Farey Sequences and the Planar Euclidean Medial Axis Test Mask

The Euclidean test mask T(r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between T(r) and the well-known Farey sequences, which allows us to propose two new algorithms. The first one computes T(r) in time O(r(4)) and space O(r(2)). The second one computes for any vector (v) over right arrow the smallest r for which (v) over right arrow T(r), in time O(r(3)) and constant space.