How to count and mark all counted objects in this image

Question

I need some help on image processing in Mathematica (I have unsuccesfully tried with OpenCV).

I have an image:

and I need to count all objects in this image and mark them.

The perfect result would look like this:

Is this possible? How?

Thank you all for your help. Alternative question: Is there a solution how to get rid of all the connections between objects without changing the rest of the image:

Thank you in advance! Lauris

Answer 1

You can play with the binarization value to tweak the results:

img = Import["http://i.stack.imgur.com/LWNaK.png"]; 
MorphologicalComponents[Binarize[img, 0.4]] // Colorize

You can then calculate the positions, means, sizes, etc of the components using ComponentMeasurements as in this answer.

As for your second question, about removing the links between objects, the straightforward approach here is Erosion. For instance

Erosion[img, 5]

nicely removes the bulk of the links. Again, you will want to play with the erosion parameter (in this case 5) for best effect.

Answer 2

Here's a set of functions, drawn mostly from here and a portion of this screencast. It is not a perfect answer at this point; the major problem being the small tendrils that link features together. It is possible that some type of filter with a DiskMatrix mask will lead you to a better result, but for the moment, I suspect there's a lot to wade through here.

seimg = Import["http://i.stack.imgur.com/LWNaK.png"];
i = GaussianFilter[FillingTransform[seimg], 15];
b = Binarize[i];
d = DistanceTransform[b, Padding -> 0];
m = MaxDetect[ImageAdjust[d, 0.2]];
w = WatershedComponents[GradientFilter[b, 3], m, Method -> "Rainfall"];
s = SelectComponents[w, "Count", 20 < # < 10000 &];
ms = ComponentMeasurements[
   s, {"Centroid", "EquivalentDiskRadius", "Label"}];
Show[seimg, 
 Graphics[{Blue, Circle @@ # & /@ (ms[[All, 2, 1 ;; 2]]), 
   MapThread[Text, {ms[[All, 2, 3]], ms[[All, 2, 1]]}]}]]