A theory of self-calibration of a moving camera
International Journal of Computer Vision
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Invariants of Six Points and Projective Reconstruction From Three Uncalibrated Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dual Computation of Projective Shape and Camera Positions from Multiple Images
International Journal of Computer Vision
Affine Structure and Motion from Points, Lines and Conics
International Journal of Computer Vision
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Euclidean Reconstruction and Reprojection Up to Subgroups
International Journal of Computer Vision - Special issue on Genomic Signal Processing
What can be seen in three dimensions with an uncalibrated stereo rig
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Autocalibration and the absolute quadric
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Trilinearity of three perspective views and its associated tensor
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Hybrid Neural Network System for Pattern Classification Tasks with Missing Features
IEEE Transactions on Pattern Analysis and Machine Intelligence
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
POP algorithm: Kernel-based imputation to treat missing values in knowledge discovery from databases
Expert Systems with Applications: An International Journal
Kernel-Based Multi-Imputation for Missing Data
Proceedings of the 2006 conference on Advances in Intelligent IT: Active Media Technology 2006
Optimized parameters for missing data imputation
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
Missing value imputation based on data clustering
Transactions on computational science I
Missing data imputation by utilizing information within incomplete instances
Journal of Systems and Software
Robotics and Autonomous Systems
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The minimal data necessary for projective reconstruction from image points is well-known when each object point is visible in all images. In this paper, we formulate and propose solutions to a new family of reconstruction problems for multiple images from minimal data, where there are missing points in some of the images. The ability to handle the minimal cases with missing data is of great theoretical and practical importance. It is unavoidable to use them to bootstrap robust estimation such as RANSAC and LMS algorithms and optimal estimation such as bundle adjustment. First, we develop a framework to parameterize the multiple view geometry needed to handle the missing data cases. Then, we present a solution to the minimal case of eight points in three images, where one different point is missing in each of the three images. We prove that there are, in general, as many as 11 solutions for this minimal case. Furthermore, all minimal cases with missing data for three and four images are catalogued. Finally, we demonstrate the method on both simulated and real images and show that the algorithms presented in this paper can be used for practical problems.