Mitiche, A.[Amar],
Habelrih, G.,
Interpretation of Straight Line Correspondences Using Angular Relations,
PR(22), No. 3, 1989, pp. 299-308.
WWW Version.
0309
BibRef
Earlier:
Interpreting the Straight Line Using Angular Relations,
ICPR88(II: 1053-1055).
IEEE DOI Link
IEEE Top Reference.
BibRef
Mitiche, A.[Amar],
Seida, S.[Steve], and
Aggarwal, J.K.,
Interpretation of Structure and Motion Using Straight
Line Correspondences,
ICPR86(1110-1112).
BibRef
8600
And:
Line-Based Computation of Structure and Motion Using Angular Invariance,
Motion86(175-180).
Argues that 2 views of lines (without end points) will not work,
you need 3 views. A total of 4 lines in 3 views is required.
BibRef
Dubé, D.[Daniel],
Mitiche, A.[Amar],
The incremental rigidity scheme for structure from motion:
The line-based formulation,
ECCV90(292-296).
Springer DOI Link
9004
BibRef
Laganiere, R., and
Mitiche, A.,
On Combining Points and Lines in an Image Sequence to
Recover 3D Structure and Motion,
Motion89(221-228).
Motion, Structure. For 2 frames, lines do not help. For 3 it helps with occlusions.
BibRef
8900
Holt, R.J.,
Netravali, A.N.,
Uniqueness of Solutions to 3 Perspective Views of 4 Points,
PAMI(17), No. 3, March 1995, pp. 303-307.
IEEE Abstract. IEEE Top Reference.
WWW Version. A unique solution for the orientation of three cameras for 4 points.
But there are rare cases when it is not unique.
BibRef
9503
Holt, R.J.,
Netravali, A.N.,
Uniqueness of Solutions to Structure and Motion from
Combinations of Point and Line Correspondences,
JVCIR(7), No. 2, June 1996, pp. 126-136.
9607
BibRef
Holt, R.J.[Robert J.], and
Netravali, A.N.[Arun N.],
Motion of Nonrigid Objects from Multiframe Correspondences,
JVCIR(3), 1992, pp. 255-271.
See also Number of Solutions for Motion and Structure from Multiple Frame Correspondence. For uniform contraction (or expansion) around an unknown point.
No matter how many points this cannot be
determined for 3 frames, 4 is required (with 3 points).
BibRef
9200
Holt, R.J.[Robert J.], and
Netravali, A.N.[Arun N.],
Motion and Structure from Line Correspondences: Some Further Results,
IJIST(5), No. 1, Spring 1994, pp. 52-61.
BibRef
9400
Holt, R.J.,
Netravali, A.N.,
Motion and Structure from Line Correspondences under
Orthographic Projection,
IJIST(8), No. 3, 1997, pp. 301-312.
9707
BibRef
Holt, R.J.,
Netravali, A.N.,
Number of Solutions for Motion and Structure from
Multiple Frame Correspondence,
IJCV(23), No. 1, May 1997, pp. 5-15.
WWW Version.
9708
BibRef
Earlier:
Motion and Structure from Multiple Frame Correspondence,
ATT11256-900706.01TM, June 1990.
Analysis of Shariat's (
See also Motion Estimation With More Than Two Frames. )
equations gives 2 solutions for 3 in 3 (1 all
positive depths), 1 solution for 2 in 4 and 16 for 1 in 5.
See also Motion from Optic Flow: Multiplicity of Solutions.
BibRef
Netravali, A.N.,
Salz, J.,
Algorithms for Estimation of Three-Dimensional Motion,
ATT Tech(64), 1985, pp. 335-346.
BibRef
8500
Lee, H.J., and
Deng, H.C.,
Three-Frame Corner Matching and Moving Object Object Extraction
in a Sequence of Images,
CVGIP(52), No. 2, November 1990, pp. 210-238.
WWW Version. Matches are refined by using three frames
rather than only 2. Consistency through the 3 is required.
BibRef
9011
Mitiche, A.,
Faugeras, O.D., and
Aggarwal, J.K.,
Counting Straight Lines,
CVGIP(47), No. 3, September 1989, pp. 353-360.
WWW Version.
BibRef
8909
Earlier:
ICPR88(II: 693-695).
IEEE DOI Link
8811
Perspective assumption.
Complete analysis of how to do general motion with matches of
straight lines. 3 Frames minimum with 6 lines. This ties together
several related papers by several different authors.
