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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
2002-08-15