In this paper, we have shown that from apparent contours of curved surfaces observed from the same but uncalibrated cameras with unknown translations, we can, up to a 3D affine ambiguity, reconstruct the curved surfaces.
We first showed that if the camera motion is a pure translation, the epipolar lines and the frontier points coincide with bi-tangent lines and bi-tangent points in sequential images. The epipolar geometry is thus recovered without any optimisation process unlike previous work [ 1 , 3 ].
We next showed that given the epipolar geometry, the curved surfaces can be reconstructed up to a 3D affine ambiguity from their apparent contours viewed from uncalibrated cameras. The result is used for distinguishing apparent contours from fixed features from uncalibrated views. It has also been shown that the time-to-contact to a curved surface can be computed just from apparent contours. We showed that for computing the time-to-contact to non-frontier points, the second derivatives in spatio-temporal images are required, and for frontier points, the time-to-contact is computed just from the first derivatives in spatio-temporal images. These are implemented and tested on artificial and real images of curved surfaces. Most of the errors with real images involve camera perturbations resulting in rotations and the small baseline geometry between views. The quantitative analysis of noise sensitivity remains to be carried out.
J. Sato