BibRef
Faugeras, O.D.,
Lustman, F.,
Motion and Structure from Motion in a Piecewise Planar Environment,
PRAI(2), 1988, pp. 485-508.
BibRef
8800
Faugeras, O.D.,
Lustman, F., and
Toscani, G.,
Motion and Structure from Motion from Point and Line Matches,
ICCV87(25-34).
Motion, Structure.
See also Counting Straight Lines.
Kalman Filter.
BibRef
8700
Navab, N.,
Faugeras, O.D.,
The Critical Sets of Lines for Camera Displacement Estimation:
A Mixed Euclidean-Projective and Constructive Approach,
IJCV(23), No. 1, May 1997, pp. 17-44.
WWW Version.
9708
BibRef
Earlier:
Insert an A2:
Vieville, T.,
ICCV93(713-723).
IEEE DOI Link Are there sets of 3-D lines that such that no number of lines
will work? -- Yes.
BibRef
Vieville, T.[Thierry],
Faugeras, O.D.[Olivier D.],
Robust and Fast Computation of Edge Characteristics in Image Sequences,
IJCV(13), No. 2, October 1994, pp. 153-179.
Springer DOI Link
BibRef
9410
Earlier:
Robust and fast computation of unbiased intensity derivatives in images,
ECCV92(203-211).
Springer DOI Link
9205
BibRef
Earlier:
Feed-Forward Recovery of Motion and Structure from a
Series of 2D-Lines Matches,
ICCV90(517-520).
IEEE DOI Link Kalman Filter.
BibRef
Vieville, T.,
Estimation of 3D-Motion and Structure from Tracking
2D-Lines in a Sequence of Images,
ECCV90(281-291).
Springer DOI Link Includes optical flow.
Motion from lines in three frames.
BibRef
9000
Weng, J.Y.[Ju-Yang],
Huang, T.S., and
Ahuja, N.,
Motion and Structure from Line Correspondences:
Closed-Form Solution, Uniqueness, and Optimization,
PAMI(14), No. 3, March 1992, pp. 318-336.
IEEE Abstract. IEEE Top Reference.
WWW Version.
BibRef
9203
Earlier:
Estimating Motion and Structure from Line Matches:
Performance Obtained and Beyond,
ICPR90(I: 168-172).
IEEE DOI Link
Motion, Structure. Closed form solutions then iterations to optimize from there.
Start with 12 lines and go up.
Three monocular, perspective views of lines gives a closed form
solution. Analysis for 12 lines or more. Simulated results.
BibRef
Aisbett, J.[Janet],
An Iterated Estimation of the Motion Parameters of a
Rigid Body from Noisy Displacement Vectors,
PAMI(12), No. 11, November 1990, pp. 1092-1098.
IEEE Abstract. IEEE Top Reference.
WWW Version. See also Optimal Visual Motion Estimation: A Note. Extension of the above 2 techniques.
BibRef
9011
Huang, T.S., and
Lee, C.H.,
Motion and Structure from Orthographic Projections,
PAMI(11), No. 5, May 1989, pp. 536-540.
IEEE Abstract. IEEE Top Reference.
WWW Version.
BibRef
8905
Earlier:
ICPR88(II: 885-887).
IEEE DOI Link
IEEE Top Reference. Orthographic assumption.
A restudy of Ullman's (
See also Interpretation of Visual Motion, The. ) conclusions.
First Orthographic views give an infinite number of solutions for 2
views. Second an algorithm using 4 points in 3 views is presented.
Later extensions:
See also Finding Point Correspondences and Determining Motion of a Rigid Object from Two Weak Perspective Views.
See also Using Motion from Orthographic Views to Verify 3-D Point Matches.
BibRef
Lee, C.H., and
Rosenfeld, A.,
Structure and Motion of a Rigid Object Having Unknown Constant Motion,
Motion86(145-150).
Parallel projection with 2 point in 3 frames.
BibRef
8600
Hoffman, D.D., and
Flinchbaugh, B.E.,
The Interpretation of Biological Motion,
BioCyber(42), No. 3, 1982, pp. 195-202.
BibRef
8200
And:
MIT AI Memo-608, December 1980.
Uses 2 points in 3 frames for parallel projection with some
constraints on the rotation (which is necessary). (No results).
BibRef
Hoffman, D.D.,
Interpreting Time-Varying Image: The Planatary Assumption,
CVWS82(92-101).
