"A Curvature Estimation For Pen Input Segmentation in Sketch-based Modeling"

by Dae Hyun Kim, Myoung-Jun Kim

Summary

This paper discusses the use of curvature to identify segmenting points in strokes. Strokes are first resampled to equally distanced points. So that the curvature at Ci with support k (support is a set of adjacent points used for the curvature estimation) can be computed by adding all directions within the range Di-k to Di+k (Di is the angle between Pi-1Pi and PiPi+1).

Then they define the local convexity: extend the support the each side of Pi with the current point Pj only if it's locally convex with respect to Pi (have the same sign of direction). But using local convexity alone sometimes indistinguishes actual segmenting point, so local monotonicity is introduced: extend the support only if the absolute direction monotonically decreases. The advantages of this method are that (1) there's no complex computation, and (2) it's invariant under the rotation and reordering of pen markings (produces the same result.)

The segmenting points are the points with local maximum absolute curvature. Experiments show a 95% accuracy (correctly found points / actual segmenting points). Also, speed information can be added to aid segmenting point detection, and adjacent points with high curvature are merged to return only one as the segmenting point.


Discussion

This paper actually uses the geometric feature of curve to dynamically adjust the window size (support) of points used to measure the curvature. This is after the wiggy edges are smoothed by resampling. So the resampling distance should be carefully chosen to both keep curvature information and smooth out the noises.