Epipolar geometry from profiles under circular motion

Abstract

ÐThis paper addresses the problem of motion estimation from profiles (also known as apparent contours) of an object rotating on a turntable in front of a single camera. Its main contribution is the development of a practical and accurate technique for solving this problem from profiles alone, which is precise enough to allow for the reconstruction of the shape of the object. No correspondences between points or lines are necessary, although the method proposed can be used equally when these features are available without any further adaptation. Symmetry properties of the surface of revolution swept out by the rotating object are exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views in a robust and elegant way. These, together with geometric constraints for images of rotating objects, are then used to obtain first the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar geometry of the image sequence. The estimation of the epipolar geometry by this sequential approach (image of rotation axisÐhomographyÐimage of the horizonÐepipoles) avoids many of the problems usually found in other algorithms for motion recovery from profiles. In particular, the search for the epipoles, by far the most critical step, is carried out as a simple one-dimensional optimization problem. The initialization of the parameters is trivial and completely automatic for all stages of the algorithm. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self-calibration techniques. Finally, the spinning object is reconstructed from its profiles using the motion estimated in the previous stage. Results from real data are presented, demonstrating the efficiency and usefulness of the proposed methods.

Structure and motion estimation from apparent contours under circular motion

“…In [34] we have developed a robust technique to tackle the same problem with trivial initializations, but it can only be applied when the image of the surface of revolution swept out by the rotating object can be obtained. The algorithm presented here overcomes this limitation, and can be used when as few as 3 images of the rotating object are available.…”

“…In this paper, the parameters of the harmonic homology and other motion parameters are estimated simultaneously by minimizing the reprojection errors of the epipolar tangents. The algorithm presented here does not require the image of such a surface of revolution and can thus cope with incomplete circular motion and more widely spaced images, an advantage over the algorithm presented in [34].…”

“…In [34], a practical algorithm has been introduced for the estimation of motion and structure from the apparent contours of a rotating object. The image of the rotation axis and the special vanishing point are first determined by estimating the harmonic homology associated with the image of the surface of revolution spanned by the rotating object.…”

Reconstruction of Surfaces of Revolution from Single Uncalibrated Views

“…By circular symmetry, the surface normals along a latitude circle will all meet at one point on the Ý-axis. Under perspective projection, the image of a surface of revolution will be invariant to a harmonic homology [22,13], given by…”

Circular motion geometry using minimal data

“…Jiang et al [11] recently developed new methods to compute single axis motion by fitting the conic locus of the tracked points in at least five images. Another interesting approach is proposed by Mendonça et al [16,17] who recovered the circular motion by using surface profiles.…”