BibRef
8200
Zhuang, X.,
Huang, T.S., and
Haralick, R.M.,
A Simple Procedure to Solve Motion and Structure from
Three Orthographic Views,
RA(4), 1988, pp. 236-239.
Motion, Structure.
BibRef
8800
Liu, Y.C.[Yun-Cai], and
Huang, T.S.,
A Linear Algorithm for Motion Estimation Using
Straight Line Correspondences,
CVGIP(44), No. 1, October 1988, pp. 35-57.
WWW Version.
BibRef
8810
Earlier:
ICPR88(I: 213-219).
IEEE DOI Link
IEEE Top Reference. Linear solution requires at least 13 line pairs in 3 frames.
First determine several candidate solutions, then find unique
solutions from physical constraints. (Simulation results.)
See also Determining Straight Line Correspondences from Intensity Images.
BibRef
Liu, Y.C.[Yun-Cai], and
Huang, T.S.,
Estimation of Rigid Body Motion Using Straight Line Correspondences,
CVGIP(43), No. 1, July 1988, pp. 37-52.
WWW Version.
BibRef
8807
Earlier:
Motion86(47-52).
BibRef
And:
Estimation of Rigid Body Motion Using Straight
Line Correspondences, Further Results,
ICPR86(306-309).
Translation requires 5 lines in 3 views, rotation requires 6 lines
in 3 views.
See also Interpretation of Structure and Motion Using Straight Line Correspondences. for 1 less line for both options.
BibRef
Liu, Y., and
Huang, T.S.,
Three-Dimensional Motion Determination from Real Scene
Images Using Straight Line Correspondences,
PR(25), No. 6, June 1992, pp. 617-639.
WWW Version. See above.
See also Determining Straight Line Correspondences from Intensity Images.
BibRef
9206
Weng, J.Y.[Ju-Yang],
Liu, Y.,
Huang, T.S., and
Ahuja, N.,
Estimating Motion/Structure from Line Correspondences:
A Robust Linear Algorithm and Uniqueness Theorems,
CVPR88(387-392).
IEEE Abstract. IEEE Top Reference.
BibRef
8800
Yen, B.L., and
Huang, T.S.,
Determining 3-D Motion and Structure of a Rigid Body Over 3 Frames
Using Straight Line Correspondence,
CVPR83(267-272).
BibRef
8300
And:
Determining 3D Motion/Structure of a Rigid Body over 2 Frames Using
Correspondences of Straight Lines Lying on Parallel Planes,
ICPR84(781-783).
BibRef
Earlier:
Determining 3-D Motion Parameters of a Rigid Body:
A Vector-Geometrical Approach,
Motion83(78-90).
(Illinois) Similar results, different insight.
BibRef
Yen, B.L., and
Huang, T.S.,
Determining 3-D Motion and Structure of a Rigid Body
Using Straight Line Correspondence,
ISPDSA83(365-394).
BibRef
8300
Liu, Y.,
Rigid Object Motion Estimation from Intensity Images
Using Straight Line Correspondences,
Ph.D.Thesis (EE), 1990,
BibRef
9000
Univ. of IllinoisUse 6 lines over 3 frames, solve for the rotations, then the
translations. The linear algorithm requires 13 lines over 3 frames.
See the published papers above.
See also Determining Straight Line Correspondences from Intensity Images.
See also Estimation of Rigid Body Motion Using Straight Line Correspondences.
BibRef
Longuet-Higgins, H.C.[H. Christopher],
A Method of Obtaining the Relative Positions of Four Points from
Three Perspective Projections,
IVC(10), No. 5, June 1992, pp. 266-270.
WWW Version.
BibRef
9206
Earlier:
BMVC91(xx-yy).
PDF Version.
9109
BibRef
Klopotek, M.A.,
Analysis of Video Image Sequences Using Point and Line Correspondences:
Comment,
PR(28), No. 2, February 1995, pp. 283-292.
WWW Version.
BibRef
9502
Shimshoni, I.[Ilan],
Basri, R.[Ronen],
Rivlin, E.[Ehud],
A Geometric Interpretation of Weak-Perspective Motion,
PAMI(21), No. 3, March 1999, pp. 252-257.
IEEE Abstract. IEEE Top Reference.
WWW Version. Reduce the problem to finding triangles, with known angles, on a sphere.
Three images.
BibRef
9903
Avidan, S.[Shai],
Shashua, A.[Amnon],
Threading Fundamental Matrices,
PAMI(23), No. 1, January 2001, pp. 73-77.
IEEE Abstract. IEEE Top Reference.
