The invariance of the MFS to spatial transforms and linear intensity transforms is proven for continuous functions, assuming infinitely small pixels. For real images, there is a limit on the smallest obtainable resolution, which is given by the pixel size. Yet, experiments showed that the MFS computed from standard size images is very robust to environmental changes.

Invariance to changes in view point

The estimated MFS (of the density of the intensity) is nearly the same for different images of the same category.

Invariance to non-rigid transformations

The estimated MFS (of the density of the intensity) is nearly the same for all images of the arm.