1. A regression method for approximating a multidimensional color transformation associated with an image output device, the regression method executed by a controller operatively connected to the image output device, and the method comprising: (a) receiving a set Γ of training samples (x i , y i ), 1≦i≦T, where x i represents input color data to the multidimensional color transformation, and y i represents corresponding output color data from the multidimensional color transformation; (b) selecting a parameterized form of a regression function f(x) that approximates the multidimensional color transformation; (c) receiving an input color x; (d) generating a cost function C representing a localized error produced by the regression function f(x) on the training set Γ, where the localized error is a function of both the parameters of f(x) and a shaping function that defines the shape and orientation of a neighborhood of training data localized around the input color x; (e) deriving the parameters of the regression function f(x) and shaping function to jointly minimize the cost function C; and (f) generating an output color y by calculating f(x) using the derived parameters of step (e).