Recovering The Geometry Of Single Axis Motions By Conic Fitting

Single axis motions play a very important role in the analysis of the structure and motion problem since any Euclidean motion can be decomposed by a rotation about one screw axis, followed by a translation along the screw axis. Acquiring 3D models from single axis motion sequences, particularly turntable sequences, also has been widely used by computer vision and graphics researchers.Generally, the whole reconstruction procedure includes the determination of camerapositions at different viewpoints, detection of object boundaries and extraction of surface models from the volume representation. The estimation of the camera positions or simply the rotation angles relative to a still camera is the most important and difficult part of the modeling process. Traditionally, rotation angles are obtained by careful calibration. Recent researches extend the single axis approach to recover unknown rotation angles from uncalibrated image sequence based on a projective geometry approach. But these methods limited by the expense of computing fundamental matrices and trifocal tensors or of the nonlinear optimization involved in computing epipolar tangencies.Through the studies of the invariants of the single axis motions, computational theories have been developed in this thesis to provide practical solutions for the problem of structure and motion from fitting the corresponding points in the whole sequence to its conic locus or conies for short.It is then shown that all single axis geometry can be directly computed either from one conic and one fundamental matrix or from at least two conies. The rotation angles then can be calculated directly from using the Laguerre formula. The advantage of these new methods over the existing ones is straightforward. First, it is intrinsically a multiple view approach as all geometric information from the whole sequence is nicely summarized in the conies. This contrasts with the computation of fundamental matrices and trifocal tensors, which use only a subsequence of 2 and 3 views respectively. Secondly, in our methods, the essential geometry of the image single axis geometry may be specified by six parameters and this may be estimated from one conic and one fundamental matrix (a total of 12 parameters) or may be minimally estimated from two conies (a total of 10 parameters). Previous methods have involved estimating more than this minimum number of parameters. For example, 18 tensor parameters from each triplet of images are required. In this thesis, a Maximum Likelihood Estimation method over all 6+2n parameters is also given for a globe optimization result.The experiments on real image sequences demonstrate the simplicity, accuracy and robustness of the new methods.