Antoine,
I've spent some time thinking about this problem because it irked me. The trouble is, you're going to have to define some threshold for what constitutes "inside" the profile.
When defining the exterior hull of a field of points it's easy to define "outside" because you can declare that no segment between any two points in the cloud crosses your outside hull.
On the inside, you can always cut across any interior shape and end up eliminating part of the area. In your figure above, if you put a vertical line across the region where it necks down you could cut off the tail to the left. That seems obviously wrong, but when you zoom in at the spacing-between-points level, how do you decide when you should make a high aspect ratio triangle that goes further out or skip across to the next point? I don't think there's a solution that doesn't involve some sort of threshold or smoothing to accomplish what you want.
If you're willing to smooth the set of points, I'd recommend using a 2D kernel estimator to approximate a distribution function that generates your points. You can then take a contour of that function (or of its gradient or del2) at whatever level you decide is a good threshold.
I have had good luck using Botev's kde2d code for such purposes. If you upload a set of example contour values I can help you run it through this code if you'd like.
