1. A method for calibrating a touch system, comprising: defining a set of calibration targets that have associated display coordinates (X i ,Y i ) that are in a display coordinate system; accepting touchscreen coordinates (x i ,y i ) that have noise, the touchscreen coordinates (x i ,y i ) each being associated with one of the calibration targets, the touchscreen coordinates being in a touchscreen coordinate system; and computing non-linear correction parameters based on the touchscreen coordinates (x i ,y i ) with respect to the display coordinates (X i ,Y i ), the non-linear correction parameters defining a one-to-one correspondence between display coordinates (X,Y) and touchscreen coordinates (x,y) that is non-linear, the computing producing the one-to-one correspondence where an average magnitude of a Laplacian of at least one of x and y touchscreen coordinates with respect to the display coordinates is smaller than an average magnitude of a Laplacian of a one-to-one correspondence computed with a conventional general fit in the presence of the noise of the touchscreen coordinates (x i ,y i ), the Laplacians of the x and y touchscreen coordinates being based on ∂ 2 /∂X 2 +∂ 2 x/∂Y 2 and ∂ 2 y/∂X 2 +∂ 2 y/∂Y 2 , respectively.