A robust shape-from-shading algorithm using two images and control of boundary conditions

In this paper, we present a shape-from-shading algorithm that uses two shading images. It is very simple to implement and enables us to estimate reliable and accurate shapes of objects in a direct way. For each of the two images, the Jacobi´s iterative method is applied to the difference between the image and the reflectance function, and the resulting two iterative relations are combined to get a single iterative relation. This iteratively reconstructs the shape in the forward or backward direction using boundary conditions along two edge lines. The operation is basically numerically stable, but a more robust algorithm is also derived which can produce more accurate shape by controlling the boundary conditions along all the four edge lines. Computer experiments show the usefulness of the algorithm. The estimation typically takes ten to twenty seconds for 50×50 images using a 1.2 GHz Pentium III PC.