Segmenting circular shapes from a binary image

Question

I have several binary images, and my task is to segment the circular shape. The circles are not a perfect rounded circle, but they will all look like a circle. Here are some sample images and what I need:

As you can see above, the left images are the original images, and the correct images are what I need to do. The circles intersect with other shapes, but I only need a circle, as indicated in red. Imaginary lines are required to close the circle. What can I do in this case when processing images?

EDIT: in case the image above is broken, here: http://imageshack.us/photo/my-images/835/circleonly.jpg/

Answer 1

You can use the hough transform, first you need an image of the edge, then you use the hough transform, as you can see in these documents

http://www.cis.rit.edu/class/simg782/lectures/lecture_10/lec782_05_10.pdf

http://www.sci.utah.edu/~gerig/CS6640-F2010/FINALPROJECT/Ballard-GHT-1981.pdf

http://www.sciencedirect.com/science/article/pii/003132039290064P

http://www.markschulze.net/java/hough/

Answer 2

Do you know the radii of the discs you are looking for? If so, morphological discoveries (erosion, then dilatation) would be simple and very quick. The result of using Mathematica:

Opening[img, DiskMatrix[15]] 

If not, as expected, computing a contour image and then using the Hough transform would be an appropriate method. The image shown above shows the outline image.