Dynamic calibration of an active stereo head

This paper presents a method for using objects in a scene to define the reference frame for 3-D reconstruction. We first present a simple technique to calibrate an orthographic projection from four non-coplanar reference points. We then show how the observation of two additional known scene points can provide the complete perspective projection. When used with a known object, this technique permits a calibration of the full projective transformation matrix. For an arbitrary non-coplanar set of four points, this calibration provides an affine basis for the reconstruction of local scene structure. When the four points define three orthogonal vectors, the basis is orthogonal, with a metric defined by the lengths of the three vectors. We demonstrate this technique for the case of a cube. We present results in which five and a half points on the cube are sufficient to compute the projective transformation for an orthogonal basis by direct observation (without matrix inversion). We then present experiments with a technique for reducing the imprecision due to pixel quantization and noise.