An Optimal Transport Based Global Similarity Index for Remote Sensing Products Comparison

Abstract

Remote sensing products, such as land cover data products, are essential for a wide range of scientific studies and applications, and their quality evaluation and relative comparison have become a major issue that needs to be studied. Traditional methods, such as error matrices, are not effective in describing spatial distribution because they are based on a pixel-by-pixel comparison. In this paper, the relative quality comparison of two remote sensing products is turned into the difference measurement between the spatial distribution of pixels by proposing a max-sliced Wasserstein distance-based similarity index. According to optimal transport theory, the mathematical expression of the proposed similarity index is firstly clarified, and then its rationality is illustrated, and finally, experiments on three open land cover products (GLCFCS30, FROMGLC, CNLUCC) are conducted. Results show that based on this proposed similarity index-based relative quality comparison method, the spatial difference, including geometric shapes and spatial locations between two different remote sensing products in raster form, can be quantified. The method is particularly useful in cases where there exists misregistration between datasets, while pixel-based methods will lose their robustness.