Occlusal surface reconstruction of human teeth from a single image based on object and sensor physical characteristics

Image formation involves understanding sensor characteristics and object reflectance. In dentistry, an accurate 3-D representation of the human jaw may be used for diagnostic and treatment purposes. Photogrammetry can offer a flexible, cost effective solution for accurate 3-D representation of the human teeth, which can be used for diagnostic and treatment purposes. Nonetheless there are several challenges, such as the non-friendly image acquisition environment inside the human mouth, problems with lighting and errors due to the data acquisition sensors. In this paper, we focus on the 3D surface reconstruction aspect for human teeth based on a single image. We introduce a more realistic formulation of the shape-from-shading (SFS) problem by considering the image formation components; the camera, the light source, and the surface reflectance. We propose a non-Lambertian SFS algorithm under perspective projection which benefits from camera calibration parameters. We take into account the attenuation of illumination due to near-field imaging. The surface reflectance is modeled using Oren-Nayar-Wolff model which accounts for the retro-reflection case. Our experiments provide promising quantitative metric results for the proposed approach.

[1]  Shree K. Nayar,et al.  Improved Diffuse Reflection Models for Computer Vision , 1998, International Journal of Computer Vision.

[2]  Shree K. Nayar,et al.  Generalization of Lambert's reflectance model , 1994, SIGGRAPH.

[3]  Jean-Denis Durou,et al.  Numerical methods for shape-from-shading: A new survey with benchmarks , 2008, Comput. Vis. Image Underst..

[4]  Berthold K. P. Horn.  SHAPE FROM SHADING: A METHOD FOR OBTAINING THE SHAPE OF A SMOOTH OPAQUE OBJECT FROM ONE VIEW , 1970 .

[5]  Aly A. Farag,et al.  A 3-D reconstruction system for the human jaw using a sequence of optical images , 2000, IEEE Transactions on Medical Imaging.

[6]  Olivier D. Faugeras,et al.  A Unifying and Rigorous Shape from Shading Method Adapted to Realistic Data and Applications , 2006, Journal of Mathematical Imaging and Vision.

[7]  Michael J. Brooks,et al.  The variational approach to shape from shading , 1986, Comput. Vis. Graph. Image Process..

[8]  Aly A. Farag,et al.  A New Formulation for Shape from Shading for Non-Lambertian Surfaces , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[9]  Aly A. Farag,et al.  Novel Image-Based 3D Reconstruction of the Human Jaw using Shape from Shading and Feature Descriptors , 2011, BMVC.

[10]  R. G. Chadwick,et al.  Challenges of photogrammetric intra-oral tooth measurement , 2008 .

[11]  Aly A. Farag,et al.  Shape from Shading Under Various Imaging Conditions , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[12]  Michael Elad,et al.  Content Based Retrieval of VRML Objects - An Iterative and Interactive Approach , 2001, Eurographics Multimedia Workshop.

[13]  Anand Rangarajan,et al.  A new point matching algorithm for non-rigid registration , 2003, Comput. Vis. Image Underst..

[14]  Bastian Goldlücke,et al.  Variational Analysis , 2014, Computer Vision, A Reference Guide.

[15]  Aly A. Farag,et al.  Shape from shading for hybrid surfaces as applied to tooth reconstruction , 2010, 2010 IEEE International Conference on Image Processing.

[16]  Edwin R. Hancock,et al.  Surface radiance correction for shape from shading , 2005, Pattern Recognit..