Computer and Robot Vision
Algebraic Functions For Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Metrischer Trifokaltensor für die Auswertung von Bildfolgen
Mustererkennung 1999, 21. DAGM-Symposium
A linear method for reconstruction from lines and points
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Unified Computation of Strict Maximum Likelihood for Geometric Fitting
Journal of Mathematical Imaging and Vision
Tracking camera parameters of an active stereo rig
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Optimal computation of 3-D similarity: Gauss-Newton vs. Gauss-Helmert
Computational Statistics & Data Analysis
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Optimally reconstructing the geometry of image triplets from point correspondences requires a proper weighting or selection of the used constraints between observed coordinates and unknown parameters. By analysing the ML-estimation process the paper solves a set of yet unsolved problems: (1) The minimal set of four linearily independent trilinearities (Shashua 1995, Hartley 1995) actually imposes only three constraints onto the geometry of the image triplet. The seeming contradiction between the number of used constraints, three vs. four, can be explained naturally using the normal equations. (2) Direct application of such an estimation suggests a pseudoinverse of a 4 × 4-matix having rank 3 which contains the covariance matrix of the homologeous image points to be the optimal weight matrix. (3) Insteadof using this singluar weight matrix one could select three linearily dependent constraints. This is discussed for the two classical cases of forward andlateral motion, and clarifies the algebraic analyis of dependencies between trilinear constraints by Faugeras 1995. Results of an image sequence with 800 images and an Euclidean parametrization of the trifocal tensor demonstrate the feasibility of the approach.