Automatic distances measure of tubes edges with Matlab

Question

I would like to automatically measure a point-to-point distance in a batch of more than 100 images using Matlab 2014a. Specifically these images are tube sections and I want to measure the distance between the inner and outer circumferences (tubes wall thickness) from 0 to 360° with a given step of discretization obtaining a profile plot. The purpose of this profile plot is to see if the profile remains constant or changes among the samples.

I tried to use the edge function (with sobel, canny etc…) to identify the image borders but this function identifies also some inner edges due to scratches of the tube and dirt captured by the microscope. Does anyone know how to identify only the inner and outer border and perform a point to point distance measure?

I would like to obtain a plot which has on the x-axis the 0-2π scale, and on the y-axis the distance between the inner and outer circumferences. Thanks in advance!

Here is link to an image sample that you can download.

Answer 1

I have been having a look at this, but I use ImageMagick and OpenCV rather than Matlab, however I am sure you can convert the ideas to Matlab quite readily if that is your preference.

Finding Circles - Well, Hough Transforms make a big mess of this and seem to create a million circles all over the place, so I am thinking that is maybe not a solution. I then got thinking about "depolarising" the image and working in the straight line space it creates. It is quite easily depolarised with a simple ImageMagick -distort command like this:

convert tubo.tif -distort depolar 0 straight.jpg

That gives you an image like this:

The next thing is to slice the image into vertical strips corresponding to your discretisation. I didn't see any mention of actual numbers so I went with dividing the image into 10 vertical strips, each one the full height of the straightened image and 10% of its width. I did that in ImageMagick like this:

convert straight.jpg -crop 10%x100% out.jpg

which gives me 10 images called out-0.jpg, out-1.jpg ... out-9.jpg

Here is one:

I then resized the width of each of the 10 images, down to 50 pixels. I think I would really resize down to 1 pixel wide then it would average the pixels across the strip and give me a single transition point from background to pipe and then back to background. But you cannot easily see a 1 pixel wide image on here, so I went with a width of 50 pixels.

After that, I animated it, so you can see what is going on. I did that like this:

convert -delay 20 -loop 0 out* animated.gif

Which gives this:

So the whole code looks like this:

convert tubo.tif -distort depolar 0 straight.jpg
convert straight.jpg -crop 10%x100% out.jpg
for f in out* ; do
   convert $f -resize 50x! $f
done
convert -delay 20 -loop 0 out* animated.gif

There are lots of things to think about still... where to choose the image centre for depolarising, what thresholds to use, whether to use any morphology to close gaps cause during binarisation, whether any contrast enhancement helps or just moves the edges.

Another thing I note is that the inner area of the original image (inside the middle of the pipe) has a mean pixel value of 89 and a standard deviation of 4.5 (meaning it is quite homogeneous) whereas the actual pipe has a mean of 120 and a MUCH higher standard deviation of 25, so this could give some insight into how to threshold - maybe by texture/homogeneity.

By the way, ImageMagick and OpenCV are readily installed on OSX with homebrew. See my answer here.

Answer 2

The tube is clearly distinguishable from its background by considering local variance or total variation. With a few lines in Matlab you can get a reasonable binary image:

  sx=filter2(ones(15)/15^2,im,'valid');
  sx2=filter2(ones(15)/15^2,im.^2,'valid');
  varMap=sx2-sx.^2;
  bin = imopen(varMap>15,ones(7));

This is clearly not enough to solve your problem, as you have to detect the edges in some manner. I can recommend one of two approaches: 1. Assume some reasonable model for the edges e.g. ellipse, find candidates for inner/outer edges in the binary, and find best parameters for your model using linear regression or ransac.

2. Convert the original image to polar and run some dynamic programming/ Dijstra's SSSP to find an (approximately horizontal) edge. As score for good edge, you can use the vertical derivative of the polar images. Dynamic Programming cannot guaranty a circular path, but good heuristics exist to solve this. The binary image can be used here for primary evaluation of the tube's center.

Answer 3

You can detect the inner and the outer circles using imfindcircles. The region between the two circles can serve as your initial segmentation. You can use it as initialization for a more sophisticated segmentation algorithm such as active contours, which may give you a more precise boundary.