I have images which contains maybe 1000 circles of different sizes. Circles may overlap: it's not a simple picture.

I'd like to do one of two things: either (1) learn the circle size probability density function (binned), or (2) count the number of circles of each size.

Can anyone refer me to any references relating to such a regression from an image of a probability distribution? I'm interested in methods to constrain neural network output so the sum of values from the output layer is 1.0 (approach 1), or to count objects without localizing their position (approach 2).

  • $\begingroup$ Will the images contain only circles, or might they also have other shapes? Also might some of the circles be filled with solid color and some not solid color? $\endgroup$ Commented Sep 28, 2018 at 15:30
  • $\begingroup$ They can contain only circles as a start.. the circles may overlap some. They will be filled with solid color. This is a toy version of a more complex problem.. learning the surface size distribution of colored rocks from a photo of them $\endgroup$ Commented Sep 29, 2018 at 1:33


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