19.9.9 Matrix Factorization Approach to Motion and Structure

Tomasi, C.[Carlo],
Shape and Motion from Image Streams: A Factorization Method,
CMU-CS-TR-91-172, September 1991. BibRef 9109 Ph.D.Thesis (CS). SVD. Motion, Factorization. The thesis that combines all the other reports. Break motion into Rotation and Structure (From the SVD decomposition). Then solve for the two matricies and produce the structure. BibRef

Tomasi, C.[Carlo], Kanade, T.[Takeo],
Shape and Motion from Image Streams: A Factorization Method 2. Full Report on the Orthographic Case [Parts 2,8,10],
CMU-CS-TR-TR-104, January 1992. Text:
PS File. Figures:
PS File. BibRef 9201

Tomasi, C.[Carlo], Kanade, T.[Takeo],
Shape and Motion from Image Streams: A Factorization Method 2. Point Features in 3D Motion,
CMU-CS-TR-91-105, January 1991.
PS File. BibRef 9101

Tomasi, C., and Kanade, T.,
Shape and Motion from Image Streams under Orthography: A Factorization Method,
IJCV(9), No. 2, November 1992, pp. 137-154.
Springer DOI BibRef 9211
Earlier:
The Factorization Method for the Recovery of Shape and Motion from Image Streams,
DARPA92(459-472). BibRef
And:
Factoring Images Sequences into Shape and Motion,
Motion91(21-28). Combination of the series of reports. Motion is decomposed into a rotation and structure matrix. Works for some kinds of motion. The other papers (below) are all related to this work. BibRef

Tomasi, C.,
Pictures and Trails: a New Framework for the Computation of Shape and Motion from Perspective Image Sequences,
CVPR94(913-918).
IEEE DOI BibRef 9400

Tomasi, C., and Kanade, T.,
Shape and Motion from Image Streams: A Factorization Method 1. Planar Motion,
CMU-CS-TR-90-166, CMU CS Dept., September 1990. Decompose the image stream into shape and camera motion using single scanline images. BibRef 9009

Tomasi, C., and Kanade, T.,
Shape and Motion from Image Streams: A Factorization Method Part 3 - Detection and Tracking of Point Features,
CMU-CS-TR-91-132, CMU CS Dept., April 1991. Given the small inter-frame distance (required), the Lucas and Kanade tracking approach is best (
See also Iterative Image Registration Technique with an Application to Stereo Vision, An. ).
PS File. Further developed by:
See also Good Features to Track. BibRef 9104

Birchfield, S.T.[Stan T.],
KLT: An Implementation of the Kanade-Lucas-Tomasi Feature Tracker,
Online1997. Code, Tracking.
WWW Link.
See also GPU_KLT: A GPU-based Implementation of the Kanade-Lucas-Tomasi Feature Tracker. BibRef 9700

Weinshall, D., and Tomasi, C.,
Linear and Incremental Acquisition of Invariant Shape Models from Image Sequences,
PAMI(17), No. 5, May 1995, pp. 512-517.
IEEE DOI BibRef 9505
Earlier: ICCV93(675-682).
IEEE DOI Generate 3D models from the motion sequence.
See also Model-Based Invariants for 3-D Vision. BibRef

Tomasi, C., and Kanade, T.,
Shape and Motion without Depth,
ICCV90(91-95).
IEEE DOI BibRef 9000
And: DARPA90(258-270). BibRef
And: CMU-CS-TR-90-128, May 1990. The shape (cylinder) is determined without depth or accurate motion by tracking many points through several frames. BibRef

Quan, L.[Long], Kanade, T.,
Affine Structure from Line Correspondences with Uncalibrated Affine Cameras,
PAMI(19), No. 8, August 1997, pp. 834-845.
IEEE DOI 9709
Motion, Three frames. Linear algorithm, 7 lines in 3 views. Introduces a one-dimensional projective camera. BibRef

Quan, L., Kanade, T.,
A Factorization Method for Shape and Motion from Line Correspondences,
CVPR96(803-808).
IEEE DOI Extension to Line features. BibRef 9600

Costeira, J.P.[Joao P.], Kanade, T.[Takeo],
A Multibody Factorization Method for Independently Moving-Objects,
IJCV(29), No. 3, September 1998, pp. 159-179.
DOI Link 9811
BibRef
Earlier:
A Multi-Body Factorization Method for Motion Analysis,
ICCV95(1071-1076).
IEEE DOI BibRef
And: ARPA96(1013-1026). BibRef
And: CMU-CS-TR-94-220. September 1994. Factorization approach to handle separate objects. Look for paper in:
HTML Version.
See also Estimating 3D shape from degenerate sequences with missing data. BibRef

Morita, T.[Toshihiko], and Kanade, T.[Takeo],
A Sequential Factorization Method for Recovering Shape and Motion from Image Streams,
PAMI(19), No. 8, August 1997, pp. 858-867.
IEEE DOI 9709
BibRef
Earlier: A2, A1: ARPA94(II:1177-1187). BibRef
And: A2, A1: CMU-CS-TR-94-158, May 1994. SVD. Singular value Decomposition based method, in a sequential manner for real time applications. SVD replaced with an updating computation of three eigenvectors. Nearly as accurate (and more applicable to real-time processing) as the original formulations.
PS File. BibRef

Poelman, C.J.[Conrad J.], Kanade, T.,
A Paraperspective Factorization Method for Shape and Motion Recovery,
PAMI(19), No. 3, March 1997, pp. 206-218.
IEEE DOI 9704
BibRef
Earlier:
A Paraperspective Factorization for Shape and Motion Recovery,
ECCV94(B:97-108).
Springer DOI BibRef
And: DARPA93(683-690). BibRef
Earlier: CMU-CS-TR-93-219, December 1993.
PS File. BibRef
Earlier: CMU-CS-TR-92-208, October 1992.
PS File. Entends the orthographic restriction. BibRef

