Let (Xi,Yi) be the positions of your stars on the sky. i in the 1 to N range. Let (Xj,Yj) be the positions of your stars images (PSF) on your picture. i in the 1 to N range. You can parametrize the distortion this way: Xj_param = Px(Xi,Yi) Yj_param = Py(Xi,Yi) where Px and Py are the two polynomials minimizing the RMS residuals in between the parametrized positions and the measured one on the picture. As the distortion is a smooth function over the field of view, low order polynomials are sufficient (order 3 or 5) to get very low RMS residuals. Pros : No optimization algorithm need. You can compute the polynomials coefficients using* pseudoinverse.* There is no question about global versus local minimum anymore. Only* pseudoinverses. Px qnd Py provides you with a full description of your system optical distortion. *Cons : I don't know. Once you have the polynomials, you can compute whatever other distortion parametrization you may prefer. Xavier

I'm doing plate reduction on astro photos. There's non-linearity in the lens. Basically, one is trying to estimate several lens parameters by look at a field of known stars versus ones measured on a photo plate. The author states it can be solved by taking first derivatives to linearize matters, and iteratively apply least squares until the change in parameters falls below some limits. Gauss-Newton seems a bit different in that it tries to minimize the sum of squares.

In a follow up paper, he refers to the process as a gradient method. Up until then, my best guess was G-N. I suspect that you are hinting at the Gradient plus LSQ (least squares). However, out of curiosity, isn't their a library of optimization methods like Marquardt or Davidon?

On 5/28/2010 12:09 PM, Charles R Harris wrote:

...

What problem are you trying to solve. The leastsq algorithm in scipy is effectively Gauss-Newton when that is appropriate to the problem.

Chuck

On Fri, May 28, 2010 at 12:36 PM, Wayne Watson <sierra_mtnview@sbcglobal.net <mailto:sierra_mtnview@sbcglobal.net>> wrote:

Is Subject method available in Python?

-- Wayne Watson (Watson Adventures, Prop., Nevada City, CA)

(121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time) Obz Site: 39° 15' 7" N, 121° 2' 32" W, 2700 feet

There are no statues or memorials dedicated to Thomas Paine for his substantial part in the American Revolution.

-- An observation in The Science of Liberty by Timoth Ferris

Web Page:<www.speckledwithstars.net/ <http://www.speckledwithstars.net/>>

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-- Wayne Watson (Watson Adventures, Prop., Nevada City, CA)

(121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time) Obz Site: 39° 15' 7" N, 121° 2' 32" W, 2700 feet

There are no statues or memorials dedicated to Thomas Paine for his substantial part in the American Revolution.

-- An observation in The Science of Liberty by Timoth Ferris

Web Page: <www.speckledwithstars.net/>

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