Full-Scale Assessment of Pansharpening Through Polynomial Fitting of Multiscale Measurements

Pansharpening techniques aim at improving the spatial resolution of a multispectral data set (MS) by using a panchromatic image (Pan) acquired on the same scene with a greater spatial resolution and consequently a lower ground sample distance (GSD). Usually, a quantitative assessment of the fused products cannot be directly performed because of the lack of a reference MS data set with the same GSD of the Pan. A well-known solution is Wald's protocol: The original MS and Pan are spatially degraded, the reducing factor being the ratio between their GSDs. Pansharpening is then performed between the reduced MS and Pan data sets, and the fused products are compared with the original MS, which can be used as reference. In this protocol, fusion performances are assumed to be independent of the scale so that the results at the reduced scale are an estimation of those at the original resolution. This hypothesis can be more or less reliable, depending on the sensor and/or the scene content. The objective of this paper is to propose a new methodology to infer the unknown performances of a pansharpening method at full scale. For this purpose, multiple sets of fused images are computed at degraded scales by downsampling Pan and MS data sets by means of the sensor modulation transfer function. Multiscale quality/distortion measurements are fitted by linear and quadratic polynomials in order to extrapolate their full-scale values. Once the proposed protocol has been assessed in the presence of reference originals, the obtained results are extended to the case where the reference image is not available.