The authors present a method for using objects in a scene to define the reference frame for 3-D reconstruction. They first present a simple technique to calibrate an orthographic projection from four non-coplanar reference points. It is then shown that 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. This technique is demonstrated for the case of a cube. Results are presented 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. Experiments are outlined for reducing the imprecision due to pixel quantization and noise.
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