Analytical Design Technique for the 2D IIR Differentiator

An efficient analytical procedure in the frequency domain is proposed for the design of a 2D IIR differentiator. This technique uses a Chebyshev-Padé rational approximation, which finally leads to a rational trigonometric function, a very accurate approximation for frequency response of the ideal differentiator. To assess its image processing capabilities, the differentiator is tested on two images: a binary image containing black objects on a white background, and then a real-life greyscale image. The designed differentiator is applied to the given test images and the simulation results are provided, showing its capability in edge detection. The designed differentiator is accurate and efficient, with separable frequency response and a low computational complexity.