How to find arc length, angle from the image?

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Dear all,
I want to find the curve length and curve orientaiton from the image. I performed the image segmentation and convert it to biary image (attached is the iamge). How can I measure the angular variation of the curves and the curve angle.
Is there a better way to perform segmentation of the image to see the more sharp and clear curvatures?
how can it be quantitatively/statistically characterise?

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