Depth from gradient fields and control points: Bias correction in photometric stereo

Photometric stereo is capable of high quality reconstruction of fine shape details, but is prone to systematic errors due to nonideal illumination or imperfect calibration. We present methods for correcting the bias, using sparse control points of known 3D location. An easy way to obtain control points is via the projection of a dot-matrix pattern using a laser pointer with a suitable adapter, and triangulation. Straight forward incorporation of control points as constraints in the computation of depth from the gradient field leads to singularities. We propose two well-behaved methods for bias correction using control points. One is based on constrained weighted least squares extension of depth from gradient-field computation. The other adds an interpolation surface to the reconstructed shape. Practical computation of depth from a gradient field requires an efficient numerical scheme. We employ full-multigrid computation with successive over-relaxation and show how to propagate the gradient field and the control points through the pyramid. Experimental results demonstrate significant bias reduction in photometric stereo, allowing high reconstruction quality even in the presence of severe setup errors.