Poelman, C.J.[Conrad J.],
The Paraperspective and Projective Factorization Methods for Recovering Shape and Motion,
CMU-CS-TR-95-173, July 1995. BibRef 9507 Ph.D.Thesis, CS. BibRef

Goldgof, D.B., Lee, H., Huang, T.S.,
Matching and Motion Estimation of Three-Dimensional Point and Line Sets Using Eigenstructure without Correspondences,
PR(25), No. 3, March 1992, pp. 271-286.
Elsevier DOI BibRef 9203

Lin, Z.C., Lee, H., and Huang, T.S.,
Finding 3D Point Correspondences in Motion Estimation,
ICPR86(303-305). BibRef 8600

Blostein, S.D., and Huang, T.S.,
Algorithms for Motion Estimation Based on Three-Dimensional Correspondences,
MU88(329-352). Motion given depths in a straightforward technique (really just generating the transformation that maps the points). BibRef 8800

Lin, Z.C., Huang, T.S., Blostein, S.D., Lee, H., and Margerum, E.A.,
Motion Estimation from 3-D Point Sets with and without Correspondences,
CVPR86(194-201). Another version of some of the earlier papers, actually a combination of 2 different papers. BibRef 8600

Sim, P.G., and Park, R.H.,
Anisotropic Hierarchical Motion Estimation Method Based on Decomposition of the Functional Domain,
JVCIR(7), 1996, pp. 259-272. BibRef 9600

Christy, S.[Stephane], Horaud, R.[Radu],
Euclidean Shape and Motion from Multiple Perspective Views by Affine Iterations,
PAMI(18), No. 11, November 1996, pp. 1098-1104.
IEEE DOI 9612
BibRef
And: TRRR-2421, INRIA, December 1994.
PS File. BibRef
Earlier:
Euclidean Reconstruction: From Paraperspective to Perspective,
ECCV96(II:129-140).
Springer DOI Motion, Multiple Frames. Incrementally coverge to the solution. Shape and motion from a sequence of images. Calibrated camera. BibRef

Zaharescu, A.[Andrei], Horaud, R.[Radu],
Robust Factorization Methods Using a Gaussian/Uniform Mixture Model,
IJCV(81), No. 3, March 2009, pp. xx-yy.
Springer DOI 0902
Factorization for both affine and perspective cameras. BibRef

Zaharescu, A.[Andrei], Horaud, R.[Radu], Ronfard, R.[Remi], Lefort, L.[Loic],
Multiple Camera Calibration Using Robust Perspective Factorization,
3DPVT06(504-511).
IEEE DOI 0606
BibRef

Soatto, S.[Stefano], Perona, P.[Pietro],
Recursive 3-D Visual-Motion Estimation Using Subspace Constraints,
IJCV(22), No. 3, March/April 1997, pp. 235-259.
DOI Link 9706
BibRef
Earlier:
Visual motion estimation from point features: unified view,
ICIP95(III: 21-24).
IEEE DOI 9510
BibRef
Earlier:
Recursive estimation of camera motion from uncalibrated image sequences,
ICIP94(III: 58-62).
IEEE DOI 9411
BibRef
And:
Dynamic visual motion estimation from subspace constraints,
ICIP94(I: 333-337).
IEEE DOI 9411
BibRef

Oskarsson, M.[Magnus], Zisserman, A.[Andrew], Astrom, K.[Kalle],
Minimal Projective Reconstruction for Combinations of Points and Lines in Three Views,
IVC(22), No. 10, 1 September 2004, pp. 777-785.
Elsevier DOI 0409
BibRef
Earlier: BMVC02(Reconstruction). 0208
BibRef

Åström, K., Heyden, A., Kahl, F., Oskarsson, M.,
Structure and Motion from Lines under Affine Projections,
ICCV99(285-292).
IEEE DOI BibRef 9900

Heyden, A., Berthilsson, R., Sparr, G.,
Recursive Structure and Motion from Image Sequences Using Shape and Depth Spaces,
CVPR97(444-449).
IEEE DOI 9704
Subspace methods. BibRef

Huynh, D.Q., Heyden, A.,
Recursive structure and motion estimation from noisy uncalibrated video sequences,
ICPR08(1-5).
IEEE DOI 0812
BibRef

Huynh, D.Q., Hartley, R.I., Heyden, A.,
Outlier correction in image sequences for the affine camera,
ICCV03(585-590).
IEEE DOI 0311
For factorization approach, outliers break the SVD computations. Iteratively correct the outliers. BibRef

Åström, K.[Kalle], Oskarsson, M.[Magnus],
Solutions and Ambiguities of the Structure and Motion Problem for 1D Retinal Vision,
JMIV(12), No. 2, April 2000, pp. 121-135.
DOI Link 0002
BibRef
Earlier: SCIA99(Computer Vision). BibRef

Åström, K.[Kalle], Kahl, F.[Fredrik],
Ambiguous Configurations for the 1D Structure and Motion Problem,
JMIV(18), No. 2, March 2003, pp. 191-203.
DOI Link 0301
BibRef
Earlier: A1, A2: ICCV01(I: 184-189).
IEEE DOI 0106
BibRef

Kahl, F.[Fredrik],
Critical Motions and Ambiguous Euclidean Reconstructions in Auto-Calibration,
ICCV99(469-475).
IEEE DOI Calibration, Self. BibRef 9900

Kahl, F.[Fredrik], Triggs, B.[Bill],
Critical Motions in Euclidean Structure from Motion,
CVPR99(II: 366-372).
IEEE DOI Motions that lead to ambiguous 3-D reconstructions. BibRef 9900

