Distances defined by neighborhood sequences
Pattern Recognition
Distance functions in digital geometry
Information Sciences: an International Journal
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast distance transformation on irregular two-dimensional grids
Pattern Recognition
Hi-index | 0.00 |
The theory of neighborhood sequences is applicable in many image-processing algorithms. The theory is well developed for the square grid. Recently there are some results for the hexagonal grid as well. In this paper, we are considering all the three regular grids in the plane. We show that there are some very essential differences occurring. On the triangular plane the distance has metric properties. The distances on the square and the hexagonal case may not meet the triangular inequality. There are non-symmetric distances on the hexagonal case. In addition, contrary to the other two grids,the distance can depend on the order of the initial elements of the neighborhood sequence.Moreover in the hexagonal grid it is possible that circles with different radii are the same (using different neighborhood sequences). On the square grid the circles with the same radius are in a well ordered set, but in the hexagonal case there can be non-comparable circles.