Legendre moment

In mathematics, Legendre moments are a type of image moment and are achieved by using the Legendre polynomial. Legendre moments are used in areas of image processing including: pattern and object recognition, image indexing, line fitting, feature extraction, edge detection, and texture analysis. Legendre moments have been studied as a means to reduce image moment calculation complexity by limiting the amount of information redundancy through approximation.

Legendre moments

Source:
With order of m + n, and object intensity function f:
where m,''n = 1, 2, 3,... with the n''th-order Legendre polynomials being:
which can also be written:
where D = floor. The set of Legendre polynomials form an orthogonal set on the interval :
A recurrence relation can be used to compute the Legendre polynomial:
f can be written as an infinite series expansion in terms of Legendre polynomials :