2D gaussian fitting using Surface Fitting Tool
in [Matlab]
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From: Tim Balmer on 8 Jun 2010 01:33 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!
From: Tim Balmer on 8 Jun 2010 20:18 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" <tbalmer2(a)student.gsu.edu> wrote in message <hukkmu$pcd$1(a)fred.mathworks.com>... > I'm trying to fit a 2D gaussian to a surface using the Surface Fitting Tool. I choose the custom equation option and enter this formula: A*exp(-x^2/(2*sigmax^2)-y^2/(2*sigmay^2)) > > I think that either my equation is wrong or I am not using the Surface Fitting Tool properly because it generates a flat surface that doesn't fit at all and has a negative R-square value. > > Any help would be greatly appreciated! > > Thanks!
From: Shu-huai ZHANG on 14 Jun 2010 22:56 Hi, Tim Balmer: I am a newcomer about MATLAB. Now want to do the same thing like you. Could you give me some help? Thanks a lot. "Tim Balmer" <tbalmer2(a)student.gsu.edu> wrote in message <hukkmu$pcd$1(a)fred.mathworks.com>... > 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!
From: Tim Balmer on 15 Jun 2010 09:05 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
From: Shu-huai ZHANG on 16 Jun 2010 21:34 Hi,Tim Thanks so much. I will try it. shu-huai ZHANG "Tim Balmer" <tbalmer2(a)student.gsu.edu> wrote in message <hv7tqg$hcm$1(a)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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