1. A method for determining shading correction coefficients of an imaging device, the method comprising: determining an inversion surface based on an image captured by the imaging device; approximating the inversion surface using the captured image and eigenvectors associated with singular values of the inversion surface, to form a plurality of reconstruction weights; applying a polynomial fit to: i) the plurality of reconstruction weights to determine a first set of polynomial coefficients and ii) the eigenvectors to determine a second set of polynomial coefficients; and storing the first and second sets of polynomial coefficients, wherein the first and second sets of polynomial coefficients are used to form the shading correction coefficients.