New Invariant Moments for Non-Uniformly Scaled Images

The usual regular moment functions are only invariant to image translation, rotation and uniform scaling. These moment invariants are not invariant when an image is scaled non-uniformly in the x- and y-axes directions. This paper addresses this problem by presenting a new technique to obtain moments that are invariant to non-uniform scaling. However, this technique produces a set of features that are only invariant to translation and uniform/non-uniform scaling. To obtain invariance to rotation, moments are calculated with respect to the x-y-axis of the image. To perform this, a neural network is used to estimate the angle of rotation from the x-y-axis and the image is unrotated to the x-y-axis. Consequently, we are able to obtain features that are invariant to translation, rotation and uniform/non-uniform scaling. The mathematical background behind the development and invariance of the new moments are presented. The results of experimental studies using English alphabets and Arabic numerals scaled uniformly/non-uniformly, rotated and translated are discussed to further verify the validity of the new moments.