Interpolating cubic spline contours by minimizing second derivative discontinuity

It is shown how a contour can be estimated from a few edge positions. The technique fits a cubic spline to edges using the position and orientations of edges (tangent slopes) and computes tangent magnitudes by a minimization based on the second derivatives. Cubic splines (piecewise third-order polynomials) are used because they are the lowest-order polynomials that can deal with inflection points. For assuring a smooth overall contour, the polynomial segments are joined such that the continuity of the first derivative is preserved and discontinuity in the second derivative is minimized. This technique can be used as an efficient means for entering and editing contours which are tied to the underlying data through the edge orientations. The time required for computing the edge orientations and the time for finding the curve parameters are linearly proportional to the number of edge fragments. The algorithm was applied to medical images, and the results are compared with the conic splines and the B-splines and the distance approximation to the cubic splines