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This paper addresses the problem of estimating the motion of a camera as it observes the outline (or apparent contour) of a solid bounded by a smooth surface in successive image frames. In this context, the surface points that project onto the outline of an object depend on the viewpoint and the only true correspondences between two outlines of the same object are the projections of frontier points where the viewing rays intersect in the tangent plane of the surface. In turn, the epipolar geometry is easily estimated once these correspondences have been identified. Given the apparent contours detected in an image sequence, a robust procedure based on RANSAC and a voting strategy is proposed to simultaneously estimate the camera configurations and a consistent set of frontier point projections by enforcing the redundancy of multiview epipolar geometry. The proposed approach is, in principle, applicable to orthographic, weak-perspective, and affine projection models. Experiments with nine real image sequences are presented for the orthographic projection case, including a quantitative comparison with the ground-truth data for the six data sets for which the latter information is available. Sample visual hulls have been computed from all image sequences for qualitative evaluation.