Design For The Freeform Prism Of Monocular Stereo Vision Based On Epipolar Constraint

Stereo vision is an important branch of computer vision.It has been widely used in many fields,such as industry,aerospace,medical treatment and so on.With the development of stereo vision technology and the expanding direction of application,the usage requirements of economization,miniaturization,lightweight of the stereo vision system are also improving,the shortcomings of the multi-view stereo vision system become more prominent,the applications in many areas are subject to varying degrees of restrictions.In order to adapt to the development needs,According to the refractive dispersion of prism,the researchers have proposed the monocular stereo vision system based on prism.Although the introduction of prism' reduces the cost of system construction,the volume and light of the system is reduced,and the distortion of the system is also brought.In order to solve the problem of image distortion of monocular stereo vision system mentioned above,design for the freeform prism of monocular stereo vision based on epipolar constraint is proposed in this paper.According to the principle of epipolar geometry of binocular stereo vision system with the parallel optical axes,and the optical properties of rich degrees of freedom of freeform surface,by changing the surface of biprism,changing the light path after twice refraction through the prism,to design a freeform prism which can meet the requirements and eliminate the nonlinear distortion of the system,fundamentally solve the problem of image distortion of the system.The main work is as follows:Firstly,based on the principle of the light refraction of the plane biprism in the monocular stereo vision imaging system,the paper presents the design idea in the monocular stereo vision system using the freeform prism to replace the plane biprism.Secondly,the paper designs an appropriate freeform prism.First,choose an initial plane biprism,according to the principle of geometrical optics analyzing of the refraction process of the light through the prism and the principle of image distortion,combined with the epipolar geometric relationships of binocular stereo vision system with parallel optical axes,and the partial differential equations of the freeform prism are deduced.Thirdly,through the Matlab programming to solve the coordinates of discrete points on the surface,then the coordinates of discrete points obtained by equidistant sampling,and then the discrete sampling points were fitted into the smooth surfaces of the freeform prism by using the OriginLab data plotting software.Finally,analyzed the fitting error.The results of fitting experiments show that the fitting method of ploy2D is the most suitable method for fitting the left bottom surface of the freeform prism,and the fitting accuracy is the highest.For the left surface fitting,fitting effect of the two methods of Extreme2D and Parabola2D were almost the same,the fitting error of the two methods were similar,and both two methods can be used,But the fitting error of Extreme2D is slightly smaller,and the fitting accuracy of the method is higher.In this paper,we analyzed the feasibility of obtaining the distortion-free monocular stereo vision system by designing the freeform prism to eliminate the image distortion of monocular stereo vision system based on prism.