A note on fuzzy set theory in scanning

Scanning of a natural picture handled by an image processing system always causes a loss of information, i.e., the micro picture elements become uncertain and vague. This is essential when the picture is to be used for measuring or evaluation of structural parameters. To make the induced uncertainty and vagueness transparent up to the computed results, specifications and procedures from fuzzy set theory are presented and suggested. In particular, distances of pixels are considered. For a demonstration of how this uncertainty can influence conclusions from the given picture, the computation of the approximate gradient of a curve is considered