From Ordinal to Euclidean Reconstruction with Partial Scene Calibration

Since uncalibrated images permit only projective reconstruction, metric information requires either camera or scene calibration. We propose a stratified approach to projective reconstruction, in which gradual increase in domain information for scene calibration leads to gradual increase in 3D information. Our scheme includes the following steps: (1) Register the images with respect to a reference plane; this can be done using limited scene information, e.g., the knowledge that two pairs of lines on the plane are parallel. We show that this calibration is sufficient for ordinal reconstruction sorting the points by their height over the reference plane. (2) If available, use the relative height of two additional out-of-plane points to compute the height of the remaining points up to constant scaling. Our scheme is based on the dual epipolar geometry in the reference frame, which we develop below. We show good results with five sequences of real images, using mostly scene calibration that can be inferred directly from the images themselves.