Sufficient Conditions for 1-D CNNs with Opposite-Sign Templates to Perform Connected Component Detection

Connected component detection (CCD) is an important image processing task done by one-dimensional cellular neural networks (1-D CNNs). Recently, some sufficient conditions for 1-D CNNs with the antisymmetric template A = [s,p, -s] to perform CCD have been derived under the assumption that the outputs of the boundary cells are set to 1 or -1. In this paper, we extend these results to 1-D CNNs with the opposite-sign template A = [r,p, -s]. It is shown that the 1-D CNN can perform CCD for a wide range of parameter space. Therefore we can design 1-D CNNs which not only can perform CCD but also are robust against small perturbations of the parameters.