2,026 research outputs found
Invariants of Six Points and Projective Reconstruction from Three Uncalibrated Images
International audienceThere are three projective invariants of a set of six points in general position in space. It is well-known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship is used to derive the space invariants, when multiple images are available. This paper establishes that the minimum number of images for computing these invariants is three, and the computation of invariants of six points from three images can have as many as three solutions. Algorithms are presented for computing these invariants in closed form. The accuracy and stability with respect to image noise, selection of the triplets of images and distance between viewing positions are studied both through real and simulated images. Applications of these invariants are also presented. Both the results of Faugeras [1] and Hartley et al. [2] for projective reconstruction and Sturm's method [3] for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points
Autocalibration with the Minimum Number of Cameras with Known Pixel Shape
In 3D reconstruction, the recovery of the calibration parameters of the
cameras is paramount since it provides metric information about the observed
scene, e.g., measures of angles and ratios of distances. Autocalibration
enables the estimation of the camera parameters without using a calibration
device, but by enforcing simple constraints on the camera parameters. In the
absence of information about the internal camera parameters such as the focal
length and the principal point, the knowledge of the camera pixel shape is
usually the only available constraint. Given a projective reconstruction of a
rigid scene, we address the problem of the autocalibration of a minimal set of
cameras with known pixel shape and otherwise arbitrarily varying intrinsic and
extrinsic parameters. We propose an algorithm that only requires 5 cameras (the
theoretical minimum), thus halving the number of cameras required by previous
algorithms based on the same constraint. To this purpose, we introduce as our
basic geometric tool the six-line conic variety (SLCV), consisting in the set
of planes intersecting six given lines of 3D space in points of a conic. We
show that the set of solutions of the Euclidean upgrading problem for three
cameras with known pixel shape can be parameterized in a computationally
efficient way. This parameterization is then used to solve autocalibration from
five or more cameras, reducing the three-dimensional search space to a
two-dimensional one. We provide experiments with real images showing the good
performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi
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