Axiomatic quantification of multidimensional image resolution

We generalize the axiomatic quantification of one-dimensional (1-D) image resolution to the multidimensional case. The imaging system of interest is characterized by a nonnegative spatially invariant point spread function. The axioms extended from the 1-D counterparts include nonnegativity, continuity, translation invariance, rotation invariance, luminance invariance, homogeneous scaling, and serial combination properties. It is proved that the only resolution measure consistent with the axioms is proportional to the square root of the trace of the covariance matrix of the point spread function.