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.
[1] Legendre moments have been studied as a means to reduce image moment calculation complexity by limiting the amount of information redundancy through approximation.
[2] Source:[3] With order of m + n, and object intensity function f(x,y): where m,n = 1, 2, 3, ...∞ with the nth-order Legendre polynomials being: which can also be written: where D(n) = floor(n/2).
The set of Legendre polynomials {Pn(x)} form an orthogonal set on the interval [−1,1]: A recurrence relation can be used to compute the Legendre polynomial: f(x,y) can be written as an infinite series expansion in terms of Legendre polynomials [−1 ≤ x,y ≤ 1.