Kahl, F.[Fredrik], Heyden, A.[Anders],
Euclidean Reconstruction and Auto-Calibration from Continuous Motion,
ICCV01(II: 572-577).
IEEE DOI 0106
BibRef

Heyden, A.[Anders], Kahl, F.[Fredrik],
Direct Affine Reconstruction,
ICPR00(Vol I: 885-888).
IEEE DOI 0009
BibRef
Earlier:
Reconstruction from Affine Cameras Using Closure Constraints,
ICPR98(Vol I: 47-50).
IEEE DOI 9808
BibRef

Heyden, A.[Anders], Kahl, F.[Fredrik],
Robust Self-Calibration and Euclidean Reconstruction via Affine Approximation,
ICPR98(Vol I: 56-58).
IEEE DOI 9808
BibRef

Kahl, F., Hartley, R.I.,
Critical Curves and Surfaces for Euclidean Reconstruction,
ECCV02(II: 447 ff.).
Springer DOI 0205

See also Critical Configurations for Projective Reconstruction from Multiple Views. BibRef

Kahl, F.[Fredrik], Hartley, R.I.[Richard I.], and Aström, K.[Kalle],
Critical Configurations for N-view Projective Reconstruction,
CVPR01(II:158-163).
IEEE DOI 0110
configuration of n >=3 cameras and m points all lying on the intersection of two distinct ruled quadrics is critical. BibRef

Kahl, F.[Fredrik], Heyden, A.[Anders],
Affine Structure and Motion from Points, Lines and Conics,
IJCV(33), No. 3, September 1999, pp. 163-180.
DOI Link BibRef 9909
Earlier:
Structure and motion from points, lines and conics with affine cameras,
ECCV98(I: 327).
Springer DOI BibRef

Hammarstedt, P.[Pär], Kahl, F.[Fredrik], Heyden, A.[Anders],
Affine Reconstruction from Translational Motion under Various Autocalibration Constraints,
JMIV(24), No. 2, March 2006, pp. 245-257.
Springer DOI 0605
BibRef
Earlier:
Affine structure from translational motion with varying and unknown focal length,
ICPR04(I: 120-123).
IEEE DOI 0409
BibRef
Earlier:
Affine Structure from Translational Motion in Image Sequences,
SCIA03(387-394).
Springer DOI 0310
BibRef

Hammarstedt, P., Heyden, A.,
Euclidean reconstruction from translational motion using multiple cameras,
3DIM05(352-359).
IEEE DOI 0508
BibRef

Nyberg, F.[Fredrik], Dahl, O.[Ola], Holst, J.[Jan], Heyden, A.[Anders],
Using a Connected Filter for Structure Estimation in Perspective Systems,
WDV06(270-284).
Springer DOI 0705
BibRef

Heyden, A.[Anders], Dahl, O.[Ola],
Provably convergent on-line structure and motion estimation for perspective systems,
WDV09(751-758).
IEEE DOI 0910
BibRef
And: A2, A1:
Dynamic structure from motion based on nonlinear adaptive observers,
ICPR08(1-4).
IEEE DOI 0812
Reformulate 3D feature point estimation as a constant, with time-varying 3D position. BibRef

Heyden, A.[Anders], Nyberg, F.[Fredrik], Dahl, O.[Ola],
Recursive Structure and Motion Estimation Based on Hybrid Matching Constraints,
SCIA07(142-151).
Springer DOI 0706
BibRef

Nyberg, F.[Fredrik], Heyden, A.[Anders],
Recursive Structure from Motion Using Hybrid Matching Constraints with Error Feedback,
WDV06(285-298).
Springer DOI 0705
For real time tracking. BibRef

Debrunner, C.H.[Christian H.], Ahuja, N.[Narendra],
Segmentation and Factorization-Based Motion and Structure Estimation for Long Image Sequences,
PAMI(20), No. 2, February 1998, pp. 206-211.
IEEE DOI 9803
BibRef
Earlier:
Motion and Structure Factorization and Segmentation of Long Multiple Motion Image Sequences,
ECCV92(217-221).
Springer DOI BibRef
And: DARPA92(543-547). Analysis of rigid motions of robot arm. BibRef

Debrunner, C.H., and Ahuja, N.,
A Direct Data Approximation Based Motion Estimation Algorithm,
ICPR90(I: 384-389).
IEEE DOI Several frames orthographic views. BibRef 9000

Heyden, A., Berthilsson, R., Sparr, G.,
An iterative factorization method for projective structure and motion from image sequences,
IVC(17), No. 13, 1 November 1999, pp. 981-991.
Elsevier DOI 9911
BibRef

Heyden, A.[Anders],
Projective Structure and Motion from Image Sequences Using Subspace Methods,
SCIA97(xx-yy)
HTML Version. 9705
BibRef

Ben-Arie, J., Wang, Z.,
Estimation of 3-D Motion Using Eigen-Normalization and Expansion Matching,
IP(9), No. 9, September 2000, pp. 1636-1640.
IEEE DOI 0008

See also Generalized Feature Extraction Using Expansion Matching. BibRef

Sun, Z.H.[Zhao-Hui], Tekalp, A.M.[A. Murat], Navab, N.[Nassir], Ramesh, V.[Visvanathan],
Interactive Optimization of 3D Shape and 2D Correspondence Using Multiple Geometric Constraints via POCS,
PAMI(24), No. 4, April 2002, pp. 562-569.
IEEE DOI 0204
POCS (projections onto convex sets). Structure from motion. BibRef

Aguiar, P.M.Q.[Pedro M.Q.], Moura, J.M.F.[Jose M.F.],
Rank 1 weighted factorization for 3D structure recovery: Algorithms and performance analysis,
PAMI(25), No. 9, September 2003, pp. 1134-1149.
IEEE Abstract. 0309
BibRef
Earlier:
Factorization as a Rank 1 Problem,
CVPR99(I: 178-184).
IEEE DOI Recover the structure from a Rank 1 matrix rather than Rank 3. Matrix has 2D motions. BibRef

