Using simple decomposition for smoothing and feature point detection of noisy digital curves

This correspondence presents an algorithm for smoothed polygonal approximation of noisy digital planar curves, and feature point detection. The resulting smoothed polygonal representation preserves the signs of the curvature function of the curve. The algorithm is based on a simple decomposition of noisy digital curves into a minimal number of convex and concave sections. The location of each separation point is optimized, yielding the minimal possible distance between the smoothed approximation and the original curve. Curve points within a convex (concave) section are discarded if their angle signs do not agree with the section sign, and if the resulted deviations from the curve are less than a threshold ε, which is derived automatically. Inflection points are curve points between pairs of convex-concave sections, and cusps are curve points between pairs of convex-convex or concave-concave sections. Corners and points of local minimal curvature are detected by applying the algorithm to respective total curvature graphs. The detection of the feature points is based on properties of pairs of sections that are determined in an adaptive manner, rather than on properties of single points that are based on a fixed-size neighborhood. The detection is therefore reliable and robust. Complexity analysis and experimental results are presented