ACCURACY OF THE DIGITAL REPRESENTATION OF A STRAIGHT LINE.

Abstract

Both in Image Processing and in Computer Graphics digital straight line segments play a role as the simplest way to connect pixels. But while in Computer Graphics the emphasis is on the generation of these lines, given the parameters intercept and slope, the focus in Image Processing is on measuring the parameters, given the lines. Aspects of this analysis are the so-called linearity conditions (specifying the necessary and sufficient conditions for a set of points to be a digitized straight line segment) and the accuracy of the representation (specifying how accurately a given digitized straight line segment describes the underlying continuous reality). Both aspects have been investigated in depth. The question of accuracy has recently been solved completely, when mathematical expressions were given for the set of all continuous line segments that could have generated a given digital straight line segment. These expressions are in fact the formulas for the inversion of the digitization process. As such, they are also interesting for Computer Graphics.