Full-scale assessment of pansharpening: why literature indexes may give contradictory results and how to avoid such an inconvenience

In this paper, we wish to explain the contradiction of quality assessments of pansharpening carried out at full and reduced spatial scales. It seems that at full scale, methods based on Component Substitution (CS) are quantitatively poorer than the other methods, but this depends on the intrinsic space varying misregistration between the two datasets. At reduced scale, the local shifts are divided by the MS-to-Pan scale ratio and thus they tend to vanish. The problem of full-scale quality indexes is that they were originally validated on aerial Multispectral (MS) data, with synthetic panchromatic (Pan) and thus total absence of misregistration. In the presence of local misregistration due to inaccurate information of the height of the imaged surface, CS methods locally align the lowpass MS components towards the sharpening Pan, thereby preserving the geometry of the scene; all the other methods produce fading contours because of shifts. The favorable property of CS, however, impacts against the (spectral) consistency property of Wald's protocol, developed when the misalignments between MS and Pan was a small fraction of the pixel size, and hence negligible. In this perspective, methods that do not shift the original MS information are better, even though the visual quality of fading contours is worse. After exposing and explaining the contradiction between full- and reduced-scale assessments, we perform an in-depth analysis of the spectral and spatial consistency indexes of three widespread full-scale protocols: QNR, KQNR and HQNR. We investigate the robustness to shifts of all consistency indexes and propose to couple the spectral index and the spatial index that are least sensitive to shifts. In this way, the ranking of methods of reduced-scale assessments is preserved in full-scale assessments.