2D Fourier transform orientation angle

In summary, the orientation of frequency components in the 2-D Fourier spectrum of an image can be used to determine the preferred orientation of features in the image, such as collagen fibers. Nonlinear microscopy techniques use this idea by obtaining power spectra for different regions of interest and inferring the orientation angle. To measure the angle of the Fourier transform, an algorithm can be used to calculate the arctangent of the ratio of the Y coefficient over the X coefficient. The standard deviation in the power spectra can also indicate the number of fibers deviating from the preferred orientation. However, the details of this algorithm are not explained in the papers.
  • #1
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The orientation of frequency components in the 2-D Fourier spectrum of an image reflect the orientation of the features they represent in the original image.

In techniques such as nonlinear microscopy, they use this idea to determine the preferred (i.e. average) orientation of certain features in a given image (e.g. the orientation of collagen fibers). For example here for different regions of interest, they obtained the power spectra (shown below in binary), and using that they inferred the orientation angle.

OkCZeve.png


So, I am not sure how they would measure the angle of the FT. Are there equations for finding the tilt angle of a certain frequency component?

I believe when they find all the angles, they would do a fitting to get the average orientation. The ##\pm## in the picture above is the standard deviation – the number of fibers that deviate from the preferred orientation.

How would an algorithm for finding the angle look like? Unfortunately, the papers did not explain this in any detail.

Any explanation would be greatly appreciated.
 

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  • #2
Actually it’s at right angles. The FT of a narrow feature is broad in the direction normal to it, etc.
 
  • #3
So, for example, if you have a single sinusoid with a spectrum like this:

gmejziO.png


The FT has the same orientation (or is at right angles) with the direction of the feature. How would you calculate the angle that the FT is making with respect to the x/y axis?

Is there an equation or an algorithm that you can use?
 

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  • #4
Take the arctangent of the absolute value of the ratio of the Y coefficient over the x coefficient of the FFT.
 
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1. What is a 2D Fourier transform orientation angle?

A 2D Fourier transform orientation angle refers to the angle at which a 2D object is oriented in a 2D Fourier transform image. It is the angle between the major axis of the object and the x-axis of the image.

2. How is the 2D Fourier transform orientation angle calculated?

The 2D Fourier transform orientation angle is calculated using the phase information of the Fourier transform image. The angle can be determined by finding the maximum amplitude in the Fourier transform image and then finding the phase angle associated with that amplitude.

3. Why is the 2D Fourier transform orientation angle important in image analysis?

The 2D Fourier transform orientation angle is important in image analysis because it can provide information about the orientation and symmetry of objects in an image. This can be useful in tasks such as object recognition and classification.

4. Can the 2D Fourier transform orientation angle be used to rotate an image?

Yes, the 2D Fourier transform orientation angle can be used to rotate an image. By calculating the angle and using it as a rotation parameter, the image can be rotated to align the objects in a specific orientation.

5. Are there any limitations to using the 2D Fourier transform orientation angle for image analysis?

Yes, there are some limitations to using the 2D Fourier transform orientation angle. It may not accurately represent the orientation of objects in an image if the objects are overlapping or if the image is noisy. Additionally, it may not work well for images with non-uniform backgrounds.

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