SHAPE FROM SHADING WITH A LINEAR TRIANGULAR ELEMENT SURFACE MODEL

We propose to combine a triangular element surface model with a linear ized reflectance map to formulate the shape-from-shading problem. The main idea is to approximate a smooth surface by the union of triangula r surface patches called triangular elements and express the approxima ting surface as a linear combination of a set of nodal basis functions . Since the surface normal of a triangular element is uniquely determi ned by heights of its three vertices (or nodes), image brightness can be directly related to nodal heights via the linearized reflectance ma p. The surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique. The pr oposed method does not require any integrability constraint or artific ial assumptions on boundary conditions. Simulation results for synthet ic and real images are demonstrated to show the performance and effici ency of our new method.