OPTIMAL LOCAL WEIGHTED AVERAGING METHODS IN CONTOUR SMOOTHING

In several applications where binary contours are used to represent an d classify patterns, smoothing must be performed to attenuate noise an d quantization error. This is often implemented with local weighted av eraging of contour point coordinates, because of the simplicity, low-c ost and effectiveness of such methods. Invoking the ''optimality'' of the Gaussian filter, many authors will use Gaussian-derived weights. B ut 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 a s the accurate estimation of contour point positions, tangent slopes, or deviation angles. A new and simple digitization noise model is prop osed to derive the best set of weights for different window sizes, for each computational task. Estimates of the fraction of the noise actua lly removed by these optimum weights are also obtained. Finally, the a pplicability of these findings for arbitrary curvature is verified, by numerically investigating equivalent problems for digital circles of various radii.