  This paper investigates how the inherent quantization of camera sensors
introduces uncertainty in the calculated position of an observed feature during
3-D mapping. It is typically assumed that pixels and scene features are points,
however, a pixel is a two-dimensional area that maps onto multiple points in
the scene. This uncertainty region is a bound for quantization error in the
calculated point positions. Earlier studies calculated the volume of two
intersecting pixel views, approximated as a cuboid, by projecting pyramids and
cones from the pixels into the scene. In this paper, we reverse this approach
by generating an array of scene points and calculating which scene points are
detected by which pixel in each camera. This enables us to map the uncertainty
regions for every pixel correspondence for a given camera system in one
calculation, without approximating the complex shapes. The dependence of the
volumes of the uncertainty regions on camera baseline length, focal length,
pixel size, and distance to object, shows that earlier studies overestimated
the quantization error by at least a factor of two. For static camera systems
the method can also be used to determine volumetric scene geometry without the
need to calculate disparity maps.
