Design of DTCNNs for edge detection

Discrete-time cellular neural networks (DTCNN) can extract edges out of gray scale images. While training a DTCNN with a 1-neighborhood using the Ada Tron algorithm, we obtained a multiple k of the well known Laplacian operator along with a threshold for the classification of a pixel. We are able to obtain an explicit expression for the threshold and the factor k depending on the requested resolution. Since the Laplacian is known for its sensitivity to noise, we developed a noise reduction. Using the special DTCNN structure, the noise reduction could be designed more effectively, than the simple application of the Laplacian followed by a noise removal. Extending the above studies to a 2-neighborhood we obtained a template with a spacial band pass filter characteristic similar to a 'Laplacian of Gaussian' (LoG), which further improves the quality of the edge detection.