Quan, L.[Long], Wei, Y.C.[Yi-Chen], Lu, L.[Le], Shum, H.Y.[Heung-Yeung],
Constrained planar motion analysis by decomposition,
IVC(22), No. 5, 1 May 2004, pp. 379-389.
Elsevier DOI 0403
Image plane permendicular to motion plane. Decompose into two 1D images. BibRef

Ma, Y.[Yi], Huang, K.[Kun], Vidal, R.[René], Kosecká, J.[Jana], Sastry, S.[Shankar],
Rank Conditions on the Multiple-View Matrix,
IJCV(59), No. 2, September 2004, pp. 115-137.
DOI Link 0404
BibRef

Miyagawa, I., Arakawa, K.,
Motion and Shape Recovery Based on Iterative Stabilization for Modest Deviation from Planar Motion,
PAMI(28), No. 7, July 2006, pp. 1176-1181.
IEEE DOI 0606
Iteratively applies a factorization method based on planar motion. BibRef

Li, J.[Jian], Chellappa, R.[Rama],
Structure From Planar Motion,
IP(15), No. 11, November 2006, pp. 3466-3477.
IEEE DOI 0610
BibRef
Earlier:
A Factorization Method for Structure from Planar Motion,
Motion05(II: 154-159).
IEEE DOI 0502
BibRef

Brandt, S.S.[Sami S.], Kolehmainen, V.,
Structure-From-Motion Without Correspondence From Tomographic Projections by Bayesian Inversion Theory,
MedImg(26), No. 2, February 2007, pp. 238-248.
IEEE DOI 0702
BibRef
Earlier:
Motion without correspondence from tomographic projections by Bayesian inversion theory,
CVPR04(I: 582-587).
IEEE DOI 0408
BibRef

Brandt, S.S.[Sami S.],
Robust Factorisation with Uncertainty Analysis,
ICPR06(I: 39-42).
IEEE DOI 0609
BibRef

Brandt, S.S.[Sami S.], Koskenkorva, P.[Pekka], Kannala, J.H.[Ju-Ho], Heyden, A.[Anders],
Uncalibrated non-rigid factorisation with automatic shape basis selection,
NORDIA09(352-359).
IEEE DOI 0910
BibRef

Oliensis, J.[John], Hartley, R.I.[Richard I.],
Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Nonconvergence,
PAMI(29), No. 12, December 2007, pp. 2217-2233.
IEEE DOI 0711
BibRef
Earlier: ECCV06(IV: 214-227).
Springer DOI 0608
Discuss problems with:
See also Factorization Based Algorithm for Multi-Image Projective Structure and Motion, A. and
See also Provably-Convergent Iterative Methods for Projective Structure from Motion. Solution: add another step and it converges better. BibRef

Quan, L.[Long], Wang, J.D.[Jing-Dong], Tan, P.[Ping], Yuan, L.[Lu],
Image-Based Modeling by Joint Segmentation,
IJCV(75), No. 1, October 2007, pp. 135-150.
Springer DOI 0709
Kanade issue. Trace factorization approaches to the original Kanade, etc. work and analyze. BibRef

Xiao, J.X.[Jian-Xiong], Quan, L.[Long],
Multiple view semantic segmentation for street view images,
ICCV09(686-693).
IEEE DOI 0909
BibRef

Xiao, J.X.[Jian-Xiong], Wang, J.D.[Jing-Dong], Tan, P.[Ping], Quan, L.[Long],
Joint Affinity Propagation for Multiple View Segmentation,
ICCV07(1-7).
IEEE DOI 0710
BibRef

Liu, S.G.[Shi-Gang], Wu, C.K.[Cheng-Ke], Tang, L.[Li], Jia, J.[Jing],
An Iterative Factorization Method Based on Rank 1 for Projective Structure and Motion,
IEICE(E88-D), No. 9, September 2005, pp. 2183-2188.
DOI Link 0509
BibRef

Jia, H.J.[Hong-Jun], Martinez, A.M.[Aleix M.],
Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion,
PAMI(31), No. 5, May 2009, pp. 841-854.
IEEE DOI 0903
BibRef
And:
Support Vector Machines in face recognition with occlusions,
CVPR09(136-141).
IEEE DOI 0906
BibRef
And:
Face recognition with occlusions in the training and testing sets,
FG08(1-6).
IEEE DOI 0809
Finding a robust low rank approximation. The more distinct, the less noise changes things. BibRef

Hu, Y.Q.[Yi-Qun], Rajan, D.[Deepu], Chia, L.T.[Liang-Tien],
Attention-from-motion: A factorization approach for detecting attention objects in motion,
CVIU(113), No. 3, March 2009, pp. 319-331.
Elsevier DOI 0902
Motion Segmentation. Visual attention; BibRef

Wang, G.H.[Guang-Hui], Wu, Q.M.J.[Q.M. Jonathan],
Guide to Three Dimensional Structure and Motion Factorization,
Springer2011, ISBN: 978-0-85729-045-8
WWW Link. Survey, Factorization. Survey, Structure from Motion. Buy this book: Guide to Three Dimensional Structure and Motion Factorization (Advances in Pattern Recognition) 1010
BibRef

Civera, J.[Javier], Davison, A.J.[Andrew J.], Montiel, J.M.M.[José María Martínez],
Structure from Motion using the Extended Kalman Filter,
SpringerNew-York, 2012.

