We first discuss the relativity of "true value and homogeneity" for quantitative remote sensing products (QRSPs), and then propose the definitions of "eigenaccuracy" and "eigenhomogeneity" under practical conditions. The eigenaccuracy and eigenhomogeneity for land surface crucial parameters such as albedo, leaf area index (LAI), and surface temperature are analyzed based on a series of experiments. Secondly, we point out the differences and similarities between the scale-free phenomena of the QRSPs and the measurements of the coastline length (1-dimensional) and the curved surface area (2-dimensional). An information fractal algorithm for the QRSPs is presented. In a case study for the LAI, when the fractal dimension is 2.16, the ratio of the LAI retrieval values obtained respectively from remote sensing data of 30 m and 6 km pixel resolution can actually reach as high as 2.86 for the same 6 km pixel using the same retrieval model. Finally, we propose an operational validation method "one test and two matches" and multipoint observation when the real situation does not allow carrying out scanning measurement without gap and overlap on the ground surface.
