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Topic: 2D gaussian fitting using Surface Fitting Tool
Replies: 10   Last Post: Jan 20, 2014 11:10 AM

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Shu-huai ZHANG

Posts: 2
Registered: 6/14/10
Re: 2D gaussian fitting using Surface Fitting Tool
Posted: Jun 16, 2010 9:34 PM
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Hi,Tim

Thanks so much. I will try it.

shu-huai ZHANG

"Tim Balmer" <tbalmer2@student.gsu.edu> wrote in message <hv7tqg$hcm$1@fred.mathworks.com>...
> Hi Shu-huai,
> I'm pretty new to Matlab myslef, and I have never had any formal instruction, so I'll explain how I have fit 2D gaussians to my own data and hopefully it will help you figure out how to use it for your application.
>
> -First you need to put your data into x, y and z variables. For instance, my z data is in a 13x19 matrix that looks like this:
> z=[0 0 0 0 0 1 0 1 0 1 0 0 0
> 0 0 0 1 1 0 0 0 0 1 1 0 0
> 0 0 1 0 0 2 1 1 0 0 1 0 1
> 0 0 0 0 0 0 1 1 1 0 1 1 0
> 0 0 0 0 0 1 2 2 3 5 0 0 0
> 0 1 2 4 1 5 13 4 3 9 0 2 0
> 1 1 8 10 10 14 22 23 9 10 0 0 0
> 5 4 6 15 21 21 24 24 17 16 0 1 0
> 4 9 12 24 20 28 34 30 13 19 0 1 0
> 2 5 13 17 31 31 35 39 20 18 0 0 0
> 2 6 13 22 28 34 46 35 13 20 0 1 1
> 5 7 12 14 31 27 39 27 14 12 0 1 0
> 6 6 10 17 18 32 28 27 17 6 1 0 1
> 3 4 7 10 15 18 17 11 11 11 2 0 1
> 1 1 7 8 12 14 8 9 4 2 1 0 1
> 1 1 1 3 3 6 5 5 3 0 0 0 1
> 1 1 0 3 1 0 1 1 0 1 0 3 0
> 1 1 0 0 0 1 0 0 1 2 0 0 1
> 0 1 1 0 0 0 0 1 1 0 0 0 2]
>
> -to make this 13x19 matrix into x, y, z variables that can be used with the surface fitting tool, do this:
> [x,y]=meshgrid(1:13,1:19);
> x=x(:);
> y=y(:);
> z=z(:);
>
> -now call the surface fitting tool:
> sftool
>
> -choose x, y and z for the inputs
>
> -choose custom equation from the drop down menu and paste in this equation:
> a1*exp(-(x-x0)^2/(2*sigmax^2)-(y-y0)^2/(2*sigmay^2))
>
> -click 'Fit'
>
> -if the equation doesn't fit at all, change the fit options:
> change all of the StartPoints to 10
>
> --after doing this you should get these results:
> General model:
> f(x,y) = a1*exp(-(x-x0)^2/(2*sigmax^2)-(y-y0)^2/(2*sigmay^2))
> Coefficients (with 95% confidence bounds):
> a1 = 39.23 (37.56, 40.9)
> sigmax = 2.332 (2.232, 2.431)
> sigmay = 2.725 (2.61, 2.841)
> x0 = 6.585 (6.486, 6.684)
> y0 = 10.64 (10.52, 10.75)
>
> Goodness of fit:
> SSE: 1723
> R-square: 0.924
> Adjusted R-square: 0.9227
> RMSE: 2.668
>
>
> --To make this much faster you can choose File/Generate M-File and it will make a function called createSurfaceFit, that can be run with any data that is named x, y and z and is in the proper format. That way you won't have to enter the sftool each time.
>
> Hope this helps!
> Tim




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