@article {13222,
	title = {Visibility Planning: Predicting Continuous Period of Unobstructed Views},
	journal = {Technical Reports from UMIACS},
	year = {2004},
	month = {2004/04/19/},
	abstract = {To perform surveillance tasks effectively, unobstructed views ofobjects are required e.g. unobstructed video of objects are often
needed for gait recognition. As a result, we need to determine 
intervals for video collection during which a desired object is
visible w.r.t. a given sensor. In addition, these intervals are in   
the future so that the system can effectively plan and schedule  
sensors for collecting these videos. We describe an approach to 
determine these visibility intervals. A Kalman filter is first
used to predict the trajectories of the objects. The trajectories 
are converted to polar coordinate representations w.r.t. a given
sensor. Trajectories with the same angular displacement w.r.t. the
sensor over time can be found by determining intersection points 
of functions representing these trajectories. Intervals between
these intersection points are suitable for video collection. We
also address the efficiency issue of finding these intersection      
points. An obvious brute force approach of $O(N^2)$ exists, where
$N$ is the number of objects. This approach suffices when $N$ is
small. When $N$ is large, we introduce an optimal segment
intersection algorithm of $O(N\log^2N+I)$, $I$ being the number of
intersection points. Finally, we model the prediction errors
associated with the Kalman filter using a circular object
representation. Experimental results that compare the performance
of the brute force and the optimal segment intersection algorithms
are shown.
(UMIACS-TR-2004-22)
},
	keywords = {Technical Report},
	url = {http://drum.lib.umd.edu/handle/1903/1349},
	author = {Lim,Ser-Nam and Davis, Larry S. and Wan,Yung-Chun (Justin)}
}
