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This paper presents a 3D segmentation framework for multiple objects or compartments embedded as level sets. Thanks to a compact representation of the level set functions of multiple objects, the framework guarantees no overlap and vacuum, and leads to a computationally efficient evolution scheme largely independent of the number of objects. Appropriate topology constraints ensure not only that the topology of each object remains the same, but that the relationship between objects is also maintained. The decomposition of objects makes the framework specifically attractive to the segmentation of related anatomical regions or the parcellation of an organ, where relationships must be maintained and different evolution forces are needed on different parts of the objects interface. Examples of 3D whole brain segmentation and thalamic parcellation demonstrate the potential of our method for such segmentation tasks.