This paper addresses the problem of structure and motion from silhouettes for turntable sequences. Previous works have exploited corresponding points induced by epipolar tangencies to estimate the image invariants under turntable motion and recover the epipolar geometry. In these approaches, however, camera intrinsics are needed in order to obtain Euclidean motion and reconstruction. This paper proposes a novel approach to precisely estimate the image invariants and the rotation angles in the absence of the camera intrinsics, and to perform auto-calibration. By exploiting a special parameterization of the epipoles, it is shown that the imaged circular points can be formulated in terms of the image invariants. A fixed scalar κ, introduced to account for the different scales in the homogeneous representations of the image invariants used in the parameterizations, is found crucial in both calibration and motion estimation. Given the image invariants, namely the horizon, the imaged rotation axis and its orthogonal vanishing point, this scalar can be determined from the epipoles in an image triplet. A robust method for estimating κ is proposed and the rotation angles can be recovered using this estimated value of κ. All the estimated variables are then refined using bundle-adjustment and auto-calibration is performed using the imaged circular points, the imaged rotation axis and the associated vanishing point. This allows the recovery of the full camera positions and orientations, and hence Euclidean reconstruction. Experimental results demonstrate the simplicity of this novel approach and the high precision in the estimated motion and reconstruction.
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