How to find out the radius and center of unknown circle and reconstruct the circle with calculated radius.

i have the image of coins ovelapped on each other which i taken through mobile phone.I want to calculate the no of coins in image and also the radius of coin.

[Matt J]

If the coins overlap, how will a fitting procedure like your message title describes help you? Do you already have ways of distinguishing between overlapping coins and attacking them as separate circles?

[Matt J]

What input data do you have currently? An edge map? Just the image itself? Once you know the radius of a coin in pixels, do you need to determine its physical radius in centimeters/millimeters etc...?

[Avadhoot Telepatil]

an edge map and i want to calculate the radius in millimeter

Answer 1

[Pierre]

You should have a look at the Hough transform in its general form and its application to circles in particular. It allows to detect (even considerably occluded) entities like lines, circles, and ellipses and provides implicitly the parametrization (that is, the centre and the radius in your case) of the entity.

Once you have the equations describing the circles, computing the overlapping regions should be relatively simple.