The Two Lines Light Source (TLLS)

Abstract

Several 3D imaging methods based on active illumina- tion, such as silhouette-based 3D reconstruction and struc- tured light 3D scanning with binary patterns, require light sources capable of generating shadows with sharp bound- aries when they are used to illuminate opaque occluders. Supported by empirical evidence suggesting that a low cost Uncollimated Laser Diode (ULD) produces shadows with sharp boundaries not requiring focusing in a wide range of depths, this paper proposes the use of ULDs as light sources in the target applications. Since due to astigmatism the Point Light Source (PLS) is not an accurate mathemati- cal model of light propagation for the ULD, the Two Lines Light Source (TLLS) model is introduced to explain the ob- served behavior of the ULD. This novel geometric model of light propagation is defined by two 3D line segments, rather than a single 3D point, and guarantees that for each illu- minated 3D point there exists a unique ray, which simul- taneously passes through the point and intersects the two line segments. Furthermore, the equation of this ray can be computed in closed form at very low computational cost, and the TLLS model reduces to the PLS model when the two line segments intersect. Finally, the paper introduces a calibration method to estimate the model parameters, and describes the experiments performed to validate the model.