3D shape reconstruction of medical images using a perspective shape-from-shading method

A 3D shape reconstruction approach for medical images using a shape-from-shading (SFS) method was proposed in this paper. A new reflectance map equation of medical images was analyzed with the assumption that the Lambertian reflectance surface was irradiated by a point light source located at the light center and the image was formed under perspective projection. The corresponding static Hamilton–Jacobi (H–J) equation of the reflectance map equation was established. So the shape-from-shading problem turned into solving the viscosity solution of the static H–J equation. Then with the conception of a viscosity vanishing approximation, the Lax–Friedrichs fast sweeping numerical method was used to compute the viscosity solution of the H–J equation and a new iterative SFS algorithm was gained. Finally, experiments on both synthetic images and real medical images were performed to illustrate the efficiency of the proposed SFS method