Derivation of invariant features using scale factors from a neural network

Conventional regular moments are only invariant to translation, rotation and equal scaling. It is shown that the conventional regular moment-invariants remain no longer invariant when the image is scaled unequally in the x- and y-directions. This paper addresses this problem by presenting a new technique to make the moments invariant to unequal scaling. Consequently, we would be able to obtain features for images that are translated, scaled equally/unequally and rotated. The problem is formulated using conventional regular moments. A neural network is trained to estimate the reference scale factor and together with another computed factor obtained from an equation involving the angle of rotation, the scaling ratio for the particular images can be obtained. From this, moments can be made invariant to unequal scaling. Invariance of rotation is achieved by using the principle of axis method to determine the angle of rotation and consequently the moments of the image can be derived in its unrotated form. Validity of this method is demonstrated by experiment.