Global solution of the finite element shape-from-shading model with a bioluminescent molecular imaging application

Only a planar bioluminescence image acquired from an ordinary cooled charge-coupled device (CCD) array every time, how to re-establish the three-dimensional small animal shape and light intensity distribution on the surface has become urgent to be solved as a bottleneck of bioluminescence tomography (BLT) reconstruction. In this paper, a finite element algorithm to solve the Dirichlet type problem for the first order Hamilton-Jacobi equation related to the shape-from-shading model is adopted. The algorithm outputting the globally maximal solution of the above problem avoids cumbersome boundary conditions on the interfaces between light and shadows and the use of additional information on the surface. The results of the optimization method are satisfied. It demonstrates the feasibility and potential of the finite element shape-from-shading (FE-SFS) model for reconstructing the small animal surface that lays one of key foundations for a fast low-cost application of the BLT in the next future.