This paper introduces a special class of Cellular Neural Networks (CNNs) where cells are uncoupled and they are initialized depending on their weighted input level. An uncoupled CNN cell operating in the bipolar output mode defines a discrete-valued Perception whose threshold is determined by the initial condition. CNNs of uncoupled cells, so called linear threshold class CNNs, can be trained by Perception learning rule for searching optimum template values in linearly separable input cases. However, just like Perceptron, conventional linear threshold class CNNs can not perform the classification of linearly nonseparable input sets. To overcome this problem, we choose the initial states of the considered CNNs as piecewise constant functions of the external inputs so that a cell defines a modified Perception having an input-dependent threshold. We show that such linear threshold class CNNs can perform some linearly nonseparable threshold functions. The results obtained by the experiments done on edge detection problem justify our design method.