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On Optimal Infinite Impulse Response Edge Detection Filters
November 1991 (vol. 13 no. 11)
pp. 1154-1171

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters, operating in two orthogonal directions. The implementation is very simple and computationally efficient. has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

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Index Terms:
filter width; optimal infinite impulse response edge detection filters; Canny's high signal to noise ratio; localization criteria; spurious response; variational method; nonlinear constrained optimization; approximating recursive digital filtering; linear filters; computerised pattern recognition; digital filters; optimisation; variational techniques
S. Sarkar, K.L. Boyer, "On Optimal Infinite Impulse Response Edge Detection Filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 1154-1171, Nov. 1991, doi:10.1109/34.103275
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