Edge detection by nonlinear derivatives

This short demo presents an efficient algorithm for edge detection.

Description

The proposed algorithm is based on nonlinear derivatives to automatically select the best edge information. This algorithm can replace the classical derivative with the following benefits:
- univocal edge localization for synthetic and real images
- noise reduction with no regularization: the noise level is weaker that the noise level in the original image
- better direction estimation of the gradient
- can product a confident edge reference map with synthetic images
- extremely efficient on salt noise OR pepper noise (this last case needs a change in the nonlinear derivatives)
- still noise reduction with regularized schemes (Canny, Demigny, ...)
- can also be adapted to the asymetrical filters (Prewitt, Sobel, ...).
These nonlinear derivatives can also be advantageously used in 1D and nD signals.
Drawback: no detection of vertical and horizontal "white" thin (1 pixel) lines
Rk: this demo only performs edge detection and does not include edge extraction (local maxima) and other steps to obtain a binary edge map.
Ref: A Nonlinear Derivative Scheme Applied to Edge Detection, Olivier Laligant, Frederic Truchetet, IEEE Transactions on Pattern Analysis and Machine Intelligence - PAMI , vol. 32, no. 2, pp. 242-257, 2010

• MATLAB release: MATLAB 7.0.4 (R14SP2)