So I think it is a mixed problem.
how to detect the goal
some image with white contours is easy to segment, but the third image with no contour, there is no easy method to segment.
some image with black line, but some image not. and how to define the R, the max vertical distance? or the max inscribed circle?
maybe you need classify your images, and process them by different method. Here I give your some advice to treat some specific image. I use ImagePy, you can get it free, (imagej has the similar method, so if you use imagej, you can also reference these method)
how to extract a white contours?
threshold > fill holes > filter region by area and solidity
how to measure the max height
region analysis then you can got the maxy and miny, max height = maxy - miny,
and you can also get the cov ellipse. the major, minor axis may be meanful for you.
how to measre the max inscribed circle?
distance transform, and find local max point, the pixel value is the max inscribed circle radius.
how to split from the black line
extract the goal > mask the raw image > threshold > watershed
then you can measure the max height, major, minor axis, or max inscribed circle like upon!
the method upon in ImagePy support sequence process, but you need put the same type together in a folder. then import them as sequence. then you can process all images at one time.
a tips: please save your image in png or bmp, tif. (jpg would lost some detail)