Polynomial representation of 2-D image boundary contours

This paper discusses a method to represent the graphical image boundary contours with a parametric polynomial equation of minimum degree. The image boundary contour is optimally sampled to ´n´ number of points. Then a curve is generated using Lagrange´s interpolation method that passes through these n points. The curve regenerated through interpolation is then compared with the original contour by the weighted distance transform method. If the error is within tolerable range, then it is concluded that this image boundary contour can be represented with these ´n´ number of control points. Otherwise, the samples are increased and the process is repeated till we get the optimum number of sampled points to reconstruct the contour through the interpolation technique.