2]. Later, Chen and Davis in [3] proposed a metric that evaluates the quality of multiple camera network configurations. The metric assesses the system based on their resolution and occlusion characteristics. The configuration is optimized based on this metric such that minimum occlusion occurs by ensuring a certain resolution. Mittal and Davis in [4] suggested a probabilistic approach for visibility analysis. The probability of visibility of an object from at least one camera was calculated. Then a cost function is defined that maps the sensor parameters to the probability. Simulated annealing is performed to minimize the cost function.
Erdem and Sclaroff in [5] suggested a binary optimization approach for the camera placement problem. The polygon representing the space is fragmented into an occupancy grid and and the algorithm tries to minimize the camera set while maintaining some specified spatial resolution. Horster and Lienhart in [6, 7, 8] proposed a linear programming approach that determines the calibration for each camera in the network that maximizes the coverage of the space assuring a certain resolution. Ram et al. in [9] proposed a performance metric that evaluates the probability of accomplishing a task as a function of set of cameras and their placement. The metric allows the camera system to be evaluated in a "directional aware" sense, i.e. that metric realizes that only images obtained in a certain direction (frontal image of the person) are useful. This metric is maximized to estimate the camera configuration. Bodor et al. in [10] proposed a method, where the goal is to maximize the aggregate observability across multiple cameras. An objective function is defined that measures the resolution of the image and the object motions (trajectories) in the scene. A variant of hill climbing method was used to maximize this objective function.
Murray et al. in [12] applied coverage optimization combined with visibility analysis to address this problem. For each camera location, the coverage was calculated using visibility analysis. Maximal covering location problem (MCLP) and backup coverage location problem (BCLP) were used to model the optimum camera combinations and locations. Malik and Bajscy in [13] suggested a method for optimizing the placement of multiple stereo cameras for 3D reconstruction. An optimization framework was defined using an error based objective function that quantifies the stereo localization error along with some constraints. Genetic algorithms were used to generate a preliminary solution and later refined using gradient descent. Kim and Murray in [14] also employed BCLP to solve the camera coverage problem. They suggested an enhanced representation of the coverage area by representing it as an continuous variable as opposed to using a discrete variable to represent the whole area. The work in [15, 16] also employed a combination of MCLP and BCLP for solving the optimum camera coverage problem. The former problem takes into consideration the 3D geometry of the environment and supplemented the MCLP/BCLP problem by including a minimal localization error variable for both monoscopic and stereoscopic cameras. The optimization problem was solved using simulated annealing. In the latter the MCLP/BCLP problem was supplemented using visibility analysis for optimization. Huang et al. in [17] proposed a 2-approximation algorithm, the first part proposes a solution for the minimum watchmen tour problem and places cameras along the estimated tour, the second one finds the solution to art gallery problem and adds extra cameras to connect the guards.
Considering the 3D geometry of the environment is of significant value for the camera coverage optimization problem. This work deals with indoor scenarios and a complete 3D model of the environment where the camera network would be deployed is designed. To the best of our knowledge, this is the first work that does not need any observations of the human activity in scenario for designing an optimal camera network. The only input to this model is the 3D geometry of the environment. In [10, 18] the observed human activity (trajectories) were used to find an optimal camera position, unlike this, in the proposed work the human trajectories are simulated in order to identify areas with high volume of human activity. Furthermore in [9] the camera position is optimized to maximize the frontal view of the humans, which again required observation, again the proposed work does not require any training to maximize the frontal view. The directional information of the trajectories were used to maximize the frontal view of the humans. Finally, the human behavior in a given scenario is influenced by the 3D geometry of that environment. To the best of our knowledge, this is the first work that incorporates this information to optimize the camera network locations for video surveillance.
