Passive photometric stereo from motion

We introduce an iterative algorithm for shape reconstruction from multiple images of a moving (Lambertian) object illuminated by distant (and possibly time varying) lighting. Starting with an initial piecewise linear surface, the algorithm iteratively estimates a new surface based on the previous surface estimate and the photometric information available from the input image sequence. During each iteration, standard photometric stereo techniques are applied to estimate the surface normals up to an unknown generalized bas-relief transform, and a new surface is computed by integrating the estimated normals. The algorithm essentially consists of a sequence of matrix factorizations (of intensity values) followed by minimization using gradient descent (integration of the normals). Conceptually, the algorithm admits a clear geometric interpretation, which is used to provide a qualitative analysis of the algorithm's convergence. Implementation-wise, it is straightforward, being based on several established photometric stereo and structure from motion algorithms. We demonstrate experimentally the effectiveness of our algorithm using several videos of hand-held objects moving in front of a fixed light and camera.