A new characterization of digital lines by least square fits

Abstract In this paper we prove that digital line segments and their least square line fits are in one-to-one correspondence and give a new simple representation ( x 1 , n , b 0 , b 1 ) of a digital line segment, where x 1 and n are the x -coordinate of the left endpoint and the number of digital points, respectively, while b 0 and b 1 are the coefficients of the least square line fit Y = b 0 + b 1 X for the given digital line segment. An O( n log n ) time algorithm for obtaining a digital line segment from its least square line fit is described.