A processing system comprises a processor and a memory having computer readable instructions stored thereon. The computer readable instructions, when executed by the processor, cause the system to obtain a reference tree of nodes and linkages based on a reference three dimensional volumetric representation of a branched anatomical formation in a reference state. The computer readable instructions also cause the system to obtain a reference three dimensional geometric model based on the reference tree and detect deformation of the branched anatomical formation due to anatomical motion based on measurements from a shape sensor. The computer readable instructions also cause the system to obtain a deformed tree of nodes and linkages based on the detected deformation and create a three dimensional deformation field that represents the detected deformation of the branched anatomical formation.
