Geometric calibration for photometric stereo under near-field point light sources using spheres

Abstract

Spheres are commonly employed for both camera calibration and light calibration. The apparent contours of spheres are utilized to determine the camera’s intrinsic parameters, while the highlights on the sphere aid in estimating the light direction. This paper introduces a novel calibration method using spheres to simultaneously calibrate both the camera and light sources. The reflected irradiance distribution of the Lambertian sphere is analyzed under illumination from a near-field point light source. Consequently, points with the same luminance form coaxial circles. Their imaging equations are formulated under a general projection model, offering orthogonal constraints on the image of the absolute conic for fully calibrating the camera. Next, the geometric determination of the sphere centers and point light source positions is implemented. Finally, a photometric constraint is constructed to minimize the discrepancy between the synthetic and real images of the sphere, aiming to optimize the entire parameters of the system. The experiments are executed on synthetic and real datasets, with results indicating the effectiveness and precision of the proposed method.