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Self-Calibration of Catadioptric Camera with Two Planar Mirrors from Silhouettes
May 2013 (vol. 35 no. 5)
pp. 1206-1220
Xianghua Ying, Key Lab. of Machine Perception (Minist. of Educ.), Peking Univ., Beijing, China
Kun Peng, Dept. of Comput. Sci., Univ. of North Carolina, Chapel Hill, NC, USA
Yongbo Hou, Key Lab. of Machine Perception (Minist. of Educ.), Peking Univ., Beijing, China
Sheng Guan, Key Lab. of Machine Perception (Minist. of Educ.), Peking Univ., Beijing, China
Jing Kong, Key Lab. of Machine Perception (Minist. of Educ.), Peking Univ., Beijing, China
Hongbin Zha, Key Lab. of Machine Perception (Minist. of Educ.), Peking Univ., Beijing, China
If an object is interreflected between two planar mirrors, we may take an image containing both the object and its multiple reflections, i.e., simultaneously imaging multiple views of an object by a single pinhole camera. This paper emphasizes the problem of recovering both the intrinsic and extrinsic parameters of the camera using multiple silhouettes from one single image. View pairs among views in a single image can be divided into two kinds by the relationship between the two views in the pair: reflected by some mirror (real or virtual) and in a circular motion. Epipoles in the first kind of pairs can be easily determined from intersections of common tangent lines of silhouettes. Based on the projective properties of these epipoles, efficient methods are proposed to recover both the imaged circular points and the included angle between two mirrors. Epipoles in the second kind of pairs can be recovered simultaneously with the projection of intersection line between two mirrors by solving a simple 1D optimization problem using the consistency constraint of epipolar tangent lines. Fundamental matrices among views in a single image are all recovered. Using the estimated intrinsic and extrinsic parameters of the camera, a euclidean reconstruction can be obtained. Experiments validate the proposed approach.
Index Terms:
Cameras,Mirrors,Reflection,Vectors,Calibration,Transmission line matrix methods,Geometry,planar mirrors,Self-calibration,circular points,silhouettes,catadioptric camera
Citation:
Xianghua Ying, Kun Peng, Yongbo Hou, Sheng Guan, Jing Kong, Hongbin Zha, "Self-Calibration of Catadioptric Camera with Two Planar Mirrors from Silhouettes," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 5, pp. 1206-1220, May 2013, doi:10.1109/TPAMI.2012.195
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