We derive a sensitivity analysis for moment invariants of multidimensional distributions. These invariants have many uses in computational systems and have recently been used for illumination-invariant recognition in color images. In this context, the sensitivity analysis predicts the response of moment invariants to partial occlusion. Using the results of the sensitivity analysis, we develop a novel surface representation called the invariant profile which captures color distribution and spatial information while remaining invariant to the spectral content of the scene illumination. Unlike previous representations, the recognition of invariant profiles does not require illumination correction. We demonstrate the sensitivity analysis and the use of invariant profiles for recognition with a set of experiments on color images.