Counting Objects with a Combination of Horizontal and Overhead Sensors

Erik Halvorson, Ronald Parr
2009 The international journal of robotics research  
Counting the number of distinct objects within a region is a basic problem in the field of surveillance, with a wide array of possible uses. One approach to this problem involves scanning a wide area and recognizing objects of interest, an approach that can be both computationally intensive and error prone. A recent geometric approach, based upon change detection, can often provide an accurate count of the new objects in a scene without solving the recognition problem. This approach uses a
more » ... l hull, which is defined as a set of polygons at the intersection of silhouette cones. The visual hull provides upper and lower bounds on the number of objects in a scene. Often, however, the visual hull is quite ambiguous, meaning these bounds are not tight. Earlier work assumes that these ambiguities will reduce as objects move in the scene. We consider using a two phase approach to counting objects. In the first phase, a set of horizontal sensors builds a visual hull. We then use a secondary network of overhead sensors to resolve ambiguous regions of the visual hull, tightening the bounds and permitting an exact count. One example of such a setup would be to use a network of ground-based cameras as the initial phase, then to use cameras on unmanned aerial vehicles to tighten the bounds. We describe several results furthering the understanding of this problem: 1) A hardness result showing that computing a tight lower bound is intractable, 2) A greedy algorithm for maximizing the number of polygons viewed by a network of overhead sensors, 3) A hardness result showing that orienting the overhead sensors to view the maximum number of polygons is intractable, 4) Results showing that a greedy algorithm can be applied to resolve ambiguous portions of the visual hull, with provable bounds relative to an optimal algorithm, and 5) Extensions of these results to two abstracted sensor models for the case when polygons can be occupied by more than one object. Due to the generality of this framework, the algorithms and results apply to counting many different kinds of objects with a wide variety of different sensors.
doi:10.1177/0278364909352256 fatcat:o66utc7xcrathosxgl5qrttvzq