A Parametrization of Digital Planes by Least-Squares Fits and Generalizations

on the xy-plane are bounded regions, called bases of digital plane segments. So, if the plane a is digitized and if a In this paper we prove that digital plane segments and their least-squares plane fit are in one-to-one correspondence, which region Q in the xy-plane is given, then the digital plane gives a simple representation of a digital plane segment by its segment P(a, Q) (more precisely, digital plane segment base description and coefficients of the least-squares plane fit. with the base Q) is defined as This leads to a constant space representation of digital rectangles in space. The method used is generalized and modified for P(a, Q) 5 h(i, j, Ai 1 Bj 1 C), constant space representation of sets which may consists of (i, j) [ Q where i and j are integersj. digital surface segments of different kinds.  1996 Academic Press, Inc.