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.

In this paper, we describe how 3D metric measurements can be determined from a single uncalibrated image, when only minimal geometric information are available in the image. The minimal information just is orthogonal vanishing points. Given such limited information, we show that the length ratios on different orthogonal directions can be directly computed. The exciting discovery of the method seems to oppose common senses: Usually, in the calibration process, all edge-lengths of cuboid are known, in this paper, cuboid edge-lengths are unknown but its edge-lengths ratios can be recovered from image. 3D metric measurements can be directly computed from the image using our linear method.