Description
For introduction please refer to Diametrical Variation.
The Crofton formula computes the perimeter using the intercept count.
Cauchy's formula shows that:
The perimeter is then approximated when the above integral is replaced by a discrete summation.
In the square grid case, the summation is computed for the four fundamental directions:
represents the intercept count along the direction 
,
a represents the distance between two points on the grid and the distance between two lines in
the 
or 
directions,
is the distance between two lines in the 
and 
directions.
Finally, this formula can be corrected for non square pixels. In such a situation, the diagonals no longer fit
the and directions.
Let 
be the four neighboring pixels on the grid, a be the distance between horizontal lines, b
be the distance between vertical lines and c the distance between diagonal lines.
| Figure 1: Figure 1: Crofton perimeter on non-square pixels |
The formula becomes:
