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.

[1]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[2]  T. Pavlidis.  Linguistic Analysis of Waveforms , 1971 .

[3]  Theodosios Pavlidis,et al.  Optimal Piecewise Polynomial L2Approximation of Functions of One and Two Variables , 1975, IEEE Transactions on Computers.

[4]  Theodosios Pavlidis,et al.  Waveform Segmentation Through Functional Approximation , 1973, IEEE Transactions on Computers.

[5]  Larry S. Davis,et al.  Understanding Shape: Angles and Sides , 1977, IEEE Transactions on Computers.

[6]  M. Cox.  Curve Fitting with Piecewise Polynomials , 1971 .

[7]  L. Goddard.  Approximation of Functions , 1965, Nature.

[8]  Theodosios Pavlidis,et al.  Segmentation of Plane Curves , 1974, IEEE Transactions on Computers.

[9]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[10]  Antonio Cantoni,et al.  Optimal Curve Fitting With Piecewise Linear Functions , 1971, IEEE Transactions on Computers.