Segmentation of volumetric medical imagery often benefits from the incorporation of a-priori knowledge of anatomical structure into the problem domain. Our previous work involved the use of active surfaces based on spherical mappings of rectangular grids to represent the anatomical structure of the object of interest. We have developed an improved method using active surfaces based on multiple geodesics which can dynamically link together to form object models. Deformable geodesic models are topologically closed structures, making them a better approximation of the types of objects found in volumetric imagery. In addition, geodesic surfaces exhibit regular sampling intervals which facilitate collision detection between different surfaces, allowing constraints among different surfaces to be included in the segmentation scheme. In this paper we present an overview of our current active surface segmentation system. Initial results of the system as applied to the problem of the segmentation of the major sub-parts of the brain are also presented. The results show favorable potential for the use of geodesic-based surfaces as a means for the segmentation of closed objects from volumetric medical imagery.