Paracatadioptric Camera Calibration Making Use Of The Sphere Image And The Pole-polar Relationship

Central catadioptric camera has a single effective viewpoint and a large imaging field of view,so it is especially important in the field of computer vision.By analyzing the imaging features of a space sphere in the paracatadioptric camera,according to the relationship between the pole-polar,the three orthogonal vanishing points and the image of the absolute conic(IAC),three novel linear algorithms are proposed to calibrate the paracatadioptric camera.Under the paracatadioptric camera,a sphere in space is projected to a pair of antipodal circles on the unit viewing sphere which has two conjugate complex intersection points,then an infinity point on the plane containing circles and the axis of symmetry through the circle centers can be obtained.The image of axis of symmetry and vanishing points become the pole and polar with regard to the IAC in the image plane.Based on the known infinity point,another point at infinity on the plane containing circles can be obtained by making using of a pairs of antipodal points on the circles.Furthermore,line at infinity on the plane containing circles can be determined.According to definition of a conic's diameter and harmonic conjugate relation under projective transformation,the circle centers and the infinity point on symmetry axis can be obtained.The vanishing point and the vanishing line satisfy the pole-polar relationship with regard to the IAC in the image plane.The direction of the polar line of the infinity point with respect to a circle is orthogonal to the direction of the infinity point,and what's more,the axis of symmetry is perpendicular to the line at infinity.Therefore,a set of three orthogonal vanishing points can be obtained in the image plane.The feasibility and effectiveness of the proposed algorithms were demonstrated through a number of experiments by MATLAB R2016b.