Fast Shape-From-Shading Algorithm for 3D Reconstruction of Hybrid Surfaces Under Perspective Projection

To address the problems associated with excessive time consumption and large errors in irradiance equation solutions using existing shape-from-shading (SFS) algorithms for three-dimensional (3D) reconstruction of hybrid surfaces under perspective projection, a fast SFS algorithm based on the Newton-Raphson method is proposed. First, the Blinn-Phong model is adopted to characterize the hybrid reflection property of object surfaces. Then, an image partial differential irradiance equation that corresponds to the 3D shape information of the surfaces is established by considering the pinhole camera perspective projection model. Second, the irradiance equation is transformed into a functional equation in the height gradient of object surfaces, which is iteratively solved using the Newton-Raphson method. Then, the solution is converted into a Hamilton -Jacobi partial differential irradiance equation whose Hamiltonian function can be obtained through Legendre transformation. Finally, a scheme to approximate the Hamiltonian function based on optimal control theory and iterative fast marching strategy is applied to obtain the viscosity solution of the Hamilton -Jacobi equation, which represents the heights of hybrid reflection surfaces. Experimental results demonstrate that the mean absolute error and root mean square error of the heights of the object surface decrease and the run time of the proposed algorithm is greatly reduced compared with the existing SFS algorithm for 3D reconstruction of hybrid surfaces based on the upwind scheme.