However, these measures are very cheap to calculate as byproducts of the segmentation strategies detailed, especially region growing. Consequently, when these measures are used in conjunction with other reliably extracted features, they can help to improve recognition techniques by constraining the search space for matches between image and object features. Invariant Measures 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. This is clearly a good property as we cannot guarantee viewing an object from identical viewpoints. Thus, while the centre of gravity of a region obviously varies with its position, its area does not.
Eccentricity is invariant with respect to scaling, rotation and translation.
Fourier Transforms are rotation invariant. We can use the Fourier transform to compute Fourier descriptors of an object which are invariant with respect to position and orientation.