A Specular Shape from Shading by Fast Marching Method

In order to reconstruct a surface which has specular reflection from the grayscale information contained in a single two-dimensional (2D) image, a specular shape from shading (SFS) using the fast marching method is presented. Under assumptions that the camera performs an orthographic projection whose direction is equal to the direction of the light source and that the Phong model is used to depict the reflectance property of the surface, the image irradiance equation for specular surface is derived and it is a first-order nonlinear partial differential equation (PDE). By transforming it into a standard Eiknoal PDE, the fast marching method is applied to compute a solution of the resultant Eiknoal equation. Experiments are tested on both a synthetic vase image and a sphere image and the results demonstrate the effectiveness of the presented specular SFS method.