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From Ted Dunning <ted.dunn...@gmail.com>
Subject Re: [math] Re: 2D Gaussian Fit
Date Mon, 17 Aug 2009 17:57:58 GMT
Depending on what you mean by a 2D Gaussian fit, you may just need to
compute mean and covariance matrix to get what you need.

Remember that a 2D Gaussian needs center{x,y} and FOUR parameters for
variance, three of which are independent.  The reason is that you can have a
Gaussian that is long and thin, but oriented at an arbitrary angle.  If x is
a vector containing a position, then the multi-variate Gaussian is typically
written as

         N(x | m, S) = Z exp( - (x-m)' R (x-m) )

R is the inverse of the covariance matrix \Sigma and the normalizing
constant Z = 1 / \sqrt((2 pi)^n | \Sigma |).

With enough data, you can get fine estimates of these quantities directly,
without any optimization.  With less data, you need to have a bit of a prior
expectation, but you can still get decent estimates.

On Mon, Aug 17, 2009 at 5:53 AM, <luc.maisonobe@free.fr> wrote:

> Hi Jean-François,
>
> First, please use a [math] marker in the subject line when asking something
> about
> commons-math. This mailing list is shared by all commons components so
> these markers
> help filtering messages.
>
> ----- "Jean-Francois Daune" <Jean-Francois.Daune@iba-group.com> a écrit :
>
> > Is it possible to perform a 2D Gaussian fit (giving center_x,
> > center_y, sigma_x, sigma_y, theta) with Commons Math?
>
> Yes it is possible. You will have to use the optimization package, and most
> probably
> the LevenbergMarquardtOptimizer class from the general subpackage. This
> will be the main
> algorithm that will perform the fit. You should implement your problem as
> your own class
> implementing the DifferentiableMultivariateVectorialFunction interface
> (i.e. a class
> that provides a "double[] value(double[] point)" method and a
> "MultivariateMatrixFunction
> jacobian()" method (which itself wraps another value function). In your
> case, the point[]
> parameters for both value functions will be the parameters of your fit,
> i.e. center_x, center_y,
> sigma_x, sigma_y and theta. You can look in the junit tests of the library.
> In the
> LevenbergMarquardtOptimizerTest class there is a Circle internal class that
> implements a fitting
> problems for observed points that should lie on a circle. You can use this
> as an example to
> implement your own Gauss2D class.
>
> If this information is not sufficient, do not hesitate to ask and I'll try
> to provide more.
>
> Luc
>
>
> >
> > Any help is appreciated.
> >
> > J-F
> >
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-- 
Ted Dunning, CTO
DeepDyve

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