Image-guided liver surgery requires the ability to identify and compensate for soft tissue deformation in the organ. The predeformed state is represented as a complete three-dimensional surface of the organ, while the intraoperative data is a range scan point cloud acquired from the exposed liver surface. The first step is to rigidly align the coordinate systems of the intraoperative and preoperative data. Most traditional rigid registration methods minimize an error metric over the entire data set. In this paper, a new deformation-identifying rigid registration (DIRR) is reported that identifies and aligns minimally deformed regions of the data using a modified closest point distance cost function. Once a rigid alignment has been established, deformation is accounted for using a linearly elastic finite element model (FEM) and implemented using an incremental framework to resolve geometric nonlinearities. Boundary conditions for the incremental formulation are generated from intraoperatively acquired range scan surfaces of the exposed liver surface. A series of phantom experiments is presented to assess the fidelity of the DIRR and the combined DIRR/FEM approaches separately. The DIRR approach identified deforming regions in 90% of cases under conditions of realistic surgical exposure. With respect to the DIRR/FEM algorithm, subsurface target errors were correctly located to within 4 mm in phantom experiments.