David Liebowitz
Merton College
Doctor of Philosophy
Trinity Term 2001
Abstract
This thesis addresses the issues of combining camera calibration constraints from various sources
and reconstructing scene geometry from single and multiple views. A geometric approach is taken,
associating both structure recovery and calibration with geometric entities.
Three sources of calibration constraints are considered: scene constraints, such as the paral-
lelism and orthogonality of lines, constraints from partial knowledge of camera parameters, and
constraints derived from the motion between views.
First, methods of rectifying the projective distortion in an imaged plane are examined. Metric
rectification constraints are developed by constraining the imaged plane circular points.
The internal camera parameters are associated with the absolute conic. It is shown how imaged
plane circular points constrain the image of the absolute conic, and are constrained by a known
absolute conic in return. A method of using planes with known metric structure as a calibration
object is developed.
Next, calibration and reconstruction from single views is addressed. A well known configuration
of the vanishing points of three orthogonal directions and knowledge that the camera has square
pixels is expressed geometrically and subjected to degeneracy and error analysis. The square pixel
constraint is shown to be geometrically equivalent to treating the image plane as a metric scene
plane.
Use of the vanishing point configuration is extended to two views, where three vanishing points
and known epipolar geometry define a three dimensional affine reconstruction. Calibration and
metric reconstruction follows similarly to the single view case, with the addition of auto-calibration
constraints from the motion between views. The auto-calibration constraints are derived from the
geometric representation of the square pixel constraints, by transferring the image plane circular
points between views. Degenerate cases for constraints from square pixels and cameras having
identical internal parameters are described.
Finally, a constraint on the metric rectification of an affine reconstruction from the relative
lengths of a pair of 3D line segments is developed. The constraint is applied to human motion
capture from a pair of affine cameras.
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