Which way is my yarn oriented?

Question

I have an image processing problem. I have pictures of yarn:

The individual strands are partly (but not completely) aligned. I would like to find the predominant direction in which they are aligned. In the center of the example image, this direction is around 30-34 degrees from horizontal. The result could be the average/median direction for the whole image, or just the average in each local neighborhood (producing a vector map of local directions).

What I've tried: I rotated the image in small steps (1 degree) and calculated statistics in the vertical vs horizontal direction of the rotated image (for example: standard deviation of summed rows or summed columns). I reasoned that when the strands are oriented exactly vertically or exactly horizontally the difference in statistics would be greatest, and so that angle of rotation is the correct direction in the original image. However, for at least several kinds of statistical properties I tried, this did not work.

I further thought that perhaps this wasn't working because there were too many different directions at the same time in the whole image, so I tired it in a small neighborhood. In this case, there is always a very clear preferred direction (different for each neighborhood), but it is not the direction that the fibers really go... I can post my sample code but it is basically useless.

I keep thinking there has to be some kind of simple linear algebra/statistical property of the whole image, or some value derived from the 2D FFT that would give the correct direction in one step... but how?

What probably won't work: detecting individual fibers. They are not necessarily the same color, and the image can shade from light to dark so edge detectors don't work well, and the image may not even be in focus sometimes. Because of that, it is not always even possible to see individual fibers for a human (see top-right in the example), they kinda have to be detected as preferred direction in a statistical sense.

Answer 1

You might try doing this in the frequency domain. The output of a Fourier Transform is orientation dependent so, if you have some kind of oriented pattern, you can apply a 2D FFT and you will see a clustering around a specific orientation.

For example, making a greyscale out of your image and performing FFT (with ImageJ) gives this:

You can see a distinct cluster that is oriented orthogonally with respect to the orientation of your yarn. With some pre-processing on your source image, to remove noise and maybe enhance the oriented features, you can probably achieve a much stronger signal in the FFT. Once you have a cluster, you can use something like PCA to determine the vector for the major axis.

For info, this is a technique that is often used to enhance oriented features, such as fingerprints, by applying a selective filter in the FFT and then taking the inverse to obtain a clearer image.

An alternative approach is to try a series of Gabor filters see here pre-built with a selection of orientations and frequencies and use the resulting features as a metric for identifying the most likely orientation. There is a scikit article that gives some examples here.

UPDATE

Just playing with ImageJ to give an idea of some possible approaches to this - I started with the FFT shown above, then - in the following image, I performed these operations (clockwise from top left) - Threshold => Close => Holefill => Erode x 3:

Finally, rather than using PCA, I calculated the spatial moments of the lower left blob using this ImageJ Plugin which handily calculates the orientation of the longest axis based on the 2nd order moment. The result gives an orientation of approximately -38 degrees (with respect to the X axis):

Depending on your frame of reference you can calculate the approximate average orientation of your yarn from this rather than from PCA.

Answer 2

I tried to use Gabor filters to enhance the orientations of your yarns. The parameters I used are:

phi = x*pi/16;  % x = 1, 3, 5, 7
theta = 3;
sigma = 0.65*theta;
filterSize = 3;

And the imag part of the convoluted image are shown below:

As you mentioned, the most orientations lies between 30-34 degrees, thus the filter with phi = 5*pi/16 in left bottom yields the best contrast among the four.