width in Gaussian fitting

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Hi, I'm doing some experimental image analysis and need to use 2D Gaussian fit. In the form of 2D Gaussian fitting function, there are factors named as "xWidth" and "yWidth". I cannot find the meaning of these two factor and want to know the relation of these factors to the peak width of half height.
xWidth and yWidth are the standard deviation in the X and Y directions, respectively. If the value of cor (the correlation factor) is zero, then these are the standard deviation of the principle components of the bivariate Gaussian. Also in the case where for = 0, the Full Width at Half Maximum will be 2*sqrt(2*ln(2)) (or about 2.355) times the xWidth or yWidth.

But if cor != 0, then the principle directions of the Gaussian are not along the X and Y axes, and then I'm not sure what the expression would be for the principle directions.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com

March 31, 2014 at 01:54 pm - Permalink

johnweeks wrote:
xWidth and yWidth are the standard deviation in the X and Y directions, respectively. If the value of cor (the correlation factor) is zero, then these are the standard deviation of the principle components of the bivariate Gaussian. Also in the case where for = 0, the Full Width at Half Maximum will be 2*sqrt(2*ln(2)) (or about 2.355) times the xWidth or yWidth.

But if cor != 0, then the principle directions of the Gaussian are not along the X and Y axes, and then I'm not sure what the expression would be for the principle directions.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com


Thanks John!

I have one question about your answer.

If cor != 0. Does that mean "2*sqrt(2*ln(2)) times the xWidth" will be the Width of fitted 2D Gaussian function at Half Maximum along x-axis, but in this condition, x-axis is not the principle direction of the the fitted 2D Gaussian? (The same as yWidth)

Thanks!

October 25, 2014 at 04:59 pm - Permalink

johnweeks wrote:
I believe so. You could confirm it with a simply measurement on a graph.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com


Thanks John,

Before, cor is the factor related to the rotation angle which is the angle principle axis to x-axis(or y-axis). But it seems not. Do you have any idea what this value means?

Thanks!

November 5, 2014 at 02:59 pm - Permalink