Solà, J.[Joan], Vidal-Calleja, T.[Teresa], Civera, J.[Javier], Montiel, J.M.M.[José María Martínez],
Impact of Landmark Parametrization on Monocular EKF-SLAM with Points and Lines,
IJCV(97), No. 3, May 2012, pp. 339-368.
WWW Link. 1203
BibRef

Li, K., Dai, Q., Xu, W., Yang, J., Jiang, J.,
Three-Dimensional Motion Estimation via Matrix Completion,
SMC-B(42), No. 2, April 2012, pp. 539-551.
IEEE DOI 1204
BibRef

Li, K., Yang, J., Jiang, J.,
Nonrigid Structure From Motion via Sparse Representation,
Cyber(45), No. 8, August 2015, pp. 1401-1413.
IEEE DOI 1506
Discrete cosine transforms BibRef

Wang, G.H.[Guang-Hui], Zelek, J.S.[John S.], Wu, Q.M.J.[Q.M. Jonathan],
Structure and Motion Recovery Based on Spatial-and-Temporal-Weighted Factorization,
CirSysVideo(22), No. 11, November 2012, pp. 1590-1603.
IEEE DOI 1211
BibRef
Earlier:
Spatial-and-Temporal-Weighted Structure from Motion,
CRV11(324-331).
IEEE DOI 1105

See also Single view based pose estimation from circle or parallel lines. BibRef

Fakih, A.H.[Adel H.], Zelek, J.S.[John S.],
On the Benefits of Using Gyroscope Measurements with Structure from Motion,
M2SFA208(xx-yy). 0810
BibRef

Fakih, A.H.[Adel H.], Asmar, D.[Daniel], Zelek, J.S.[John S.],
Augmenting analytic SFM filters with frame-to-frame features,
CVIU(129), No. 1, 2014, pp. 1-14.
Elsevier DOI 1411
Structure from motion BibRef

Fakih, A.H.[Adel H.], Zelek, J.S.[John S.],
Extending Filter-based Structure from Motion to Large Baselines,
CRV11(332-339).
IEEE DOI 1105
BibRef
Earlier:
Efficient Augmentation of the EKF Structure from Motion with Frame-to-Frame Features,
CRV10(47-54).
IEEE DOI 1005
BibRef
Earlier:
Scalable Near-Optimal Recursive Structure from Motion,
CRV09(23-30).
IEEE DOI 0905
BibRef
Earlier:
Structure from Motion: Combining features correspondences and optical flow,
ICPR08(1-4).
IEEE DOI 0812
BibRef
Earlier:
A Factorized Recursive Estimation of Structure and Motion from Image Velocities,
CRV07(355-362).
IEEE DOI 0705
BibRef

Wang, G.H.[Guang-Hui], Zelek, J.S., Wu, Q.M.J., Bajcsy, R.,
Robust rank-4 affine factorization for structure from motion,
WACV13(180-185).
IEEE DOI 1303
BibRef

Glashoff, K.[Klaus], Bronstein, M.M.[Michael M.],
Structure from Motion Using Augmented Lagrangian Robust Factorization,
3DIMPVT12(379-386).
IEEE DOI 1212
BibRef

Angst, R.[Roland], Pollefeys, M.[Marc],
Multilinear Factorizations for Multi-Camera Rigid Structure from Motion Problems,
IJCV(103), No. 2, June 2013, pp. 240-266.
WWW Link. 1306
BibRef
Earlier:
5D Motion Subspaces for Planar Motions,
ECCV10(III: 144-157).
Springer DOI 1009
BibRef
Earlier:
Static multi-camera factorization using rigid motion,
ICCV09(1203-1210).
IEEE DOI 0909
BibRef

Jacquet, B.[Bastien], Angst, R.[Roland], Pollefeys, M.[Marc],
Articulated and Restricted Motion Subspaces and Their Signatures,
CVPR13(1506-1513)
IEEE DOI 1309
Factorization, Motion subspaces, Signature BibRef

Cohen, A.[Andrea], Zach, C.[Christopher], Sinha, S.N.[Sudipta N.], Pollefeys, M.[Marc],
Discovering and exploiting 3D symmetries in structure from motion,
CVPR12(1514-1521).
IEEE DOI 1208
BibRef

Angst, R.[Roland], Zach, C.[Christopher], Pollefeys, M.[Marc],
The generalized trace-norm and its application to structure-from-motion problems,
ICCV11(2502-2509).
IEEE DOI 1201
trace-norm for SfM. BibRef

Khan, I.,
Non-Rigid Structure-From-Motion With Uniqueness Constraint and Low Rank Matrix Fitting Factorization,
MultMed(16), No. 5, August 2014, pp. 1350-1357.
IEEE DOI 1410
computer vision BibRef

Khan, I.,
Robust Sparse and Dense Nonrigid Structure From Motion,
MultMed(20), No. 4, April 2018, pp. 841-850.
IEEE DOI 1804
Estimation, Image reconstruction, Optimization, Robustness, Shape, Trajectory, Sparse and dense NRSfM, supervised Gauss-Newton BibRef

Zhang, H., Hu, S., Zhang, X., Luo, L.,
Visual Tracking via Constrained Incremental Non-negative Matrix Factorization,
SPLetters(22), No. 9, September 2015, pp. 1350-1353.
IEEE DOI 1503
Image reconstruction BibRef

Kennedy, R.[Ryan], Balzano, L.[Laura], Wright, S.J.[Stephen J.], Taylor, C.J.[Camillo J.],
Online algorithms for factorization-based structure from motion,
CVIU(150), No. 1, 2016, pp. 139-152.
Elsevier DOI 1608
BibRef
Earlier: WACV14(37-44)
IEEE DOI 1406
Structure from motion. Cameras BibRef

Wang, H.Y.[Heng-You], Cen, Y.G.[Yi-Gang], He, Z.H.[Zhi-Hai], Zhao, R.Z.[Rui-Zhen], Cen, Y.[Yi], Zhang, F.Z.[Feng-Zhen],
Robust Generalized Low-Rank Decomposition of Multimatrices for Image Recovery,
MultMed(19), No. 5, May 2017, pp. 969-983.
IEEE DOI 1704
GLRAM. Approximation algorithms BibRef

