2D gaussian fitting using Surface Fitting Tool

Tim Balmer

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Jun 8, 2010, 1:33:19 AM6/8/10

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I'm trying to fit a 2D gaussian to a surface using the Surface Fitting Tool. I choose the custom equation option and enter this formula: A*exp(-x^2/(2*sigmax^2)-y^2/(2*sigmay^2))

I think that either my equation is wrong or I am not using the Surface Fitting Tool properly because it generates a flat surface that doesn't fit at all and has a negative R-square value.

Any help would be greatly appreciated!

Thanks!

Tim Balmer

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Jun 8, 2010, 8:18:04 PM6/8/10

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Alright, I figured it out. Here is my solution. First, I changed the custom equation to this: A*exp(-(x-x0)^2/(2*sigmax^2)-(y-y0)^2/(2*sigmay^2)) It was also necessary to change the 'Fit Options'. I changed the StartPoint of all the Unknows to 10.

Now it works great. I hope this helps someone out there who is trying to fit 2D gaussians to their data using the Surface Fitting Tool.

"Tim Balmer" <tbal...@student.gsu.edu> wrote in message <hukkmu$pcd$1...@fred.mathworks.com>...

Shu-huai ZHANG

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Jun 14, 2010, 10:56:04 PM6/14/10

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Hi, Tim Balmer:

I am a newcomer about MATLAB. Now want to do the same thing like you.
Could you give me some help?

Thanks a lot.

"Tim Balmer" <tbal...@student.gsu.edu> wrote in message <hukkmu$pcd$1...@fred.mathworks.com>...

Tim Balmer

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Jun 15, 2010, 9:05:20 AM6/15/10

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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

Shu-huai ZHANG

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Jun 16, 2010, 9:34:04 PM6/16/10

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Hi,Tim

Thanks so much. I will try it.

shu-huai ZHANG

"Tim Balmer" <tbal...@student.gsu.edu> wrote in message <hv7tqg$hcm$1...@fred.mathworks.com>...

pasino pasin

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Aug 9, 2010, 4:54:04 PM8/9/10

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I have similar problem but I need to fit multipeak Gaussians. I have a 2D data, xy plane is my pixels and z axis is the values corresponding to each pixel(like an image).
I want to model my z data with Gaussians,but not only one Gaussian, it needs to detect peaks, cluster them and fit Gaussians
Is there such a package of Matlab or any other way, code etc.?

"Shu-huai ZHANG" <zh...@cc.hirosaki-u.ac.jp> wrote in message <hvbu2c$aqf$1...@fred.mathworks.com>...

Zoltan

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Mar 12, 2012, 12:13:11 PM3/12/12

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Hi Tim
Thanks for your post. It is working great with my own data too. Unfortunatelly, I don't know why, but it happens very often, that the fit didn't work due to an error message: "CAT arguments dimensions are not consistent." . It is very strange, that I always used the same data, without any modification, and sometimes it worked, and more often it didn't. It is frustrating, that I don't know why.
best regards
Zoltan

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Mat

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Apr 3, 2012, 10:10:16 AM4/3/12

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"Shu-huai ZHANG" <zh...@cc.hirosaki-u.ac.jp> wrote in message <hvbu2c$aqf$1...@fred.mathworks.com>...

Thanks Tim for this solution. It worked for me too, what a surprise. But I'd like to disable the datapoints in the sftool environment. How can I do that? Bcs of the high amount of datapoints, the fit is barely visible through all the datapoints.

greetings

Maja

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Oct 14, 2013, 5:13:06 PM10/14/13

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Great help, Thanks!!

cpraj

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Oct 22, 2013, 10:42:47 PM10/22/13

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Hi Tim,

Thanks for simplifying the steps.

By the way- "how to call sftool"?

jamin2

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Jan 20, 2014, 11:10:13 AM1/20/14

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Just type "sftool" in the command window

PARTHA PRATIM DEKA

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Dec 8, 2016, 8:27:07 AM12/8/16

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What is 'z' here? Is it a function of x and y? What I want to know is that the rows and the columns of the 2D matrix are defined by x and y and the values of the matrix elements are given by z, is it correct? Please help as soon as possible. Thanks!

"Mat" wrote in message <jlf0c8$f14$1...@newscl01ah.mathworks.com>...