[Trilinos-Users] Model-fitting applications in trilinos

[Kevin Long]

Ali,

Trying to fit a bunch of Gaussians in one shot is a non-convex problem 
(because you can obviously exchange the positions of any two Gaussians to 
produce a new solution). I've seen talks by people trying "brute force" 
fitting of a large number of peaks, and they've found it's rather tricky to 
pull off in practice.  You'd certainly want a good initial guess. 

How isolated are your objects? If they are widely spaced (i.e., 
object-to-object distance more than a few times sigma) you could look at 
smaller segments of the picture to get rough fits for a few peaks in each 
segment, then use those fits as initial guesses in a final fit including all 
objects. This could of course be done recursively.

Can you have ellipsoidal Gaussians? (i.e., different sigmas along two 
different principal axes, oriented arbitrarily). That makes the problem even 
more fun. Astronomers have to do this when deducing models of individual 
models from clusters of galaxies; the objects can overlap quite a bit, and 
worse, can be significantly distorted from ellipsoids (due to tidal effects, 
and even in undisturbed galaxies there are distortions due to projection of a 
3D triaxial body onto 2D). 

- kevin


On Monday 28 January 2008 16:17, Ali - wrote:
> Ross,
>
> Thanks for refering me to DAKOTA. I am trying to carry out model-based
> segmentation image processing using optimisation approches. As an example,
> assume an image involving randomly distributed Gaussian intensities, or
> something like this:
>
> http://piv.vsj.or.jp/piv/data/01/piv01_1.bmp .
>
> The aim is to detect all the Gaussian objects in the image by fitting them
> to a 2D Gaussian model which has 4 parameters: (x, y, sigma, I) with x and
> y being the centre, sigma being the deviation and I being the peak
> intensity. Typically each image includes a few hundereds of these little
> Gaussian objects, multiplied by the 4 parameters, we are dealing with over
> 1e+3 parameters in total.
>
> Normally people solve this problem by segmenting the individual object (eg
> using watershed algorithm) and then fit them one by one using
> Levenberg-Marquadt method. But I was wondering, while the Trilinos solvers
> can handle millions of unknown in a typical PDE problem solved by FEM, why
> shouldn't it be possible to fit 'all' of the objects at once to a model
> which is simply a linear superposition of the individual models?
>
>
> -Ali
>
>
> Subject: RE: [Trilinos-Users] Model-fitting applications in trilinos
> Date: Mon, 28 Jan 2008 13:35:27 -0700
> From: rabartl at sandia.gov
> To: saveez at hotmail.com; trilinos-users at software.sandia.gov
>
>
>
>
>
>
>
>
>
>
> Ali,
>
> Depending on what you need there are a few possibilities.
> Without knowing the details, I would recommend that you first look at a
> related project called Dakota which as parameter estimation and
> least-squares fitting methods.  You can find more information at:
>
>     http://www.cs.sandia.gov/DAKOTA/software.html
>
> If you only need to fit a smaller
> number of parameters, I would definitely look at Dakota first.  Fitting a
> large number of parameters (i.e. 1e+3 and up) is a lot of work to set up
> and requires some serious optimization algorithms.
>
> Cheers,
>
> Ross
>
>
>
>
> From: trilinos-users-bounces at software.sandia.gov
> [mailto:trilinos-users-bounces at software.sandia.gov] On Behalf Of Ali
> -
> Sent: Monday, January 28, 2008 12:19 PM
> To:
> trilinos-users at software.sandia.gov
> Subject: [Trilinos-Users]
> Model-fitting applications in trilinos
>
>
>
> Hi,
>
> Is there any packages in Trilinos (or
> other Sandia software) specifically designed for model-fitting
> (curve-fitting)?
>
>
> -Ali
>
>
>
> Messenger on the move. Text MSN to 63463 now!
>
> _________________________________________________________________
> Telly addicts unite!
> http://www.searchgamesbox.com/tvtown.shtml

-- 
Dr. Kevin Long
Department of Mathematics and Statistics
Texas Tech University
Lubbock TX 79409
kevin.long at ttu.edu