Update: not the first to use 3d model "automated camera placement for large scale surveillance networks"
Erdem and Sclaroff in [5] suggested a binary optimization approach for the camera placement problem. The polygon representing the space is fragmented into an occupancy grid and and the algorithm tries to minimize the camera set while maintaining some specified spatial resolution. Horster and Lienhart in [6, 7, 8] proposed a linear programming approach that determines the calibration for each camera in the network that maximizes the coverage of the space assuring a certain resolution. Ram et al. in [9] proposed a performance metric that evaluates the probability of accomplishing a task as a function of set of cameras and their placement. The metric allows the camera system to be evaluated in a "directional aware" sense, i.e. that metric realizes that only images obtained in a certain direction (frontal image of the person) are useful. This metric is maximized to estimate the camera configuration. Bodor et al. in [10] proposed a method, where the goal is to maximize the aggregate observability across multiple cameras. An objective function is defined that measures the resolution of the image and the object motions (trajectories) in the scene. A variant of hill climbing method was used to maximize this objective function.
Murray et al. in [12] applied coverage optimization combined with visibility analysis to address this problem. For each camera location, the coverage was calculated using visibility analysis. Maximal covering location problem (MCLP) and backup coverage location problem (BCLP) were used to model the optimum camera combinations and locations. Malik and Bajscy in [13] suggested a method for optimizing the placement of multiple stereo cameras for 3D reconstruction. An optimization framework was defined using an error based objective function that quantifies the stereo localization error along with some constraints. Genetic algorithms were used to generate a preliminary solution and later refined using gradient descent. Kim and Murray in [14] also employed BCLP to solve the camera coverage problem. They suggested an enhanced representation of the coverage area by representing it as an continuous variable as opposed to using a discrete variable to represent the whole area. The work in [15, 16] also employed a combination of MCLP and BCLP for solving the optimum camera coverage problem. The former problem takes into consideration the 3D geometry of the environment and supplemented the MCLP/BCLP problem by including a minimal localization error variable for both monoscopic and stereoscopic cameras. The optimization problem was solved using simulated annealing. In the latter the MCLP/BCLP problem was supplemented using visibility analysis for optimization. Huang et al. in [17] proposed a 2-approximation algorithm, the first part proposes a solution for the minimum watchmen tour problem and places cameras along the estimated tour, the second one finds the solution to art gallery problem and adds extra cameras to connect the guards.
Considering the 3D geometry of the environment is of significant value for the camera coverage optimization problem. This work deals with indoor scenarios and a complete 3D model of the environment where the camera network would be deployed is designed. To the best of our knowledge, this is the first work that does not need any observations of the human activity in scenario for designing an optimal camera network. The only input to this model is the 3D geometry of the environment. In [10, 18] the observed human activity (trajectories) were used to find an optimal camera position, unlike this, in the proposed work the human trajectories are simulated in order to identify areas with high volume of human activity. Furthermore in [9] the camera position is optimized to maximize the frontal view of the humans, which again required observation, again the proposed work does not require any training to maximize the frontal view. The directional information of the trajectories were used to maximize the frontal view of the humans. Finally, the human behavior in a given scenario is influenced by the 3D geometry of that environment. To the best of our knowledge, this is the first work that incorporates this information to optimize the camera network locations for video surveillance.
Update: not the first to use 3d model "automated camera placement for large scale surveillance networks"
References
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[17] H. Huang, C.-C. Ni, X. Ban, J. Gao, A. Schneider, and S. Lin, "Connected wireless camera network deployment with visibility coverage," in INFOCOM, 2014 Proceedings IEEE, pp. 204-1212, April 2014.
[18] F. Janoos, R. Machiraju, R. Parent, J. W. Davis, and A. Murray, "Sensor con figuration for coverage optimization for surveillance applications," 2007.
[17] H. Huang, C.-C. Ni, X. Ban, J. Gao, A. Schneider, and S. Lin, "Connected wireless camera network deployment with visibility coverage," in INFOCOM, 2014 Proceedings IEEE, pp. 204-1212, April 2014.
[18] F. Janoos, R. Machiraju, R. Parent, J. W. Davis, and A. Murray, "Sensor con figuration for coverage optimization for surveillance applications," 2007.
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