Fitting a conic A-spline to contour image data

In this paper an algorithm for constructing contours from image data by means of a G¹ conic A-spline is presented. A conic A-spline is a piecewise smooth chain of connected real quadratic algebraic curves meeting G¹ at the junction points. Once the contour of the image data has been extracted, the algorithm computes the breakpoints of the conic A-spline, i.e. the junction points for the conic curves make up the curve. Infection points are also added to the set of junction points of the A-spline. Tangent lines at the junction points are computed using a weighted least square linear fit instead of the classical divided difference techniques. The conic A-spline interpolates the junction points along with the tangent directions and least-squares approximates the given data between junction points. We discuss and compare our experience with the approaches reported in the recent literature. Additionally, we propose some improvements.