Shape-from-shading using sensor and physical object characteristics applied to human teeth surface reconstruction

Image formation involves understanding the sensors characteristics and object reflectance. In dentistry, for example an accurate three-dimensional (3D) representation of the human jaw may be used for diagnostic and treatment purposes. Photogrammetry can offer a flexible, cost-effective solution in that regard. Nonetheless there are several challenges, such as non-friendly image acquisition environment inside the human mouth, problems with lighting (specularity effects because of saliva, gum discolourisation, and occlusion because of the tongue in the lower jaw), and errors because of the data acquisition sensors (e.g. camera calibration errors, lens distortion and so on). In this study, the authors focus on the 3D surface reconstruction aspect for human jaw modelling based on physical surface characteristics and sensor properties. Owing to apparent lens distortion imposed by near-field imaging, the authors propose a new flexible calibration for lens radial distortion based on a single image of a sphere. The authors propose a non-Lambertian shape-from-shading (SFS) algorithm under perspective projection which benefits from camera calibration parameters. Our experiments provide quantitative metric results for the proposed approach. The reflectance of the tooth surface is modelled by the Oren-Nayar reflectance model for rough surfaces whose roughness parameter is physically computed from an optical surface profiler measurements. As compared to state-of-the-art SFS approaches, our approach is able to recover geometric details of tooth occlusal surface. This work is fundamental for establishing an optical-based approach for reconstructing the human jaw, that is inexpensive and does not use ionising radiation.