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The Legendre moments [18] of order are defined as:

(45) 
where
, 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:

(46) 
and are the Legendre coefficients given by:

(47) 
So, for a discrete image with current pixel , Equation 1.45 becomes:

(48) 
and are defined over the interval .
Jamie Shutler
20020815