A system comprises one or more processors. The system further comprises memory having computer readable instructions stored thereon that, when executed by the one or more processors, cause the system to: obtain a reference tree of nodes and linkages for a reference three dimensional volumetric representation of a branched anatomical formation in a reference state; based on the reference tree, generate a reference three dimensional geometric model; based on measurements from a sensor system, detect deformation of the branched anatomical formation; based on the detected deformation, obtain a deformed tree of nodes and linkages; and generate a three dimensional deformation field that represents the detected deformation of the branched anatomical formation.