How to create a model which predicts the radius of a circle? My training set is made up of 2d images with one imperfect but broadly circular shape in them (plus plenty of noise).  I wish to train a model to predict the "radius" (obviously it's a somewhat subjective concept here) of the shape.

Let's say that I know the approximate center of the shape.

What approach would you use?  Have each input to the model be one of the pixels including that pixel's distance from the center, as well as its colour?

What if I also wanted to predict the volume of the shape, and it was less regular?
Finding reasonably-regular shapes in noisy data? I'd try classical techniques first, like RANSAC or a Hough transform.

Why machine learning?