  Given a continuous sensor field, we can apply the Euler characteristic
integral approach to count the number of targets in the sensor field. If the
sensor field is discrete, the Euler integral approach introduces errors into
our target count. In this paper, we study the behavior of the Euler integral
when applied to discrete sensor fields. Under precise assumptions, we count the
number of first- and second-order errors in target count, and discover a
formula proportional to much higher order errors. This allows us to derive a
point estimator for the number of targets in a discrete sensor field. Finally
we derive an asymptotic result, providing insight into how the discrete Euler
integral behaves for a large number of targets.
