Image analysis with symmetry properties of Legendre moments

In this research, we have studied the symmetrical properties of Legendre moments. Our research leads to the conclusion that if the original image is centrally symmetrical, all Legendre moments composed of any odd order of Legendre polynomials are nil. We conducted the image reconstructions from different sets of Legendre moments, and verified the proposed symmetry properties. Our experimental results show that the reconstructed central symmetrical images from the Legendre moments with only even orders of Legendre polynomials are identical to those from the corresponding complete order sets of Legendre moments.