Cutting the blood pool at narrowings

Mathias John's paper discusses how the atrium can be segmented by cutting the blood pool at narrowings. I have been trying to identify the narrowings where I would ideally like to cut the blood pool. Here are two images which show the left atrium, the narrowings at which the atrium needs to be cut at, in order to segment it.

After implementing a system, that can identify the local-maximums of the EDT-transformed image, it has been possible to perform a preliminary segmentation of the left atrium.

There are 220 local maximums, and some of these maximums lie within the vicinity of the left atrium. These local maximums play a crucial role in segmentation. My theory is (and possibly M. John's theory) voxels which will lie within the atrium will be part of a basic component centered only by those local maximums.

I have run several test cases to check this and all of them strongly suggest that this is the case.