Lighting variation is commonly handled by methods invariant to additive and multiplicative changes in image intensity. It has been demonstrated that comparing images using the direction of the gradient can produce broader insensitivity to changes in lighting conditions, even for 3D scenes. We analyze two common approaches to image comparison that are invariant, normalized correlation using small correlation windows, and comparison based on a large set of oriented difference of Gaussian filters. We show analytically that these methods calculate a monotonic (cosine) function of the gradient direction difference and hence are equivalent to the direction of gradient method. Our analysis is supported with experiments on both synthetic and real scenes.