Abstract:
We typically think of fitting data with an approximating curve in the linear least squares
sense, where the sum of the residuals in the vertical direction is minimized. The problem
addressed here is to fit a curve to an ordered set of data in the total least squares sense,
where the sum of the residuals in both the horizontal and vertical directions is minimized. In
this thesis we concern two curve fitting methods including: least-squares regression and
interpolation. Regression focuses mainly on functions, that is, on data points linearly ordered
with respect to their abscissa. After reviewing existing methods for curve fitting using
regression, we introduce a more general representation of curves. Comparative results show
that the proposed method provides smaller errors or better compression ratios (i.e. our
approach hqs shown an efficient performance over the existing methods).