Wang, H.Y.[Heng-You], Cen, Y.G.[Yi-Gang], He, Z.Q.[Zhi-Quan], He, Z.H.[Zhi-Hai], Zhao, R.Z.[Rui-Zhen], Zhang, F.Z.[Feng-Zhen],
Reweighted Low-Rank Matrix Analysis With Structural Smoothness for Image Denoising,
IP(27), No. 4, April 2018, pp. 1777-1792.
IEEE DOI 1802
Image denoising, Image restoration, Matrix decomposition, Minimization, Optimization, Sparse matrices, TV, smooth BibRef

Kou, W.[Wen], Cheong, L.F.[Loong-Fah], Zhou, Z.Y.[Zhi-Ying],
Proximal robust factorization for piecewise planar reconstruction,
CVIU(166), No. 1, 2018, pp. 88-101.
Elsevier DOI 1712
Dense planar reconstruction and 3D motion. BibRef

Tang, J.J.[Jin-Jiang], Qian, W.J.[Wei-Jie], Zhao, Z.J.[Zhi-Jun], Liu, W.L.[Wei-Liang], He, P.[Ping],
Multi-view non-negative matrix factorization for scene recognition,
JVCIR(59), 2019, pp. 9-13.
Elsevier DOI 1903
Non-negative matrix factorization, Scene recognition, Multi-view BibRef

Jin, C.C.[Cong-Cong], Zhu, J.[Jihua], Li, Y.C.[Yao-Chen], Pang, S.M.[Shan-Min], Chen, L.[Lei], Wang, J.[Jun],
Multi-view registration based on weighted LRS matrix decomposition of motions,
IET-CV(13), No. 4, June 2019, pp. 376-384.
DOI Link 1906
BibRef

Fonal, K., Zdunek, R.,
Fast Recursive Nonnegative Standard and Hierarchical Tucker Decomposition,
SPLetters(26), No. 9, September 2019, pp. 1265-1269.
IEEE DOI 1909
computational complexity, matrix decomposition, tensors, nonnegative matrix factorization algorithm, nonnegative Tucker decomposition BibRef

Kaloga, Y., Foare, M., Pustelnik, N., Jensen, P.,
Discrete Mumford-Shah on Graph for Mixing Matrix Estimation,
SPLetters(26), No. 9, September 2019, pp. 1275-1279.
IEEE DOI 1909
gradient methods, image denoising, image segmentation, matrix algebra, minimisation, nonconvex optimisation BibRef

Wang, J.Y.[Jing-Yu], Zhao, Y.[Yue], Zhang, K.[Ke], Wang, Q.[Qi], Li, X.L.[Xue-Long],
Spatio-Temporal Online Matrix Factorization for Multi-Scale Moving Objects Detection,
CirSysVideo(32), No. 2, February 2022, pp. 743-757.
IEEE DOI 2202
Object detection, Heuristic algorithms, Dynamics, Adaptation models, Video sequences, Interference, Robustness, low-rank matrix factorization BibRef

Brandt, S.S., Ackermann, H., Grasshof, S.,
Uncalibrated Non-Rigid Factorisation by Independent Subspace Analysis,
RSL-CV19(569-578)
IEEE DOI 2004
emotion recognition, face recognition, image motion analysis, image reconstruction, iterative methods, matrix algebra, affine reconstruction BibRef

Mu, Y., Dimitrakopoulos, R., Ferrie, F.P.[Frank P.],
Decoupling Spatial Pattern and its Movement Via Complex Factorization Over Orthogonal Filter Pairs,
CRV19(1-8)
IEEE DOI 1908
Task analysis, Optical imaging, Buildings, Artificial neural networks, Training, representation learning, optical flow BibRef

Ahuja, N.A., Subedar, M., Tickoo, O., Lee, Y.,
A Factorization Approach for Enabling Structure-from-Motion/SLAM Using Integer Arithmetic,
Matrix-Tensor17(554-562)
IEEE DOI 1802
Covariance matrices, Jacobian matrices, Kalman filters, Mobile communication, Program processors, Real-time systems, Simultaneous localization and mapping BibRef

Dong, Q.[Qiulei], Hu, H.[Hao],
Sequential factorization for nonrigid structure from motion via LBFGS,
ICPR16(1731-1736)
IEEE DOI 1705
Cameras, Matrix decomposition, Minimization, Motion estimation, Optimization, Shape, Three-dimensional, displays BibRef

Wang, M.Y.[Mei-Yuan], Li, K.[Kun], Wu, F.[Feng], Lai, Y.K.[Yu-Kun], Yang, J.Y.[Jing-Yu],
3-D motion recovery via low rank matrix analysis,
VCIP16(1-4)
IEEE DOI 1701
Cameras BibRef

Qiu, C.L.[Chen-Lu], Wu, X.D.[Xiao-Dong], Xu, H.Y.[Hui-Ying],
Recursive projected sparse matrix recovery (ReProSMR) with application in real-time video layer separation,
ICIP14(1332-1336)
IEEE DOI 1502
Estimation BibRef

Ikeuchi, R., Sugaya, Y.,
Camera Motion Estimation by Geometric AIC for Factorization with Missing Data,
ACPR13(241-245)
IEEE DOI 1408
cameras BibRef

Angst, R.[Roland], Pollefeys, M.[Marc],
A Unified View on Deformable Shape Factorizations,
ECCV12(VI: 682-695).
Springer DOI 1210
BibRef

Ricco, S.[Susanna], Tomasi, C.[Carlo],
Video Motion for Every Visible Point,
ICCV13(2464-2471)
IEEE DOI 1403
BibRef
Earlier:
Simultaneous Compaction and Factorization of Sparse Image Motion Matrices,
ECCV12(VI: 456-469).
Springer DOI 1210
BibRef
And:
Dense Lagrangian motion estimation with occlusions,
CVPR12(1800-1807).
IEEE DOI 1208
BibRef

