Self-calibration from turn-table sequences in presence
of zoom and focus
Xiaochun Cao
a,
*
, Jiangjian Xiao
b
, Hassan Foroosh
a
, Mubarak Shah
c
a
Computational Imaging Lab, University of Central Florida, Orlando, FL 32816, USA
b
Sarnoff Corporation, Princeton, NJ 08540, USA
c
Computer Vision Lab, University of Central Florida, Orlando, FL 32816, USA
Received 1 April 2005; accepted 9 January 2006
Available online 31 March 2006
Abstract
This paper proposes a novel method, using constant inter-frame motion, for self-calibration from an image sequence of an object
rotating around a single axis with varying camera internal parameters. Our approach makes use of the facts that in many commercial
systems rotation angles are often controlled by an electromechanical system, and that the inter-frame essential matrices are invariant if
the rotation angles are constant but not necessary known. Therefore, recovering camera internal parameters is possible by making use of
the equivalence of essential matrices which relate the unknown calibration matrices to the fundamental matrices computed from the
point correspondences. We also describe a linear method that works under restrictive conditions on camera internal parameters, the solu-
tion of which can be used as the starting point of the iterative non-linear method with looser constraints. The results are refined by
enforcing the global constraints that the projected trajectory of any 3D point should be a conic after compensating for the focusing
and zooming effects. Finally, using the bundle adjustment method tailored to the special case, i.e., static camera and constant object rota-
tion, the 3D structure of the object is recovered and the camera parameters are further refined simultaneously. To determine the accuracy
and the robustness of the proposed algorithm, we present the results on both synthetic and real sequences.
Ó 2006 Elsevier Inc. All rights reserved.
Keywords: Constant inter-frame motion; Self-calibration; Turn-table; Conic
1. Introduction
Acquiring 3D models from circular motion sequences,
particularly turn-table sequences, has been widely used by
computer vision and graphics researchers, e.g.,
[36,31,4,35], since these methods are simple and robust.
Generally, the whole reconstruction procedure includes:
first, the determination of camera positions at different
viewpoints or, equivalently, the different positions of the
rotating device; second, the detection of object boundaries
or silhouettes; third, the extraction of a visual hull as the
surface model from a volume representation [21]. Fitzgib-
bon et al. [9] extended the analysis of the circular motion
to recover unknown rotation angles from uncalibrated
image sequences based on a projective geometry approach
and multi-view geometric constraints. [28,29] recovered the
circular motion by using surface profiles. Wong et al. [42]
also presented a method for camera calibration using sur-
faces of revolution, which is related to circular motion since
an object placed on a turn-table spans a surface of revolu-
tion. Recently, Jiang et al. [19,18] developed new methods
to compute single axis motion by either fitting the conic to
the locus of the tracked points in at least five images or
computing a plane homography from a minimal of two
points in four images. Colombo et al. [6] improved the
approach [42] in which the calibration of a natural camera,
a pinhole camera with zero skew and unit aspect ratio [22],
requires the presence of two different surfaces of revolu-
tions in the same view. In addition, the method [6] relaxes
the conditions claimed by Bougnoux [19], that three ellipses
are needed to compute the imaged circular points.
1077-3142/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.cviu.2006.01.004
*
Corresponding author.
E-mail address: xccao@cs.ucf.edu (X. Cao).
www.elsevier.com/locate/cviu
Computer Vision and Image Understanding 102 (2006) 227–237