An efficient CNN implementation of a 2D orientation and scale tunable low-pass filter based on the approximation of an oriented 2D Gaussian filter

Oriented two dimensional spatial low-pass filters are useful for image processing tasks such as adaptive smoothing. We propose an oriented low-pass filter suitable for CNN implementations. The filter design procedure starts with an oriented Gaussian filter with the final CNN implementation involves only five non-zero coefficients in its feedback template, but achieving both orientation and scale tunable responses. By elaborating on the existing linear CNN stability criterion in terms of multidimensional signals theory, the stability of our CNN filter is also analyzed. Simulation results confirm the spatial impulse response of the CNN is indeed orientation and scale tunable.