Geometric properties of multiple reflections in catadioptric camera with two planar mirrors

• Published in: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition pp. 1126 - 1132
• Main Authors: Xianghua Ying, Kun Peng, Ren Ren, Hongbin Zha
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2010
• Subjects: Calibration; Cameras; Closed-form solution; Geometry; Image reconstruction; Laboratories; Lenses; Mirrors; Reflection; Shape
• ISBN: 1424469848; 9781424469840
• ISSN: 1063-6919; 1063-6919
• DOI: 10.1109/CVPR.2010.5540088

A catadioptric system consisting of a pinhole camera and two planar mirrors is deeply investigated in this paper. The two mirrors combine to form a corner and face-to-face with the pinhole. Their relative pose is unknown. An object will be reflected in the mirror corner one-time or multiple-times. Using the pinhole, we may take an image containing the object and its reflections, i.e., simultaneously imaging multiple views of an object by a single camera. We discovered that each 3D point and its reflections lie on a circle. We call the point set composed of a 3D point and its reflections, a Reflection Point Group (RPG), and the circle related to a RPG is called a RPG circle. All RPG circles are parallel to one another. Furthermore, each RPG can be partitioned into two separate subgroups. Shape formed by all points in a subgroup is invariant with respect to location of the 3D point. From these geometric properties, two calibration approaches can be utilized: One is based on parallel circles; the other is using 2D homographies among invariant shapes. Experiments validate our approaches.