TY - JOUR
T1 - Revisiting Projective Structure from Motion
T2 - A Robust and Efficient Incremental Solution
AU - Magerand, Ludovic
AU - Del Bue, Alessio
N1 - This work was partially supported by the European Regional Development Fund under the project IMPACT (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000468).
PY - 2020/2
Y1 - 2020/2
N2 - This paper presents a solution to the Projective Structure from Motion (PSfM) problem able to deal efficiently with missing data, outliers and, for the first time, large scale 3D reconstruction scenarios. By embedding the projective depths into the projective parameters of the points and views, we decrease the number of unknowns to estimate and improve computational speed by optimizing standard linear Least Squares systems instead of homogeneous ones. In order to do so, we show that an extension of the linear constraints from the Generalized Projective Reconstruction Theorem can be transferred to the projective parameters, ensuring also a valid projective reconstruction in the process. We use an incremental approach that, starting from a solvable sub-problem, incrementally adds views and points until completion with a robust, outliers free, procedure. To prevent error accumulation, a refinement based on alternation between new estimations of views and points is used. This can also be done with constrained non-linear optimization. Experiments with simulated data shows that our approach is performing well, both in term of the quality of the reconstruction and the capacity to handle missing data and outliers with a reduced computational time. Finally, results on real datasets shows the ability of the method to be used in medium and large scale 3D reconstruction scenarios with high ratios of missing data (up to 98 percent).
AB - This paper presents a solution to the Projective Structure from Motion (PSfM) problem able to deal efficiently with missing data, outliers and, for the first time, large scale 3D reconstruction scenarios. By embedding the projective depths into the projective parameters of the points and views, we decrease the number of unknowns to estimate and improve computational speed by optimizing standard linear Least Squares systems instead of homogeneous ones. In order to do so, we show that an extension of the linear constraints from the Generalized Projective Reconstruction Theorem can be transferred to the projective parameters, ensuring also a valid projective reconstruction in the process. We use an incremental approach that, starting from a solvable sub-problem, incrementally adds views and points until completion with a robust, outliers free, procedure. To prevent error accumulation, a refinement based on alternation between new estimations of views and points is used. This can also be done with constrained non-linear optimization. Experiments with simulated data shows that our approach is performing well, both in term of the quality of the reconstruction and the capacity to handle missing data and outliers with a reduced computational time. Finally, results on real datasets shows the ability of the method to be used in medium and large scale 3D reconstruction scenarios with high ratios of missing data (up to 98 percent).
KW - Cameras
KW - Estimation
KW - Image reconstruction
KW - Optimization
KW - perspective cameras
KW - projective reconstruction
KW - Robustness
KW - Structure from motion
KW - Structure-from-Motion
KW - Three-dimensional displays
UR - http://www.scopus.com/inward/record.url?scp=85049064425&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2018.2849973
DO - 10.1109/TPAMI.2018.2849973
M3 - Article
C2 - 29994468
AN - SCOPUS:85049064425
VL - 42
SP - 430
EP - 443
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
SN - 0162-8828
IS - 2
M1 - 8395064
ER -