Single-image optical center estimation from vignetting and tangential gradient symmetry

In this paper, we propose a method for estimating the optical center of a camera given only a single image with vignetting. This is accomplished by identifying the center of the vignetting effect in the image through an analysis of semicircular tangential gradients (SCTGs). For a given image pixel, the SCTG is the image gradient along the tangential direction of the circle centered at the currently estimated optical center and passing through the pixel. We show that for natural images with vignetting, the distribution of SCTGs is generally symmetric if the optical center is estimated accurately, but is skewed otherwise. By minimizing the asymmetry of the SCTG distribution with nonlinear optimization, our method is able to obtain reliable estimates of the optical center. Experiments on simulated and real vignetting images demonstrate the effectiveness of this technique.