Several of the statistical measures we have met are invariant measures, which is to say that the value of the measure does not vary with, for example, the position of the region in the image, or perhaps its orientation or scale.
Thus, while the centre of gravity of a region obviously varies with its position, its area does not.
While area does vary with scale (and thus closeness of the camera to the object, for example), compactness as defined above is invariant with respect to scale as well as position and orientation. Invariant measures can be quite useful in recognising objects.
Other invariant measures we have met before are: