Resolving ambiguities in auto–calibration

Abstract

Three-dimensional (3D) projective structure, that is structure modulo a projectivity of 3D space, can be recovered from its projection in multiple perspective images. The images might be acquired, for example, by a moving monocular camera or a stereo rig. This projective structure can be upgraded to Euclidean structure by identifying two entities, the plane at infinity and the absolute conic.Auto-calibration methods use constraints induced by the rigid motion of the camera to determine the Euclidean structure (or equivalently the camera calibration). Often these motion constraints are supplemented by known values of the camera's internal parameters or scene constraints in order to resolve ambiguities or stabilize the algorithms.It is shown in this paper that in certain common situations this supplementary information may not resolve the ambiguity. This is illustrated for the particular ambiguity arising for motions with a single direction of the rotation axis. Four types of constraint are analysed, and the conditions under which the ambiguity is not resolved are given. The constraint cases are: perpendicular image axes (the zeroskew constraint); specified image aspect ratio; specified image principal point; and perpendicularity of scene features.

Camera calibration and the search for infinity

“…Thus, calibration is reduced to finding the plane at infinity. As has been noted previously ( [4,12]), the real difficulty in calibration is finding the plane at infinity.…”

From synthesis to analysis: fitting human animation models to image data

“…In theory, given high precision matches, bundle-adjustment can recover both intrinsic parameters and camera motion [11]. The same holds true for recent auto-calibration techniques but, typical sequences of head images are close to exhibiting degenerate motions [12,13]. Again, extremely precise matches would be required.…”

Camera Self-calibration with Parallel Screw Axis Motion by Intersecting Imaged Horopters

“…However, if the rotation direction r has zero x or y components, then the zero skew constraint (16) is satisfied by every conic in the family (4) [20,2]. In this case, if the rotations are not about axes parallel to the z axis, assuming zero skew, s = 0, and unit aspect ratio, α u = α v , determines uniquely ω * ∞ .…”

“…Similarly to planar motion, the scene can be recovered up to a 1-D affinity in the screw direction. To resolve this ambiguity, some assumptions on the camera pixel geometry can be made that lead us to a complete camera calibration (zero-skew constraint, known image aspect ratio or known principal point); the screw direction conditions the necessary additional assumptions [20,2].…”