The computation of a piecewise smooth function that approximates a finite set of data points is decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function is then computed as the optimal estimator with respect to this measure field. Applications to image processing and time series prediction are presented as well.