The image of mandrel as seen from above will be rectangular, if the mandrel is cylindrical then is there any software (compatible with Arduino) which can be used to calculate Mandrel Dimensions. Using wither image processing / CV???
Well I know imageJ works for manual measurement within images. If you have a known dimension then it is possible to calculate other dimensions with the image. Otherwise look at openCV for c++ for image processing functions.
I would be happy to show you what our new software MIPAR (http://MIPAR.us) can do, as I am quite confident it can quantify exactly what you need. So you have any images of the actual mandrel as you describe, or do you need to quantify some dimension from the sketch you posted.