  In this work we describe a fast and stable algorithm for the computation of
the orthogonal moments of an image. Indeed, orthogonal moments are
characterized by a high discriminative power, but some of their possible
formulations are characterized by a large computational complexity, which
limits their real-time application. This paper describes in detail an approach
based on recurrence relations, and proposes an optimized Matlab implementation
of the corresponding computational procedure, aiming to solve the above
limitations and put at the community's disposal an efficient and easy to use
software. In our experiments we evaluate the effectiveness of the recurrence
formulation, as well as its performance for the reconstruction task, in
comparison to the closed form representation, often used in the literature. The
results show a sensible reduction in the computational complexity, together
with a greater accuracy in reconstruction. In order to assess and compare the
accuracy of the computed moments in texture analysis, we perform classification
experiments on six well-known databases of texture images. Again, the
recurrence formulation performs better in classification than the closed form
representation. More importantly, if computed from the GLCM of the image using
the proposed stable procedure, the orthogonal moments outperform in some
situations some of the most diffused state-of-the-art descriptors for texture
classification.
