Accurate Orthogonal Circular Moment Invariants of Gray-Level Images

Abstract

Problem statement: Orthogonal circular moments of gray level images such as Zernike, pseudo Zernike and Fourier-Mellin moments are widely used in different applications of image processing, pattern recognition and computer vision. Computational processes of these moments and their translation and scale invariants still an open area of research. Approach: a unified methodology is presented for efficient and accurate computation of orthogonal circular moment invariants. The orthogonal circular moments and their translation and scale invariants are expressed as a linear combination of radial moments of the same order in polar coordinates, where the later moments are accurately computed over a unit disk. A new mapping method is proposed where the unit disk is divided into non-overlapped circular rings; each of these circular rings is divided into a number of circular sectors of the same area. Each circular sector is represented by one point in its centre. The total number of input Cartesian image pixels is equal to the number of mapped circular pixels. Results: The implementation of this method completely removes both approximation and geometrical errors produced by the conventional methods. Numerical experiments are conducted to prove the validity and efficiency of the proposed method. Conclusion: A unified methodology is presented for efficient and accurate computation of orthogonal circular moment invariants.

Detection Copy-Move Forgery in Image Via Quaternion Polar Harmonic Transforms

“…As demonstrated in [29], moments in the polar regions can be calculated using QPCET. We use the same approach as in [30,31] to replace the pixels from traditional square to circular form. For any colour image f (x, y), the right-hand side of quaternion moments (QPCET) are precisely calculated in polar coordinates as follows [29]:…”