Invertible piecewise linear approximations for color reproduction

We consider the use of linear splines with variable knots for the approximation of unknown functions from data, motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in a closed form. For the one-dimensional case, we present a study comparing PL and neural network (NN) approximations for several function families. Preliminary results suggest that PL, in addition to their analytical benefits, are at least competitive with NN in terms of sum square error, computational effort and training time.