How to identify different directions' periodic patterns in an image?

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I have an image from my lab work. It has periodic pattern in three separate directions(120 degrees apart). As you can see, the dark regions has all three direction's pattern(so it looks like a triangle lattice); while for the brighter regions, there is only one dominant direction's periodic pattern. I know the periodicity and angles. I can also tell which area has one(or three) direction's pattern by the brightness. But on the brighter regions, can someone tell me how to point out which direction has the periodicity? For example, 0 represent it's in dark regions, 1(2 ;3) represent it has the 1st(2nd,3rd) direction's pattern. I want to make a matrix of the same size of the image whose element is 0,1,2,or 3. Please help me if you know how.

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