Analysis of signal propagation in 1-D CNNs with the antisymmetric template

This paper studies some fundamental properties on signal propagation in one-dimensional cellular neural networks with the antisymmetric template under the assumption that the initial output has only one connected component. A new sufficient condition for the component to propagate without attenuation is derived through theoretical analysis. It is also proved that under the same condition the final output is a black-and-white image having only one black at the right-most pixel, which means that the network can perform connected component detection when the input image has only one connected component.