Mean sets for building 3D probabilistic liver atlas from perfusion MR images

This paper is concerned with liver atlas construction. One of the most important issues in the framework of computational abdominal anatomy is to define an atlas that provides a priori information for common medical task such as registration and segmentation. Unlike other approaches already proposed so far (to our knowledge), in this paper we propose to use the concept of random compact mean set to build probabilistic liver atlases. To accomplish this task a two-tier process was carried out. First a set of 3D images was manually segmented by a physician. We see the different 3D segmented shapes as a realization of a random compact set. Secondly, elements of two known definitions of mean set were applied to build a probabilistic atlas that captures the variability of the cases, keeping nevertheless the essential shape of the liver.