A geostatistical point of view on heterosupport and heterotopic co-regionalization of remote sensed information

The growing use of remote sensing data (typically multi / hyperspectral satellite / drone images) has pushed towards the exploitation of indirect information known throughout the field of study. The use of remote sensing as indirect information, together with a limited number of direct and indirect field data, should improve the characterization of the target variable. The main challenge is to seek and quantify the possible correlations between the available information. The starting point is the regularized nature of the information associated with the pixels. This prevents the identification and quantification of existing correlations, if at a scale below resolution. An intuitive correlation study must be handled carefully for many reasons, including the position model of each terrestrial data within the corresponding pixel resolution surface, being the sample positions isotopic / heterotopic with the pixel or randomly distributed. Often, comparing different images ignores some important issues. A typical problem is that images derived from different satellites / drones / equipment have different pixel resolution, therefore different support (heterosupport). Finally, the image data is generally heterotopic, even in the case of the same scene shot by the same satellite at different times. Grasping the meaning of an experimental correlation coefficient becomes a sensitive issue. This contribution focuses on these issues and by a geostatistical approach explains the different meaning of apparently equivalent operations. There is a need to deepen the geostatistical co-regionalization analysis to quantify and overcome the inaccuracies and uncertainties of any experimental correlation study. And the solution tool remains the modelling of the cross covariance for different supports.