How can I generate a branchless centerline in a tubelike section of a binary image?

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Hello everyone,
I need to somehow automatically find a unbranched centerline in a tubelike section of a binary image. With that centerline I want to calculate the mean length of the tubeless section, but the branches keep falsifying the values! So far I used
% Centerline = bwmorph(bw,'thin','inf');
which gets me a perfect line of pixels, but at the end there are always one or two braches.
I already tried the skeleton-operation, but this only results in a pixelline with even more branches...
% Centerline_2 = bwmorph(bw,'skel','inf')
I would be very happy if someone could help me out. Maybe I´m thinking in a completely wrong direction and there´s an very easy way to tackle this problem?
Thanks in advance for any suggestions!

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