The number of nodes in a quadtree region representation for a simple polygon (i.e. with nonintersecting edges and without holes) is O(p+q) for a 2^q× 2^q image with perimeter p measured in pixel widths. In most cases, q is negligible, and thus, the number of nodes is proportional to the perimeter. It also holds for three-dimensional data where the perimeter is replaced by surface area, and in general for d-dimensions where instead of perimeter we have the size of the (d-1)-dimensional interfaces between the d-dimensional objects.