Adaptive contour coding using warped polynomials

This paper presents a new method for compactly representing contours. The new method is a generalization of the Fourier descriptor (FD) method. Like the FD method it approximates a complex-valued parameter representation of the contour by a trigonometric polynomial (TP). In the FD method, the TP is the best least mean squares approximation of the parameter representation. However, the mean squared error is not a good a criterion for judging the accuracy of a contour approximation. The paper proposes a better criterion and a method for computing the corresponding optimal TP. It shows that computing this optimal TP is equivalent to fitting a so-called warped TP to the parameter representation in the least mean squares sense. The paper presents preliminary results which show that the new method produces more accurate contour approximations than FD approximations of the same degree.