skimage2.measure.perimeter_crofton#

skimage2.measure.perimeter_crofton(image, directions=4)[source]#

Calculate total Crofton perimeter of all objects in binary image.

Parameters:

imagendarray of shape (M, N): Input image. If image is not binary, all values greater than zero are considered as the object.
directions2 or 4, optional: Number of directions used to approximate the Crofton perimeter. By default, 4 is used: it should be more accurate than 2. Computation time is the same in both cases.

Returns:

perimeterfloat: Total perimeter of all objects in binary image.

Notes

This measure is based on Crofton formula [1], which is a measure from integral geometry. It is defined for general curve length evaluation via a double integral along all directions. In a discrete space, 2 or 4 directions give a quite good approximation, 4 being more accurate than 2 for more complex shapes.

Similar to skimage2.measure.perimeter(), this function returns an approximation of the perimeter in continuous space.

References

[1]

https://en.wikipedia.org/wiki/Crofton_formula

[2]

S. Rivollier. Analyse d’image geometrique et morphometrique par diagrammes de forme et voisinages adaptatifs generaux. PhD thesis, 2010. Ecole Nationale Superieure des Mines de Saint-Etienne. https://tel.archives-ouvertes.fr/tel-00560838

Examples

>>> import _skimage2 as ski2
>>> # coins image (binary)
>>> img_coins = ski2.data.coins() > 110
>>> # total perimeter of all objects in the image
>>> ski2.measure.perimeter_crofton(img_coins, directions=2)
8144.578...
>>> ski2.measure.perimeter_crofton(img_coins, directions=4)
7837.077...