The Illumination Robustness of Phase Correlation for Image Alignment

Phase correlation (PC) is a well-established image matching algorithm. It is robust to the variation of image contrast and brightness, but whether it is invariant to local illumination change, particularly sun angle change, is yet to be investigated. This paper presents our study to prove and demonstrate the robustness of illumination invariance of the PC algorithm via mathematical analysis and image matching experiments. First, a 3-D space named slope-aspect-intensity (SAI) is proposed to characterize the 3-D relationship between image intensity and terrain slope/aspect angles for a given illumination geometry. Based on the SAI space, the mathematical relationship between PC cross-power spectra and illumination direction (e.g., solar azimuth and zenith angles) is analyzed. The impact of illumination angle variation between two images for matching is then rigorously investigated via experiments using simulated terrain shading images from a digital elevation model and real optical images taken under different sun illumination conditions. Our study confirms that PC is robustly invariant to illumination and therefore can achieve reliable matching between images taken under different solar illumination conditions for various remote sensing applications.