Mailing-List: contact user-help@commons.apache.org; run by ezmlm
Precedence: bulk
Reply-To: "Commons Users List" <user@commons.apache.org>
Received-SPF: pass (athena.apache.org: domain of ted.dunning@gmail.com
 designates 209.85.211.185 as permitted sender)
DomainKey-Signature: a=rsa-sha1; c=nofws;
        d=gmail.com; s=gamma;
        h=mime-version:in-reply-to:references:from:date:message-id:subject:to
         :content-type;
        b=u1mP6aOAszhPhwKWyAQ0ZsWM6l/x1yO/TC0jW+/4g3cN2IIG33E4h6r79dYnjuXOEi
         Mqs5hK6GvNISsjflk7Ui2Qg0KeaTcpiZHLDasDE03Nf05wpgsCKnCXmtdgnS5pnzhMwe
         2wjC8tsy94cS/5pSfnmVt9XOWDDBM6+oop6UU=
MIME-Version: 1.0
In-Reply-To: 
 <1922261993.829481250513609872.JavaMail.root@spooler6-g27.priv.proxad.net>
References: 
 <1118961004.829281250513602282.JavaMail.root@spooler6-g27.priv.proxad.net>
	<1922261993.829481250513609872.JavaMail.root@spooler6-g27.priv.proxad.net>
From: Ted Dunning <ted.dunning@gmail.com>
Date: Mon, 17 Aug 2009 10:57:58 -0700
Message-ID: <c7d45fc70908171057g6b5935fn8295301d9f0c9944@mail.gmail.com>
Subject: Re: [math] Re: 2D Gaussian Fit
To: Commons Users List <user@commons.apache.org>
Content-Type: multipart/alternative; boundary=000e0cd2989c90c4ca04715a2508

--000e0cd2989c90c4ca04715a2508
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

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 i=
s
a vector containing a position, then the multi-variate Gaussian is typicall=
y
written as

         N(x | m, S) =3D Z exp( - (x-m)' R (x-m) )

R is the inverse of the covariance matrix \Sigma and the normalizing
constant Z =3D 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 prio=
r
expectation, but you can still get decent estimates.

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

> Hi Jean-Fran=C3=A7ois,
>
> First, please use a [math] marker in the subject line when asking somethi=
ng
> 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 =C3=A9c=
rit :
>
> > 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 mo=
st
> 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 librar=
y.
> In the
> LevenbergMarquardtOptimizerTest class there is a Circle internal class th=
at
> implements a fitting
> problems for observed points that should lie on a circle. You can use thi=
s
> as an example to
> implement your own Gauss2D class.
>
> If this information is not sufficient, do not hesitate to ask and I'll tr=
y
> to provide more.
>
> Luc
>
>
> >
> > Any help is appreciated.
> >
> > J-F
> >
> > The contents of this e-mail message and any attachments are intended
> > solely for
> > the recipient (s) named above. This communication is intended to be
> > and to
> > remain confidential and may be protected by intellectual property
> > rights. Any
> > use of the information contained herein (including but not limited to,
> > total or
> > partial reproduction, communication or distribution of any form) by
> > persons
> > other than the designated recipient(s) is prohibited. Please notify
> > the sender
> > immediately by e-mail if you have received this e-mail by mistake and
> > delete
> > this e-mail from your system. E-mail transmission cannot be guaranteed
> > to be
> > secure or error-free. Ion Beam Applications does not accept liability
> > for any
> > such errors. Thank you for your cooperation.
> >
> > ---------------------------------------------------------------------
> > To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
> > For additional commands, e-mail: user-help@commons.apache.org
>
> ---------------------------------------------------------------------
> To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
> For additional commands, e-mail: user-help@commons.apache.org
>
>


--=20
Ted Dunning, CTO
DeepDyve

--000e0cd2989c90c4ca04715a2508--