FREQUENCY-DOMAIN DESIGN OF FIR AND IIR LAPLACIAN OF GAUSSIAN FILTERS FOR EDGE-DETECTION

This work addresses the design of LoG filters in the frequency domain within a structure formed by the cascade of quasi-Gaussian and discret e Laplacian filters. The main feature of such a structure is that it r equires half the number of convolutions of the classical structure in which the LoG transfer function is expressed as the sum of two separab le transfer functions of 1-D Gaussian and LoG type. Such a perspective allows one to rephrase the design of IIR and FIR filters for edge det ection as a frequency domain approximation problem solvable by standar d digital filter design tools. The zero-phase IIR solutions have a goo d performance at low orders and approximation errors practically indep endent of the aperture parameter. The characteristics of the nearly li near-phase IIR filters solving the problem suggest the consideration o f linear-phase FIR filters with zeros constrained on the unit circle. The use of such filters leads to remarkable computational savings with respect to the filters designed by impulse response sampling. The agr eement between the edge values obtained by the filters designed accord ing to the scheme proposed in this work and those obtained by standard techniques is very good.