Sufficient conditions for one-dimensional cellular neural networks to perform connected component detection

It is well known that one-dimensional cellular neural networks (1D CNNs) with the template A=[1,2,−1]A=[1,2,−1] can perform connected component detection (CCD). However, this has been confirmed only by numerical and laboratory experiments. In this paper, sufficient conditions for 1D CNNs to perform CCD are obtained through theoretical analysis. Main result shows that a wide class of templates including A=[1,2,−1]A=[1,2,−1] can be used for CCD.