Grouping contour points to line segments using signature functions

A technique to group contour points into line segments is presented in this paper. A Hough transform extended signature function with the angle parameter as a reference parameter is defined to reduce the contour grouping from 2D to 1D. An analysis shows that the signature function is piecewise linear with transition point corresponding to the turning points of a contour. Its stepwise derivative function is computed for the separation points in a set of contour points. With a changing angle as the reference parameter, we can vary the strength of the discontinuity of the signature function, to find almost all significant separation points. These points are further evaluated by three criteria (angle, piecewise error and total error) proposed later for the most representative separation points, between which the contour points are grouped together and are fitted into different line segments. Experiments with generated and real images are given to demonstrate the functionality of the algorithm.