Next: Complex Zernike moments
Up: Orthogonal moments
Previous: Orthogonal moments
The Legendre moments  of order are defined as:
, and are the Legendre polynomials and is the continuous image function.
The Legendre polynomials are a complete orthogonal basis set defined over the interval .
For orthogonality to exist in the moments, the image function is defined over the same
interval as the basis set, where the order Legendre polynomial is defined as:
and are the Legendre coefficients given by:
So, for a discrete image with current pixel , Equation 1.45 becomes:
and are defined over the interval .