A NOVEL SYMMETRY-BASED METHOD FOR EFFICIENT COMPUTATION OF 2D AND 3D GEOMETRIC MOMENTS

Moment invariants are widely used in reconstruction, recognition and discrimination of 2D and 3D images. Accurate and efficient computation of these moment invariants is a big challenge to the community of image processing and pattern recognition. Since the wide class of moment invariants of digital images is generally expressed as a combination of geometric moments, highly accurate and efficient computation of 2D and 3D geometric moments is a very desirable target. In this work, a novel highly efficient symmetry-based method is proposed for exact computation of 2D and 3D geometric moments. Exact values of 2D and 3D geometric moments are calculated by using pixel- and voxel-wise integration of the monomial terms over digital image pixels/voxels. Three types of symmetry are applied to reduce the computational complexity of 2D geometric moments by 87\%. The proposed method is extended to compute 3D geometric moments, where the computational complexity is reduced by more than 93\%. The proposed method is adapted to compute different families of continuous and discrete orthogonal moments. A comparison with other existing methods is performed where the numerical experiments and the memory storage analysis ensure the efficiency of the proposed method.