Enhanced variational approach by Fast-Marching to recover a 3D shape from shading
Lyes Abada, Saliha Aouat · 2016
Although variational approaches are popular techniques in the Shape from shading field, they have in general many inconvenients. They necessitate the computation of the surface gradient, they have to determine the 3D surface and also they need several constraints to enforce the integrability and the smoothness of the solution. The convergence is very slow due to the big number of the possible solutions values for each pixel. There are also the propagation methods that use several pixels at the same time like the Fast-Marching. Generally, these methods need some known points such as the local maximums or boundary conditions. This paper demonstrates how a minimization approach can be used to determine directly the local maximum and compute the 3D object using the Fast-marching method with only the smoothness constraint. The idea is to search local maximum points that minimize an energy function. The energy function uses only the smoothness constraint since the inerrability of the surface is guaranteed by the Fast-Marching method which determines the depth around the local maximum points. We show that the new shape from shading method leads to determine the 3D surface.