Rotation Invariant Moments and Transforms for Robust Image Watermarking

Moments and transforms are the scalar quantities that characterise a function and capture its significant properties. More specifically, these are the descriptors that correspond to the projection of the function on a specific basis function, where the type or characteristic of the basis function gives the name to the moment or transform [82]. Normally, moments and transforms are treated separately in many image processing applications, but we cluster rotation invariant moments and transforms in the same group owing to the fact that mathematical formulation of the two is similar except that radial part of the basis functions in case of moments are polynomial functions whereas in case of transforms they are sinusoidal functions. Further, a moment or transform can be categorised depending on its domain of computation (discrete vs. continuous), resilience to particular deformation (invariant vs. non-invariant) and orthogonality (orthogonal vs. nonorthogonal). These categorizations give rise to many moments and transform families, such as discrete non-orthogonal, discrete orthogonal, continuous orthogonal rotation invariants, etc.