Polygonal Approximations by Newton´s Method

The problem of locating optimally the breakpoints in a continuous piecewise-linear approximation is examined. The integral square error E of the approximation is used as the cost function. Its first and second derivatives are evaluated and this allows the application of Newton´s method for solving the problem. Initialization is performed with the help of the split-and-merge method [8]. The evaluation of the derivatives is performed for both waveforms and contours. Examples of implementation of both cases are shown.