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Invariants of Six Points and Projective Reconstruction from Three Uncalibrated Images

Long Quan 1, 2
1 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : There 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.
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https://hal.inria.fr/inria-00590047
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Long Quan. Invariants of Six Points and Projective Reconstruction from Three Uncalibrated Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 1995, 17 (1), pp.34--46. ⟨10.1109/34.368154⟩. ⟨inria-00590047⟩

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