While most of existing methods use facial intensity images, a newest ones focus on introducing depth information to surmount some of classical face recognition problems such as pose, illumination, and facial expression variations. This abstract summarizes a new face recognition approach invariant to facial expressions based on dimensional surface matching. The core of our recognition/authentication scheme consists of aligning then comparing a probe face surface and gallery facial surfaces. In the o®-line phase, we build the 3D face database with neutral expressions. The models inside include both shape and texture channels. In the on-line phase, a partial probe model is captured and compared either to all 3D faces in the gallery for identification scenario or compared to the genuine model for authentication scenario. The first step aligns probe and gallery models based only on static regions of faces within a new variant of the well known Iterative Closest Point called on R-ICP (Region-based Iterative Closest Point) which approximates the rigid transformations between the presented probe face and gallery one. R-ICP result is two matched sets of vertices in the both static and mimic regions of the face surfaces. For the second step, two geodesic maps are computed for the pair of vertices in the matched face regions. The recognition and authentication similarity score is based on the distance between these maps. Our evaluation experiments are done on 3D face dataset of IV2 French project.