Objective supervised edge detection evaluation by varying thresholds of the thin edges

Supervised edge detection evaluation with a threshold loop

This code present several supervised edge detection evaluations which compute a score between a ground truth edge map and a candidate image thin absolute gradient image. Theoretically, by varying thresholds of the thin edges, the minimum score of the measure corresponds to the best edge map, compared to the ground truth which corresponds to an objective evaluation.
Edge evaluations coded:

Hausdorff distance:
D. P. Huttenlocher and W. J. Rucklidge,
A multi-resolution technique for comparing images using the Hausdorff distance,
IEEE Trans. on Pattern Analysis and Machine Intel.: Vol. 15(9), pp. 850–863, 1993.

Psi :
H. Abdulrahman, B. Magnier, and P. Montesinos, “A new normalized supervised edge detection evaluation,” in IbPRIA - to appear-, 2017.

Hn:
Percentage of maximum distance of Hausdorff measure:
M.P. Dubuisson, A.K. Jain,
A modified Hausdorff distance for object matching,
12th IAPR Int. Conf. on Pattern Recognition: Vol. 1, pp. 566–568, 1994.

phi:
S. Venkatesh and P.L. Rosin, Dynamic threshold determination by local and global edge evaluation, Comp. Vision, Graphics, and Image Proc.: Vol. 57(2), pp. 146–160, 1995.

xhi2:
Y. Yitzhaky and E. Peli, A method for objective edge detection evaluation and detector parameter selection, IEEE Trans. on Pattern Analysis and Machine Intel., vol. 25, no. 8, pp. 10271033, 2003.

Falpha:
D. R. Martin, C. C. Fowlkes and J. Malik, Learning to detect natural image boundaries using local brightness, color, and texture cues, IEEE Trans. on Pattern Analysis and Machine Intel.: Vol. 26(5), pp. 530–549, 2004.

P = Performance measure:
P. Sneath and R. Sokal, Numerical taxonomy. The principles and practice of numerical classification, 1973.

SSR : Segmentation Success Ratio (results similar to P)
R. Usamentiaga, D. F. Garc?a, C. Lopez, and D. Gonzalez, A method for assessment of segmentation success considering uncertainty in the edge positions, EURASIP J. on Applied Signal Proc., Vol. 2006, pp. 207–207, 2006.

PE = Localization-error
S. U. Lee, S. Y. Chung, and R. H. Park, A comparative performance study of several global thresholding techniques for segmentation, CVGIP, Vol. 52(2), pp. 171–190, 1990.

P1 and P2
E. Deutsch and J. R. Fram, A quantitative study of the orientation bias of some edge detector schemes, IEEE Trans. on Computers: Vol. 27(3), pp. 205–213, 1978.

Ground truth image:
H. Abdulrahman, B. Magnier, and P. Montesinos, "From Contours to Ground Truth: How to Evaluate Edge Detectors by Filtering", WSCG 2017, 25th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, May 29 - June 2, 2017

You can create your ground truth edge map and compare with other methods.