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.
Additional Metadata
Publisher A.M.S.
Editor R. Melter , P. Bhattacharya , A. Rosenfeld
Series Contemporary mathematics
Note ftp://ftp.wins.uva.nl/pub/computer-systems/aut-sys/reports/DorSme91.ps.gz
Dorst, L, & Smeulders, A.W.M. (1991). Discrete Straight Line Segments: Parameters, Primitives and Properties. In R Melter, P Bhattacharya, & A Rosenfeld (Eds.), Vision Geometry (pp. 45–62). A.M.S.