A Method to Derive Moment Invariants

Functions of moments that are invariant under geometric transformations are useful for image analysis and pattern recognition. The basic model of computer vision is projective transformation. Yet it is known that moment invariants for general projective transformations do not exist. This paper presents a novel method to derive moment invariants under restricted projective transformations. The form of the moment invariants is in a ratio of two determinants of moments. We first derive the relative moment invariants relating moments of the transformed image and moments of the original image. Then the absolute moment invariant is obtained by cancellation of the factors. The method is straightforward and extendible.