Rehan, A.[Ali], Zaheer, A.[Aamer], Akhter, I.[Ijaz], Saeed, A.[Arfah], Usmani, M.H.[Muhammad Haris], Mahmood, B.[Bilal], Khan, S.[Sohaib],
NRSfM using local rigidity,
WACV14(69-74)
IEEE DOI 1406
Optimization, Trajectory, Transforms BibRef

Zaheer, A.[Aamer], Akhter, I.[Ijaz], Baig, M.H.[Mohammad Haris], Marzban, S.[Shabbir], Khan, S.[Sohaib],
Multiview structure from motion in trajectory space,
ICCV11(2447-2453).
IEEE DOI 1201
3d from multiple static cameras BibRef

Bernet, S.[Sacha], Sturm, P.F.[Peter F.], Cudel, C.[Christophe], Basset, M.[Michel],
Study on the interest of hybrid fundamental matrix for head mounted eye tracker modeling,
BMVC11(xx-yy).
HTML Version. 1110
BibRef

Li, P.[Ping], Gunnewiek, R.K.[Rene Klein], de With, P.[Peter],
Detecting Critical Configurations for Dividing Long Image Sequences for Factorization-Based 3-D Scene Reconstruction,
ACCV09(II: 381-394).
Springer DOI 0909
BibRef

Cheriyadat, A.M.[Anil M.], Radke, R.J.[Richard J.],
Non-negative matrix factorization of partial track data for motion segmentation,
ICCV09(865-872).
IEEE DOI 0909
BibRef

Shaji, A.[Appu], Chandran, S.[Sharat], Suter, D.[David],
Manifold optimisation for motion factorisation,
ICPR08(1-4).
IEEE DOI 0812
BibRef

Wang, L., Wu, F.C.,
A factorization algorithm for trifocal tensor estimation,
ICPR08(1-4).
IEEE DOI 0812
BibRef

Matikainen, P.K., Sukthankar, R., Hebert, M., Ke, Y.,
Fast Motion Consistency through Matrix Quantization,
BMVC08(xx-yy).
PDF File. 0809
BibRef

Tardif, J.P.[Jean-Philippe], Bartoli, A.E.[Adrien E.], Trudeau, M.[Martin], Guilbert, N.[Nicolas], Roy, S.[Sebastien],
Algorithms for Batch Matrix Factorization with Application to Structure-from-Motion,
CVPR07(1-8).
IEEE DOI 0706
BibRef

Li, T.[Ting], Kallem, V.[Vinutha], Singaraju, D.[Dheeraj], Vidal, R.[Rene],
Projective Factorization of Multiple Rigid-Body Motions,
CVPR07(1-6).
IEEE DOI 0706
BibRef

Lemuz-López, R.[Rafael], Arias-Estrada, M.[Miguel],
Iterative Closest SIFT Formulation for Robust Feature Matching,
ISVC06(II: 502-513).
Springer DOI 0611
Shape and motion from multiple feature matches. incremental factorization. BibRef

Lemuz-López, R.[Rafael], Arias-Estrada, M.[Miguel],
A Domain Reduction Algorithm for Incremental Projective Reconstruction,
ISVC06(II: 564-575).
Springer DOI 0611
BibRef

Chikatsu, H., Ohdake, T.,
Ubiquitous digital photogrammetry by consumer grade digital camera,
IEVM06(xx-yy).
PDF File. 0609
BibRef

Jung, Y.Y.[Yoon-Yong], Hwang, Y.H.[Yong-Ho], Hong, H.K.[Hyun-Ki],
Frame grouping measure for factorization-based projective reconstruction,
ICPR04(IV: 112-115).
IEEE DOI 0409
BibRef

Saito, H., Kamijima, S.,
Factorization Method Using Interpolated Feature Tracking via Projective Geometry,
BMVC03(xx-yy).
HTML Version. 0409
BibRef

Urfalioglu, O.,
Robust estimation of camera rotation, translation and focal length at high outlier rates,
CRV04(464-471).
IEEE DOI 0408
BibRef

Langer, M.S., Chapdelaine-Couture, V., Mann, R., Roy, S.,
Motion Parallax without Motion Compensation in 3D Cluttered Scenes,
3DPVT06(65-72).
IEEE DOI 0606

See also Spectrum analysis of motion parallax in a 3D cluttered scene and application to egomotion. BibRef

Chapdelaine-Couture, V., Langer, M.S.,
Can Lucas-Kanade be used to estimate motion parallax in 3D cluttered scenes?,
CRV07(63-72).
IEEE DOI 0705
BibRef

Navab, N., Genc, Y., Khamene, A., Mitschke, M.,
Direct Method for Motion Estimation: An Alternative to Decomposition of Planar Transformation Matrices,
DAGM02(575 ff.).
Springer DOI 0303
BibRef

Goncalves, B.B., Aguiar, P.M.Q.,
Complete 3-d models from video: a global approach,
ICIP04(IV: 2479-2482).
IEEE DOI 0505
BibRef

Guerreiro, R.F.C., Aguiar, P.M.Q.,
3D structure from video streams with partially overlapping images,
ICIP02(III: 897-900).
IEEE DOI 0210
BibRef

Vidal, R., Oliensis, J.,
Structure from Planar Motions with Small Baselines,
ECCV02(II: 383 ff.).
Springer DOI 0205
Addresses the factorization problem of small baselines. BibRef

Brand, M.[Matthew],
Morphable 3D Models from Video,
CVPR01(II:456-463).
IEEE DOI 0110
Award, CVPR. Combine non-rigid motion and structure from optical flow to get structure. BibRef

