Scale invariants of three-dimensional legendre moments

Three-dimensional digital images are gaining more attention in pattern recognition field. Mostly literatures, however, only focus on theoretical framework of two-dimensional moment invariants, that are only implemented on two-dimensional images. Consequently, it reduces the invariance flexibilily to support three-dimensional objects. In this paper, we introduce three-dimensional scale invariants of Legendre moments. They are algebraically derived directly from Legendre polynomials. Simulated experiments using three-dimensional binary images are carried out to verify the validity of proposed invariance.