Optimal local weighted averaging methods in contour smoothing

In several applications where binary contours are used to represent and classify patterns, smoothing must be performed to attenuate noise and quantization error. This is often implemented with local weighted averaging of contour point coordinates, because of the simplicity, low-cost and effectiveness of such methods. Invoking the "optimality" of the Gaussian filter, many authors will use Gaussian-derived weights. But generally these filters are not optimal, and there has been little theoretical investigation of local weighted averaging methods per se. This paper focuses on the direct derivation of optimal local weighted averaging methods tailored towards specific computational goals such as the accurate estimation of contour point positions, tangent slopes, or deviation angles. A new and simple digitization noise model is proposed to derive the best set of weights for different window sizes, for each computational task. Estimates of the fraction of the noise actually removed by these optimum weights are also obtained. Finally, the applicability of these findings for arbitrary curvature is verified, by numerically investigating equivalent problems for digital circles of various radii.