Theoretical Analysis of Finite Difference Algorithms for Linear Shape from Shading

This paper presents and analyzes four explicit, two implicit and four semi-implicit finite difference algorithms for the linear shape from shading problem. Comparisons of accuracy, solvability, stability and convergence of these schemes indicate that the weighted semi-implicit scheme and the box scheme are better than the other ones because they can be calculated more easily, they are more accurate, faster in convergence and unconditionally stable. 1 The University of Auckland, Tamaki Campus, Centre for Image Technology and Robotics, Computer Vision Unit, Auckland, New Zealand Analysis of Finite Di erence Algorithms for Linear Shape from Shading Tiangong Wei and Reinhard Klette CITR, University of Auckland, Tamaki Campus, Building 731 Auckland, New Zealand Abstract. This paper presents and analyzes four explicit, two implicit and four semi-implicit nite di erence algorithms for the linear shape from shading problem. Comparisons of accuracy, solvability, stability and convergence of these schemes indicate that the weighted semi-implicit scheme and the box scheme are better than the other ones because they can be calculated more easily, they are more accurate, faster in convergence and unconditionally stable. This paper presents and analyzes four explicit, two implicit and four semi-implicit nite di erence algorithms for the linear shape from shading problem. Comparisons of accuracy, solvability, stability and convergence of these schemes indicate that the weighted semi-implicit scheme and the box scheme are better than the other ones because they can be calculated more easily, they are more accurate, faster in convergence and unconditionally stable.