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
Olivier LALIGANT (2020). Edge detection by nonlinear derivatives (https://www.mathworks.com/matlabcentral/fileexchange/31029-edge-detection-by-nonlinear-derivatives), MATLAB Central File Exchange. Retrieved .
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