A Pixel-wise Varifocal Camera Model for Ef!cient Forward Projection and Linear Extrinsic Calibration of Underwater Cameras with Flat Housings

This paper is aimed at presenting a new virtual camera model which can ef!ciently model refraction through "at housings in underwater photography. The key idea is to employ a pixel-wise virtual focal length concept to encode the refractive projection inside the "at housing. The radiallysymmetric structure of the varifocal length around the normal of the housing surface allows us to encode the refractive projection with a compact representation. We show that this model realizes an ef!cient forward projection computation and a linear extrinsic calibration in water. Evaluations using synthesized and real data demonstrate the performance quantitatively and qualitatively.