A theory of multi-layer flat refractive geometry

Flat refractive geometry corresponds to a perspective camera looking through single/multiple parallel flat refractive mediums. We show that the underlying geometry of rays corresponds to an axial camera. This realization, while missing from previous works, leads us to develop a general theory of calibrating such systems using 2D-3D correspondences. The pose of 3D points is assumed to be unknown and is also recovered. Calibration can be done even using a single image of a plane. We show that the unknown orientation of the refracting layers corresponds to the underlying axis, and can be obtained independently of the number of layers, their distances from the camera and their refractive indices. Interestingly, the axis estimation can be mapped to the classical essential matrix computation and 5-point algorithm [15] can be used. After computing the axis, the thicknesses of layers can be obtained linearly when refractive indices are known, and we derive analytical solutions when they are ...

• Type: Journal
• Year: 2012
• Where: CVPR
• Authors: Amit Agrawal, Srikumar Ramalingam, Yuichi Taguchi, Visesh Chari
• Keywords: Computer Vision, Cvpr 2012, Matrix Computation, Perspective Camera, Point Algorithm