Discrete straight line segments: parameters, primitives, and properties
Leo Dorst, Arnold W. M. Smeulders · Contemporary mathematics - American Mathematical Society · 1991
Digitizing the continuous world unavoidably looses information; as a consequence, geometrical properties of real-world objects can only be estimated from the digital data. For continuous straight lines and straight object boundaries, we show the best accuracy that can be reached in the estimation of length (and other properties), in the absence of noise. In the process, we give an analytical expression for the set of continuous pre-images of a digitized straight line segment. That fundamental result has found many applications in analyses of geometrical digitization processes; several of these are indicated, as well as recent extensions of the method to arbitrary objects. 1 Introduction In digital image analysis the aim is to measure some aspects of the continuous world on the basis of digital images. In many applications, geometrical properties are foremost among the aspects to be measured. Therefore it is of interest to study how accurately these continuous properties can still be ...