Distortion of orientation data introduced by digitizing procedures

Abstract

SUMMARYFor a given set of lines or outlines, the orientation distribution function, h(α), i.e. the line length per angle of orientation, is a useful measure of anisotropy. In order to obtain this function, it is most convenient to digitize the original, continuously curved lines, that is to replace them by an approximate set of straight line segments. h(α) is then given by the total length of line segment per angular interval. It is generally assumed that the orientation distribution function of the digitized lines approaches that of the original lines if the line segments are sufficiently small. However, in as much as the point density of a square lattice is not constant for all directions, the digitized lines, whose end points are lattice points of the digitizing grid, cannot represent all directions equally well. In this paper, the nature of the distortions introduced by the digitizing procedure and their dependence on sampling length and angular sampling interval are explored, and conditions for minimal distortions are discussed. For computer applications, it is recommended to perform a two‐dimensional smoothing spline operation on the digitized input. In doing so the distortion problem is altogether avoided.