Need help with implementing a 2D elliptical Gaussian function
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I'm trying to implement a 2D gaussian function, which has an elliptical shape rather than circular. For example if I have a standard Gaussian fuction such as: f=a1*exp(-(((x-b1)/c1).^2+((y-b1)/c1).^2))
where [x,y]=meshgrid(xmin:spacing:xmax,ymin:spacing,yman); I can just f=a1*exp(-((r-b1)/c).^2) where r=sqrt(x^2+y^2);
however if my c1 is not the same, I will have an ellipse. I'm not sure how to implement this. Any help will be highly appreciated.
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David Young
2011년 7월 5일
You can make an elliptical filter aligned with the axes by replacing the second occurrence of c1 by a different variable, say c2, and giving c1 and c2 different values. Here's some code that demonstrates what I mean; I've taken the opportunity to change b1 to b2 as well, so the centre of the filter can be moved to an arbitrary point:
% Set up mesh
xmin = -100;
xmax = 100;
ymin = -100;
ymax = 100;
spacing = 1;
xvals = xmin:spacing:xmax+spacing/2;
yvals = ymin:spacing:ymax+spacing/2;
[x,y] = meshgrid(xvals, yvals);
% parameters for the gaussian
a1 = 1;
b1 = 20;
b2 = 40;
c1 = 10;
c2 = 40;
% Compute the filter and display it
f=a1.*exp(-(((x-b1)./c1).^2+((y-b2)./c2).^2));
contour(x, y, f);
If you want the ellipse to be oriented in an arbitrary direction, you need to rotate the axes before the computation. This involves multiplying x and y by a rotation matrix. Please say if you also need help with this.
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MJ HL
2017년 8월 22일
Hello David, ... As you guessed I'm from that kind of people that need more help in rotating this filter :) . How should I do this? I need to rotate this filter in an arbitrary direction... thanks
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