Mahamud, S., Hebert, M., Omori, Y., Ponce, J.,
Provably-Convergent Iterative Methods for Projective Structure from Motion,
CVPR01(I:1018-1025).
IEEE DOI
PS File. 0110
Minimization of distance between prediction and image points. Compare to Bundle Adjustment and Strum-Triggs (
See also Factorization Based Algorithm for Multi-Image Projective Structure and Motion, A. ). BibRef

Huynh, D.Q., Heyden, A.,
Outlier Detection in Video Sequences under Affine Projection,
CVPR01(I:695-701).
IEEE DOI 0110
Factorization for shape from motion. BibRef

Han, M.[Mei],
Linear and Bilinear Subspace Methods for Structure from Motion,
CMU-RI-TR-01-13, February, 2001. BibRef 0102 Ph.D.Thesis.
PDF File.
PS File. 0205
BibRef

Han, M.[Mei], Kanade, T.[Takeo],
Creating 3D Models with Uncalibrated Cameras,
WACV00(178-185).
IEEE DOI 0010
Factorization approach to do Perspective Projection and get focal length (i.e. zoom camera), principal point, and aspect ratio. So, really calibrate the cameras then create the model (but with factorization approach these are all one step). Requires 5 poitsn 4 frames, but works better with more. Requires points to be in all frames, but does handle errors somewhat. Reconstructions depend on matched points. BibRef

Han, M., and Kanade, T.,
Perspective Factorization Methods for Euclidean Reconstruction,
CMU-RI-TR-99-22, August, 1999.
HTML Version. BibRef 9908

Han, M., and Kanade, T.,
The Factorization Method with Linear Motions,
CMU-RI-TR-99-23, October, 1999.
HTML Version. BibRef 9910

Vasiliu, M., Devos, F.,
Real-time 3D Reconstruction on High Resolution Focal Plane Array,
ICIP00(Vol I: 573-576).
IEEE DOI 0008
BibRef

Papadopoulo, T., Lourakis, M.I.A.,
Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications,
ECCV00(I: 554-570).
Springer DOI 0003
BibRef

Kurata, T.[Takeshi], Fujiki, J.[Jun], Kourogi, M.[Masakatsu], Sakaue, K.[Katsuhiko],
A Fast and Robust Approach to Recovering Structure and Motion from Live Video Frames,
CVPR00(II: 528-535).
IEEE DOI 0005
BibRef

Mahamud, S.[Shyjan], Hebert, M.,
Iterative Projective Reconstruction from Multiple Views,
CVPR00(II: 430-437).
IEEE DOI 0005
BibRef

Hornegger, J., Tomasi, C.,
Representation Issues in the ML Estimation of Camera Motion,
ICCV99(640-647).
IEEE DOI BibRef 9900

Ichimura, N.,
Motion Segmentation based on Factorization Method and Discriminant Criterion,
ICCV99(600-605).
IEEE DOI BibRef 9900

Kurata, T.[Takeshi], Fujikiy, J.[Jun], Kourogiz, M.[Masakatsu], Sakauey, K.[Katsuhiko],
A Robust Recursive Factorization Method for Recovering Structure and Motion from Live Video Frames,
Frame-Rate99().
HTML Version. BibRef 9900

Li, Y.H.[Yan-Hua], Brooks, M.J.[Michael J.],
An Efficient Recursive Factorization Method for Determining Structure from Motion,
CVPR99(I: 138-143).
IEEE DOI BibRef 9900

Ng, T.K.[Teck Khim], Kanade, T.,
PALM: portable sensor-augmented vision system for large-scene modeling,
3DIM99(473-482).
IEEE DOI 9910
BibRef

Yokoya, N.[Naokazu], Takemura, H.[Haruo], Hwang, K.C.[Kuo-Chang], Yamazawa, K.,
A Factorization Method Using 3-D Linear Combination for Shape and Motion Recovery,
ICPR98(Vol II: 959-963).
IEEE DOI 9808
BibRef

Ma, J.B.[Jian-Bo], Ahuja, N.[Narendra],
Dense Shape and Motion from Region Correspondences by Factorization,
CVPR98(219-224).
IEEE DOI BibRef 9800

Morris, D.D.[Daniel D.], and Kanade, T.[Takeo],
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models,
ICCV98(696-702).
IEEE DOI BibRef 9800

Ueshiba, T., Tomita, F.,
A Factorization Method for Projective and Euclidean Reconstruction from Multiple Perspective Views via Iterative Depth Estimation,
ECCV98(I: 296).
Springer DOI BibRef 9800

Held, A.,
Piecewise Shape Reconstruction by Incremental Factorization,
BMVC96(Motion-Based Reconstruction). 9608
Real World Computing Partnership, Japan BibRef

Yu, H., Chen, Q.[Qian], Xu, G., Yachida, M.,
3D Shape and Motion by SVD under Higher-Order Approximation of Perspective Projection,
ICPR96(I: 456-460).
IEEE DOI 9608
(Osaka Univ., J) BibRef

Triggs, B.[Bill],
Factorization Methods for Projective Structure and Motion,
CVPR96(845-851).
IEEE DOI BibRef 9600

Sturm, P.F., Triggs, B.,
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion,
ECCV96(II:709-720).
Springer DOI BibRef 9600

Boult, T.E., and Brown, L.G.,
Motion Segmentation Using Singular Value Decomposition,
DARPA92(495-506). BibRef 9200
Earlier:
Factorization-Based Segmentation of Motions,
Motion91(179-186). Building on the work of Tomasi at CMU, find multiple motions in the image. BibRef

Chapter on Motion Analysis -- Low-Level, Image Level Analysis, Mosaic Generation, Super Resolution, Shape from Motion continues in
Motion with Matrix Factorization, Missing Data Issues, Articulated Motion .