Central Catadioptric Camera Calibration Using The Pole-polar Relationship Between The Proiection Of Three Lines

The camera calibration is an indispensable and important step in three-dimensional reconstruction,image depth information extraction,virtual view synthesis,instant location and map construction.The central catadioptric camera has a larger imaging field of view in comparison with the ordinary camera,and its application value in the industrial field is becoming more and more prominent.Therefore,the calibration of the central catadioptric camera has important research significance and application value.By analyzing the imaging properties of three straight lines with different positions in the space under the central catadioptric camera,three algorithms are proposed to obtain the orthogonal vanishing points or the imaged circular points,and then the camera parameters are calibrated.Under the central catadioptric camera,three non-parallel lines in space are projected onto the surface of the unit viewing sphere through the center of the unit viewing sphere,forming three great circles with the center of the unit viewing sphere as the center of the circles.Two great circles intersect a pair of antipodal points on the unit viewing sphere,and three great circles intersect each other.There are two pairs of antipodal points on each great circle,and then two infinity points are obtained.The direction of the polar line of an infinity point with respect to the circle is orthogonal to the direction of its infinity point.According to the affine invariance under the projective transformation,two pairs of the orthogonal vanishing points and one vanishing line are obtained on the image plane.The intersections of the line image and the vanishing line are the imaged circular points.Six pairs of the orthogonal vanishing points and three pairs of the imaged circular points are determined from the three line images.According to the constraint relationship between the orthogonal vanishing points or the imaged circular points and the image of the absolute conic,the camera parameters are calibrated.Three straight lines in the space intersect at a point,forming three large circles on the unit viewing sphere that intersect at a pair of antipodal points.In the light of the affine invariance under the projective transformation,three pairs of the vanishing points can be gotten on the image plane.Based on algebraic projective geometry,the camera parameters are calibrated by the constraint relationship between the vanishing points and the image of the absolute conic.The effectiveness of the proposed algorithm is verified by a large number of simulation experiments and real experiments.In the real experiments,the reprojection error distortion is considered and the three-dimensional reconstruction experiments are carried out.The results show that the proposed algorithms are robust.