How can I extract the outline of bubbles in my image?

I have an image:

I tried to extract the outline of the bubbles, but I met with some problems. Firstly I tried the method used in Mathematica documentation for Analyze Segmented Cells In An Image, but it didn't work well, I got an irregular figure:

Then I tried the function EdgeDetect. Things got a little bit better, but it's still not what I want. Could you please help me with my problem?

Answer

image = Import["http://i.stack.imgur.com/UNXEV.jpg"];
n = TotalVariationFilter[image, 0.05]
b = LocalAdaptiveBinarize[n, 50]
s = DeleteSmallComponents[ColorNegate[DeleteSmallComponents[b, 20^2]], 20^2]
(d = DistanceTransform[s]) // ImageAdjust

m = MaxDetect[d, 10]
(w = WatershedComponents[ColorNegate[d], m]) // Colorize
c = ComponentMeasurements[w, {"Centroid", "EquivalentDiskRadius"}, #2 < 50 &];
Show[image, Graphics[{Thick, Red, Circle @@@ c[[All, 2]]}], ImageSize -> 1280]

^{(Click for bigger.)}

Run the code to see the intermediate steps.

Thanks to nikie for the second half of this answer.

LocalAdaptiveBinarize is new in version 10, but all it does is "creates a binary image by replacing values above the mean of the range-$r$ neighborhood with $1$ and others with $0$." So you can replace it with something like, say,

b = Binarize[ImageSubtract[n, MeanFilter[n, 50]], 0]

which gives similar results, though not identical for some reason. Possibly there's a more elegant way to do it.