Invariants of six points and projective reconstruction from three uncalibrated images
- 1 January 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 17 (1) , 34-46
- https://doi.org/10.1109/34.368154
Abstract
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 pointsKeywords
This publication has 19 references indexed in Scilit:
- Projective invariants of shapesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Some invariant linear methods in photogrammetry and model-matchingPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Extracting projective structure from single perspective views of 3D point setsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Accurate corner detection: an analytical studyPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Relative 3D Reconstruction Using Multiple Uncalibrated ImagesThe International Journal of Robotics Research, 1995
- Projective reconstruction and invariants from multiple imagesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1994
- Euclidean constraints for uncalibrated reconstructionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1993
- View variation of point-set and line-segment featuresPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1993
- Invariant descriptors for 3D object recognition and posePublished by Institute of Electrical and Electronics Engineers (IEEE) ,1991
- Motion from point matches: Multiplicity of solutionsInternational Journal of Computer Vision, 1990