How can I automatically find the boundary of a high intensity region inside an image? I have an image I(x,y): 



Red indicates high values and blue low values. Everything in black is drawn onto the image afterwards.
The black dot (xp,yp) represents a point clicked by an user and the black curve a boundary around the high value region around the user clicked point.

How can I automatically find this boundary?

As can be seen from the picture; I do not want the boundary to propagate through narrow gaps.
One method that I have had lots of success with, and others have too, is Circular Shortest Path (CSP). Here is one paper, but there are quite a few more and possibly some code floating around the web. Another technique that are perhaps more popular, and for which code might be more common, are snakes (active contours).

These techniques work by finding a connected path that minimises a certain function. In your case, it would be to find the path that goes through many edge pixels while still remaining somewhat round. The roundness constraint is what keeps the path from going off down the narrow gaps. Snakes are different from CSP in that the boundary is 'grown' out from a seed area; CSP performs a polar transformation about the centre point.

Another possibility is some kind of morphological operator. These can be used to find regions of a particular size. One would convert the image to binary, the apply a morphological opening using a structuring element of a big enough size to fit inside the area of interest, but not anywhere else.