## 2 Materials and Methods
#### Spectral and Spatial Quality Evaluation of Pansharpened Images  
Using [PERSON]'s three property criteria, we tested the spectral synthesis and consistency properties of the pansharpened images using image quality indices. According to [PERSON] [41], the first property stipulates that the pansharpened image, once degraded from its original resolution, should be as identical as possible to the original image. Secondly, the pansharpened image should be as identical as possible to the image that a matching sensor would detect with the highest resolution. Last, the multispectral pansharpened image should be as identical as possible to the multispectral set of images that the matching sensor would detect with the highest resolution. For assessment purposes, these three properties are further condensed into two properties: consistency and synthesis. The [PERSON] protocol for the quality assessment of pansharpened imagery stipulates that consistency can be tested by downsampling the merged image from the higher spatial resolution to its original spatial resolution. The nearest neighbor resampling method was used in the downsampling process to ensure minimum transformation of the pixel values. To validate the synthesis property, the original high spatial resolution panchromatic band and the lower spatial resolution multispectral bands were downsampled to their lower resolutions. To validate the synthesis property, we first degraded both the multispectral images and the panchromatic band by a factor of 4. This downsampling procedure meant the spatial resolution of the multispectral images changed from 6 m to 24 m while the panchromatic band changed from 1.5 m to 6 m. The degraded multispectral and pansharpened images were then fused and the pansharpened image was then subsequently compared to the original multispectral images for quality assessment. To verify the consistency property, we first pansharpened the native multispectral and panchromatic images to create a fused image that we further downsampled by a factor of 4, thus changing its spatial resolution of the pansharpened image from 1.5 m to 6 m. We subsequently compared the downsampled pansharpened image to the original 6 m multispectral image. The process was applied for all eight pansharpening techniques assessed in this paper. To quantitatively assess the spectral consistency of the pansharpened results the following statistical measures were used: correlation coefficient (CC), Erreur Relative Global Adimensionnelle de Synthese (ERGAS), difference in variance (DIV), bias, root mean square error (RMSE), relative average spectral error (RASE), and universal image quality index (UIQI). The quality of the synthesis in an important property in pansharpening and we used the ERGAS indices using the original multispectral and panchromatic band as a reference to assess the quality of the synthesis. The ERGAS index, when used in the spatial and spectral dimension, is indicative of the amount of spatial and spectral distortions, respectively. The spatial consistency of the pansharpened results was assessed using a spatial metric that computes the spatial correlation coefficient (SCC) between the high-frequency components of the fusion product and the original PAN. In this case, we used a \(3\times 3\) Laplacian edge detection convolution filter to filter the bands of the pansharpened images and the original panchromatic band before computing the correlation coefficients between them. The CC is one of the most widely used statistical measures of the strength and direction of the linear relationship between two images [37]. It is used to determine the amount of preservation of spectral content in two images. The CC between each band of the reference and the pansharpened image indicates the spectral integrity of the pansharpened image. The best fusion will have a higher value close to +1. RMSE measures the similarity between each band of the original and fused image.