Fast computation of 3D Meixner's invariant moments using 3D image cuboid representation for 3D image classification

In this paper, we propose a new fast computation method of 3D discrete orthogonal invariant moments of Meixner. This proposed method is based on two fundamental notions: the first is the extraction of the invariants of the 3D Meixner moments from the invariant of 3D geometric moments. The second is the use of 3D image cuboid representation (ICR). In this representation, the invariant moments of Meixner will be extracted from the cuboids instead of the overall image which allows reducing considerably the invariant computation time of 3D Meixner moments and consequently reducing the time of 3D image classification as well. In fact, the proposed method is tested by using several well-known computer vision data sets, including the moment invariability and the 3D image classification. Hence, the results obtained show the moments' invariance extracted by the method proposed under the three different affine transformations: translation, scale and rotation of the 3D images, and clearly guarantee the efficiency of the proposed method in terms of calculation time and classification accuracy compared to existing methods.