Talk:Pseudo-Zernike polynomials

Hi,

In the definition of $$D_{n,|m|,s}$$, i think that the term $$(n-|m|-s+1)!$$ should be replaced by $$(n+|m|-s+1)!$$. Could someone else confirm there is an issue in the definition of $$D_{n,|m|,s}$$? J.F. 77.194.224.177 (talk) 15:12, 6 June 2008 (UTC)

There are quite a lot of errors in this page. The restriction on the (n,m) pairs for which the polynomials are defined should be not only that |m|<=n but also that n-m is even, the polynomial for R should be a sum over only even values of s in that range, the formula for the coefficients D is wrong, and most of the example polynomials need deleting or correcting.Fathead99 (talk) 15:00, 6 June 2011 (UTC)


 * "On image analysis by the methods of moments" states that unlike for the Zernike radial polynomials, which are defined for |m|<=n only where n-m is even, pseudo-Zernike radial polynomials are defined for |m|<=n with no additional conditions on n-m. Cafet (talk) 20:11, 13 December 2011 (UTC)

I'm not sure how to correct it, but the proper link for the refernce to "An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments" is: http://ir.canterbury.ac.nz/bitstream/10092/448/1/12584534_ivcnz01.pdf —Preceding unsigned comment added by 147.197.140.136 (talk) 09:39, 24 November 2009 (UTC)

Used in Optics ?
I am an optical engineer and I have never heard of anyone using these "pseudo" Zernike polynomials. We use the Zernike polynomials, which are not defined the same way have their own page on wikipedia: https://en.wikipedia.org/wiki/Zernike_polynomials. I think that assertion needs a reference. — Preceding unsigned comment added by 212.203.64.194 (talk) 16:31, 6 October 2016 (UTC)

Original Definition of the pseudo-Zernike Polynomials
The pseudo-Zernike polynomials is similar than the Zernike polynomials. The differences between them are two. These was derived by Bhatia and Wolf. The first is that it must to eliminate the condition n − |m| = even regarding the Zernike polynomials. The second is that the radial polynomial equation changes slightly from the Zernike polynomials. Since the set of pseudo-Zernike orthogonal polynomials is analogous to that of Zernike polynomials, most of the previous discussion for the Zernike Moments(ZM) can be adapted to the case of pseudo-Zernike Moments (PZM).