Shape from Shading with Perspective Projection

Most conventional SFS (shape from shading) algorithms have been developed under the assumption of orthographic projection. However, the assumption is not valid when an object is not far away from the camera and, therefore, it causes severe reconstruction error in many real applications. In this research, we develop a new iterative algorithm for recovering surface heights from shaded images obtained with perspective projection. By dividing an image into a set of nonoverlapping triangular domains and approximating a smooth surface by the union of triangular surface patches, we can relate image brightness in the image plane directly to surface nodal heights in the world space via a linearized reflectance map based on the perspective projection model. To determine the surface height, we consider the minimization of a cost functional defined to be the sum of squares of the brightness error by solving a system of equations parameterized by nodal heights. Furthermore, we apply a successive linearization scheme in which the linearization of the reflectance map is performed with respect to surface nodal heights obtained from the previous iteration so that the approximation error of the reflectance map is reduced and accuracy of the reconstructed surface is improved iteratively. The proposed method reconstructs surface heights directly and does not require any additional integrability constraint. Simulation results for synthetic and real images are demonstrated to show the performance and efficiency of our new method.