1-Attempt and Equivalent Thinning on the Hexagonal Grid

Thinning in 2D is an iterative object reduction to produce centerlines of discrete binary objects. A thinning algorithm is 1-attempt if whenever a border point is not deleted in the actual iteration step, it belongs to the resulting centerline. Parallel thinning algorithms alter all deletable points simultaneously, while sequential ones traverse object points in the current picture, and delete the actually visited one if it is designated as deletable. A pair of thinning algorithms are equivalent if they produce the same centerline for any input picture. This paper presents the very first 1-attempt, equivalent, and topology-preserving pair of parallel and sequential thinning algorithms acting on the nonconventional hexagonal grid. It is also illustrated that 1-attempt property involves a remarkable speed up.