An Enumeration Problem In Digital Geometry.

Abstract

We prove that the number L(N) of digital line segments of length N(corresponding to the line y=ax+b <= a < 1, 0 < b < 1) has the asymptotic expansion: L(N)=N^3/PI^2+0(N^2 log N) This expression has applications in image registration problems and originated in a question posed by NASA.