Fast Fourier Transform (FFT) power spectrum angle

[physical101]

Dear Physics Buddies,

How are well all, okay I hope. I was wondering if I might browse all your infinite intellects and ask you a very simple question.

I am working with some medical images in MATLAB and my collaborators would like to know the orientation of the fibres that it contains.

So far I have:

Tiled the images (with an increasing tile size of the power of 2)
Calculated the regions ft

Then I was going to use PCA to find the largest eigen vector and declare that as the most dominant orientation for this region. However, I am a little stuck.

Someone suggested using the interia matrix of the ft power spectrum. This involves computing:

∑(ki,kj)(ki-kic)(ki-kic),∑(ki,kic)(ki-kic),(kj-kjc)
∑(ki,kj)(ki-kic)(kj-kjc),∑(ki,kj)(kj-kjc)(kj-kjc)

I am using brocploc in MATLAB and so I was wondering if any of you guys new of quick ways to compute this for image?

Hoping you can help

Physical101

 

[Baluncore]

I guess the method used would be highly dependent on the patterns in the image and the colour / grey scale format. Are you trying to measure the principal axis in each subsections of the image or over the whole of the image? The fibres must be significantly more than 2 pixels wide to process the image.

I would consider a quick and dirty arithmetic technique such as sampling the circumference of a circle described on each subsection. By accumulating the absolute differences of sequential pixel values around the circle and saving all the values you will have a ramp with variable slope. Now subtract a linear fit to put the final value at zero. The resulting plot will have two peaks and two troughs. The positive slope will be where the circle is crossing the fibres, the negative slope will be where the fibres are tangent. Fit a 2nd harmonic to the plot, the phase reveals the principle direction of fibres.