Shape From Shading Algorithms Under Different Imaging Conditions

Shape from shading (SFS) is the process of computing the three-dimensional shape from one image of a surface. SFS only needs simple equipments and has widespread compatibility. In recent years SFS has attained great improvements and rapid developments in methodology and application. It has become a new research highlight of the three-dimensional shape reconstruction.As SFS is intrinsically an ill-posed problem, existing SFS algorithms can not reconstruct the shape very precisely. Therefore it is very important to enhance the restoration precision of SFS. This thesis mainly presents how to improve SFS algorithms and enhance their restoration precision based on several SFS models under different imaging conditions. These models include the orthographic SFS with a far light source (Model-1), Model-1 under frontal illumination, the perspective SFS with a far light source (Model-2), the perspective SFS with a point light source at the optical center (Model-3) as well as a generic form of models mentioned above. The innovations in the thesis include several aspects:1. After analyzing the weaknesses of the algorithm based on needle-map consistency constraint and hard image irradiance equation constraint (NCCHIC) on Model-1, the thesis proposes an improved NCCHIC to remedy the weaknesses. The improvement mainly includes the revision of the image gradients and the consideration of different situations of the equation set solution. The revision of the image gradient is to revolve it to the reverse direction of the normal vector's projection on the image plane. When the equation set has no solution, the closest vector on the cone of ambiguity to the half-plane is chosen. When the equation set has two solutions, we make the choice according to the place of the grid point. Experimental results on synthetic and real images show that the modified algorithm not only solves the weaknesses of NCCHIC, but also obtains better restoration precision than NCCHIC.2. Based on the fast marching method (FMM), the thesis proposes a double-stencils multi-sources fast marching method (DMFMM) on Model-1 under frontal illumination. Our object is to make the algorithm get better restoration precision and adapt to the multi-sources (many extreme points whose values are known) SFS problem. The algorithm makes use of the information provided by diagonal points by using two stencils which are vertical to each other. The algorithm also analyzes the situation of directions of wave fronts at grid points where the fronts meet and modifies the solution of Eikonal equation at the points. Experimental results on synthetic images show that DMFMM obtains more precise results than FMM, the multi-stencils fast marching method (MFMM) and the isoline-tracking fast marching method (ITFMM).3. After analyzing the weaknesses of the perspective fast marching method (PFMM), the thesis proposes an adaptive perspective fast marching method (APFMM) on Model-2 . By adding constraints to the Eikonal equation coefficients and adjusting them adaptively, APFMM reduces the dependence of PFMM on initial data and improves its robustness. Also, we have proven that APFMM can generalize PFMM. Experimental results on synthetic and real images show that APFMM obtains more precise results than PFMM.4. An optimized algorithm based on the static Hamilton-Jacobi (HJ) equation is proposed to solve the generic model of SFS. It uses the high-order local Lax-Friedrichs (LLF) scheme and the modified weighted essentially non-oscillatory (WENO) scheme according to the characteristics of the generic model to carry on the optimization to the static HJ equation. Experimental results on synthetic and real images show that the optimized algorithm increases the SFS restoration precision.To enhance the restoration precision of SFS, the thesis proposes the above improved and optimized algorithms on several SFS models under different imaging conditions. The research has important academic and practical significance for the precise three-dimensional shape restoration.