Segmenting curves into elliptic arcs and straight lines

A method is described for segmenting edge data into a combination of straight lines and elliptic arcs. The two-stage process first segments the data into straight line segments. Ellipses are then fitted to the line data. This is much faster than curve fitting directly to pixel data since the lines provide a great reduction in data. Segmentation is performed in the paradigm suggested by D.G. Lowe (1987). A measure of significance is defined that produces a scale-invariant description and allows the replacement of sequences of line segments by ellipses without requiring any thresholds. A method for fitting ellipses to arbitrary curves, essential for this algorithm, has been developed, based on an iterative Kalman filter. This is guaranteed to produce an elliptical fit even though the best conic fit may be a hyperbola or parabola.>