Correction of miss-alignment between object and surface normal vectors coordinate systems in photometric methods with the help of least squares estimation

Photometry is a well-known method for 3D reconstruction of objects using images taken in different lighting conditions. In this method, by knowing the light sources' direction, the normal vectors of the surface are recovered in a dense grid through the intensities recorded in the captured images. Each normal vector is then converted to the height difference in two orthogonal directions, and the simultaneous estimation of the heights for the dense grid is done by solving a system of linear, overdetermined and inconsistent equations. The miss-alignment of the coordinate system represents normal vectors and the dense grid frame of 3D reconstruction causes a systematic error in the estimation of the gridded heights map. Photometric self-calibration methods for determining the light sources’ direction are one of the causes of miss-alignments in object and surface normal vectors coordinate systems. In this paper, a sequential and iterative process is proposed to estimate and perform an appropriate rotation to the surface normal vectors. In each iteration of this method, a portion of the necessary rotation is identified in order to parallelize of the two object coordinate systems and surface normal vectors through fitting a geometric transformation to the estimated residuals of the 3D reconstruction process. The results of using the proposed method in various experiments have demonstrated a noticeable improvement in the precision and accuracy of 3D reconstruction.