Optimal Edge Detector Design II: Coefficient Quantization

A companion paper describes the design and implementation of the Laplacian of a Gaussian edge detection filter which localizes edges through zero crossings in the filtered image. Accuracy in the presence of noise has been found to be proportional to the square root of the filter´s standard deviation. Digital implementation of any continuous filter requires sampling and coefficient quantization. The sampled filter was examined, but a method is proposed here for selection of a minimum coefficient word size for direct-form implementation to satisfy in-band rejection bounds.