Objective: The aim of this study is to develop automatic methods of geometric coordination registration (GCR) for the virtual planning and evaluation of implant surgery. Methods: The target modalities of the image to be registered are cone-beam computed tomography (CBCT) or optical surface (OS) scan. Several geometric fiducial markers, cubic corners (CC) and discs, are fabricated on the patient's oral stent and digitized into a 3D mesh model. By analyzing the distribution of vertices and normal vectors of the mesh model, a novel descriptor is proposed to detect the position of the geometric fiducial markers. CC edges and disc centers are then used to find the transformation matrix to align the input point cloud to the target Cartesian axes. Results: CBCT and OS scans of the plaster models with implants of 29 patients were collected. The implant positions found by using the proposed algorithm were compared to the Gold standard developed with a coordinate measuring machine (CMM). Experimental results show that the target registration error (TRE) of the proposed method was 0.43mm. Conclusion: The proposed method performs better than existing manual or semi-automatic GCR (TRE 0.52mm).