Image processing has become a critical component in Engineering and technology and has numerous applications ranging from nanotechnologies to the digital communication technologies. This book is about the problem of accurate computation of orthogonal rotation invariant moments. The moments and orthogonal polynomials are classical concepts in mathematical analysis due to its attractive properties. This book gives excellent overview of the various image moments. Several new techniques to increase the accuracy and efficiency of moment descriptors are proposed. We utilize these results for solving the problem of reconstruction of images from orthogonal moments. The proposed method provides much improved accuracy of rotation invariant moments which provide very accurate reconstructed images, numerical stability and invariance.