WWW Version.
0101
BibRef
Earlier:
ECCV98(I: 124).
WWW Version.
Fundamental Matrix.
Trifocal Tensor.
BibRef
Earlier:
Tensor Embedding of the Fundamental Matrix,
SMILE98(xx-yy).
BibRef
Earlier:
Novel View Synthesis in Tensor Space,
CVPR97(1034-1040).
IEEE Abstract. IEEE Top Reference.
WWW Version.
9704
Novel views generated from a few given correspondence.
Connect two consecutive fundamental matrices using the trifocal
tensor. This forces a common 3-D model. Apply to recovery of egomotion,
stabilization and multiview rendering.
BibRef
Avidan, S.[Shai],
Shashua, A.[Amnon],
Unifying Two-View and Three-View Geometry,
DARPA97(863-868).
BibRef
9700
Shashua, A.,
Avidan, S.,
The Rank 4 Constraint in Multiple (over 3) View Geometry,
ECCV96(II:196-206).
Springer DOI Link Trilinear constraints are all you get, but how to get them with
more views.
BibRef
9600
Avidan, S.,
Tensorial Transfer: Representation of N>3 Views of 3d Scenes,
ARPA96(821-824).
N tensors for N+2 views.
BibRef
9600
Shashua, A.,
Anandan, P.,
Trilinear Constraints Revisited:
Generalized Trilinear Constraints and the Tensor Brightness Constraint,
ARPA96(815-820).
BibRef
9600
Shashua, A.[Amnon],
Werman, M.[Michael],
Trilinearity of Three Perspective Views and its Associated Tensor,
ICCV95(920-925).
IEEE DOI Link
WWW Version.
BibRef
9500
Shashua, A.,
Trilinearity in Visual Recognition by Alignment,
ECCV94(A:479-484).
Springer DOI Link
BibRef
9400
Navab, N.[Nassir],
Genc, Y.[Yakup],
Appel, M.[Mirko],
Lines in One Orthographic and Two Perspective Views,
PAMI(25), No. 7, July 2003, pp. 912-917.
IEEE Abstract. IEEE Top Reference.
0307
BibRef
Earlier:
CVPR00(II: 607-614).
IEEE Abstract. IEEE Top Reference.
WWW Version.
0005
Match the lines to find structure and motion. Lines given by the
2-D plans.
BibRef
Quan, L.[Long],
Triggs, B.[Bill],
Mourrain, B.[Bernard],
Some Results on Minimal Euclidean Reconstruction from Four Points,
JMIV(24), No. 3, May 2006, pp. 341-348.
Springer DOI Link
0605
Reconstruction from 4 points in 3 or more calibrated images.
BibRef
Quennesson, K.[Kevin],
Dellaert, F.[Frank],
Rao-Blackwellized Importance Sampling of Camera Parameters from Simple
User Input with Visibility Preprocessing in Line Space,
3DPVT06(893-899).
IEEE DOI Link
0606
BibRef
Stewenius, H.[Henrik],
Åström, K.[Kalle],
Structure and Motion Problems for Multiple Rigidly Moving Cameras,
ECCV04(Vol III: 252-263).
WWW Version.
0405
3 points in 2 images or 2 points in 3 images.
BibRef
Etoh, M.[Minoru],
Aoki, T.[Toshimichi],
Hata, K.[Koichi],
Estimation of Structure and Motion Parameters for a Roaming Robot that
Scans the Space,
ICCV99(579-584).
IEEE DOI Link Translation on the floor and rotation about its axis.
5 features in 3 frames.
BibRef
9900
Quan, L.[Long],
Lhuillier, M.,
Structure from motion from three affine views,
ICPR02(IV: 1-6).
IEEE DOI Link
0211
BibRef
Quan, L.[Long],
Ohta, Y.[Yuichi],
A New Linear Method for Euclidean Motion/structure from
Three Calibrated Affine Views,
CVPR98(172-177).
IEEE Abstract. IEEE Top Reference.
BibRef
9800
Trautwein, S.[Stefan],
Mühlich, M.[Matthias],
Feiden, D.[Dirk],
Mester, R.[Rudolf],
Estimating Consistent Motion from Three Views:
An Alternative to Trifocal Analysis,
CAIP99(311-320).
WWW Version.
9909
BibRef
Chapter on Motion -- Feature-Based, Long Range, Motion and Structure Estimates, Tracking, Surveillance, Activities continues in
Motion Estimates Using 4 Frames .