On Multilayer Flat Refrctive Imaging

In real applications,we usually use a pin-hole camera capturing objects through a single or multiple parallel flat refractive planes,for observation,location,measurement and 3D reconstruction,such as the underwater camera used under water.In this paper,such imaging is named as multi-layer refraction imaging.When observing objects by a pin-hole camera through multiple refractive planes,distortions along with the illusion of close and magnified scene,will be brought into the imaging system.Therefore,the traditional pin-hole camera model becomes invalid.As a consequence,to study the theory of imaging through multiple parallel medium is of high theoretical significance and practical value.In this paper,we propose a novel general multi-layer camera model.Based on the proposed camera model,a number of key issues in the multi-layer refraction imaging have been studied,such as camera calibration,epipolar geometry,triangulation,etc.In sum,our main contributions in this paper can be extracted as follows.(1)Proposing a novel and smart multi-layer refraction camera model,and proposing a fast computation method for forward projection with theoretical proof.This paper presents a novel general camera model,which is in fact a virtual pixel-wise varifocal model and can be used to encode multilayer refractions effectively.The model is built up based on two important findings.One is that the air between the camera centre and the nearest layer can be modeled as an air layer.The other one is that a ray passing through the air layer and these multiple layers causes only lateral displacement without changing its direction.The proposed camera model guarantees fast calculation of the backward projection.We also derive the forward projection equation and propose an efficient solving algorithm with proof.(2)Proposing a camera intrinsic parameters calibration method.Firstly,we proposed a plate refraction camera calibration method,the method can be utilized to restore the camera focal length,principal point and lens distortion with high accuracy.Then,we designed two camera calibration methods to calibrate the camera without removing the infrared filter.Finally,we proposed a calibration method for multi-layer fractions,it recovers not only the camera's intrinsic and distortion parameters but also the distance between the camera and the first refractive interface.(3)Analyzing the epipolar constraint and proposed a concept of dynamic epipolar constraint.Firstly,we obtained the generalized projection matrix of a space line,which is a 4-order curve not a line.Secondly,we got the generalized fundamental matrix.Finally,due to the higher dimensions of the generalized fundamental matrix,we proposed a concept of dynamic epipolar constraint,which can be used in verifying the corresponding image points satisfying the epipolar constraint.(4)Proposing a framework to solve the multi-layer triangulation problem.In geometric vision,the triangulation problem is one of the most important problems,it is the foundation of 3D reconstruction.In this paper,we proposed a framework to apply traditional triangulation methods to solve the multi-layer refraction triangulation problem,which contributed to prove the precision of 3D reconstruction.