For either
or
, it is possible to discretize
a bounded portion of the world into rectangular cells that may or may
not be occupied. The resulting model looks very similar to Example
2.1. The resolution of this discretization determines
the number of cells per axis and the quality of the approximation.
The representation may be considered as a binary image in which each
``1'' in the image corresponds to a rectangular region that contains
at least one point of , and ``0'' represents those that do not
contain any of . Although bitmaps do not have the elegance of the
other models, they often arise in applications. One example is a
digital map constructed by a mobile robot that explores an environment
with its sensors. One generalization of bitmaps is a *gray-scale
map* or *occupancy grid*. In this case, a numerical value may be
assigned to each cell, indicating quantities such as ``the probability
that an obstacle exists'' or the ``expected difficulty of traversing
the cell.'' The latter interpretation is often used in terrain maps
for navigating planetary rovers.

Steven M LaValle 2012-04-20