1. A method for determining the number of objects in a working volume, the method comprising: determining a first set of one or more polygons by intersecting a first plurality of planar projections of three-dimensional shapes, the three-dimensional shapes being intersections of silhouette cones and the working volume; and determining a first set of one or more lower bounds, a lower bound being associated with a polygon in the first set of one or more polygons, a lower bound being a lowest number of objects that can be contained in the associated polygon.