TY - GEN
T1 - Minimal solutions for pose estimation of a multi-camera system
AU - Hee Lee, Gim
AU - Li, Bo
AU - Pollefeys, Marc
AU - Fraundorfer, Friedrich
PY - 2016
Y1 - 2016
N2 - In this paper, we propose a novel formulation to solve the pose estimation problem of a calibrated multi-camera system. The non-central rays that pass through the 3D world points and multi-camera system are elegantly represented as Plücker lines. This allows us to solve for the depth of the points along the Plücker lines with a minimal set of 3-point correspondences. We show that the minimal solution for the depth of the points along the Plücker lines is an 8 degree polynomial that gives up to 8 real solutions. The coordinates of the 3D world points in the multi-camera frame are computed from the known depths. Consequently, the pose of the multi-camera system, i.e. the rigid transformation between the world and multi-camera frames can be obtained from absolute orientation. We also derive a closed-form minimal solution for the absolute orientation. This removes the need for the computationally expensive Singular Value Decompositions (SVD) during the evaluations of the possible solutions for the depths. We identify the correct solution and do robust estimation with RANSAC. Finally, the solution is further refined by including all the inlier correspondences in a non-linear refinement step. We verify our approach by showing comparisons with other existing approaches and results from large-scale real-world datasets.
AB - In this paper, we propose a novel formulation to solve the pose estimation problem of a calibrated multi-camera system. The non-central rays that pass through the 3D world points and multi-camera system are elegantly represented as Plücker lines. This allows us to solve for the depth of the points along the Plücker lines with a minimal set of 3-point correspondences. We show that the minimal solution for the depth of the points along the Plücker lines is an 8 degree polynomial that gives up to 8 real solutions. The coordinates of the 3D world points in the multi-camera frame are computed from the known depths. Consequently, the pose of the multi-camera system, i.e. the rigid transformation between the world and multi-camera frames can be obtained from absolute orientation. We also derive a closed-form minimal solution for the absolute orientation. This removes the need for the computationally expensive Singular Value Decompositions (SVD) during the evaluations of the possible solutions for the depths. We identify the correct solution and do robust estimation with RANSAC. Finally, the solution is further refined by including all the inlier correspondences in a non-linear refinement step. We verify our approach by showing comparisons with other existing approaches and results from large-scale real-world datasets.
UR - http://www.scopus.com/inward/record.url?scp=84964916759&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-28872-7_30
DO - 10.1007/978-3-319-28872-7_30
M3 - Conference paper
AN - SCOPUS:84964916759
SN - 9783319288703
VL - 114
T3 - Springer Tracts in Advanced Robotics
SP - 521
EP - 538
BT - Springer Tracts in Advanced Robotics
PB - Springer Verlag
T2 - 16th International Symposium of Robotics Research, ISRR 2013
Y2 - 16 December 2013 through 19 December 2013
ER -