A processing system may comprise a central processing unit, a graphics processing unit, and a memory having computer readable instructions. The computer readable instructions may cause the processing system to obtain a reference tree of nodes and linkages based on a reference 3D volumetric representation of a branched anatomical formation in a reference state and obtain, by the central processing unit, a reference 3D geometric model based on the reference tree. The instructions may also cause the processing system to receive, by the graphics processing unit, a non-rigid transform for the nodes of the reference tree and determine, by the graphics processing unit, a rigid transform for the reference tree nodes based on the non-rigid transform. The instructions may also cause the processing system to transform each node into a deformed node, create a 3D deformation field, and create a deformed 3D geometric model of the branched anatomical formation.