On the Farey sequence and its augmentation for applications to image analysis - Pratihar, Sanjoy; Bhowmick, Partha (Zielona Góra: Uniwersytet Zielonogórski)
We introduce a novel concept of the "augmented Farey table" (AFT). Its purpose is to store the ranks of fractions of a "Farey sequence" in an efficient manner so as to return the rank of any query fraction in constant time. As a result, computations on the digital plane can be crafted down to simple integer operations; for example, the tasks like determining the extent of collinearity of integer points or of parallelism of straight lines - often required to solve many image-analytic problems - can be made fast and efficient through an appropriate AFT-based tool.
Keywords: Farey sequence; Farey table; fraction rank; theory of fractions; image analysis