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This paper describes a four layer cellular neural network architecture implementing image processing inspired by the functionality of neurons in the visual cortex: linear orientation selective filtering and half wave rectification. The network implements both even and odd symmetric Gabor-like filters simultaneously, with pairs of layers representing the positive and negative components of the filter outputs. Each layer is an array of analog nonlinear continuous time processing elements ("cells" or "neurons"), each corresponding to one pixel in the image. Because neurons are feedback interconnected only with neurons from nearest neighbor pixels, we can easily implement this network in VLSI. For example, a recent implementation filters a 32 x 64 pixel image in parallel within a few milliseconds while dissipating only a few milliwatts. This paper analyzes the dynamics of this network mathematically, deriving the spatial transfer functions of the orientation selective filters and proving stability.