Low Dimensional and Easily Interactive Method of 3D Shape from Shading

A low dimensional and easily interactive method is proposed for reconstruction of the shape of an object from its single image. By sing quadric curve surface model and Lambert light reflectance model for a continuous surface segment of the object, the number of unknowns in the reconstruction equations of that surface segment is lowed to 26 nonlinear algebra equations. Only 13 points on the corresponding region in the image are thus needed for the reconstruction. Surface visibility constraints that are set up automatically are introduced into the solution of the reconstruction so that the ambiquity of choosing one of the intersecting points of the projection line with the surface is avoided. The solution of the governing equations is transformed into optimization problem subjected to visible constraints in order to overcome the singularity in direct solving the set of nonlinear algebra equations. Genetic algorithm is used to solve the optimization. A complicate surface of an object are be partitioned into several continuous segments which in turn be reconstructed with our proposed method. The mean absolute difference of curvatures of reconstructed surface and the true surface is used to evaluate the precision of our methods. Experiments on synthetic images show that the precision of our reconstruction method is fair but the simpleness of choosing points for the reconstruction makes our method suitable to be automatized to apply to micro-robots.