# 16.2.2 Motion Estimates Using 3 Frames

Chapter Contents (Back)
Motion, Three Frames.

Mitiche, A.[Amar], Habelrih, G.,
Interpretation of Straight Line Correspondences Using Angular Relations,
PR(22), No. 3, 1989, pp. 299-308.
Elsevier DOI 0309
BibRef
Earlier:
Interpreting the Straight Line Using Angular Relations,
ICPR88(II: 1053-1055).
IEEE DOI 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

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 DOI 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.[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.
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

Lee, H.J.[Hsi-Jian], Deng, H.C.[Hsi-Chou], 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.
Elsevier DOI 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.
Elsevier DOI BibRef 8909
Earlier: ICPR88(II: 693-695).
IEEE DOI 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

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.
BibRef
Earlier: Insert an A2: Vieville, T., ICCV93(713-723).
IEEE DOI 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 BibRef 9410
Earlier:
Robust and fast computation of unbiased intensity derivatives in images,
ECCV92(203-211).
Springer DOI 9205
BibRef
Earlier:
Feed-Forward Recovery of Motion and Structure from a Series of 2D-Lines Matches,
ICCV90(517-520).
IEEE DOI 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 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 DOI BibRef 9203
Earlier:
Estimating Motion and Structure from Line Matches: Performance Obtained and Beyond,
ICPR90(I: 168-172).
IEEE DOI 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 DOI 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 DOI BibRef 8905
Earlier: ICPR88(II: 885-887).
IEEE DOI 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

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.
Elsevier DOI BibRef 8810
Earlier: ICPR88(I: 213-219).
IEEE DOI 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], Huang, T.S.[Thomas S.],
Estimation of Rigid Body Motion Using Straight Line Correspondences,
CVGIP(43), No. 1, July 1988, pp. 37-52.
Elsevier DOI 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.C.[Yun-Cai], Huang, T.S.[Thomas S.],
Three-Dimensional Motion Determination from Real Scene Images Using Straight Line Correspondences,
PR(25), No. 6, June 1992, pp. 617-639.
Elsevier DOI See above. See also Determining Straight Line Correspondences from Intensity Images. BibRef 9206

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

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

Klopotek, M.A.[Mieczyslaw A.],
Analysis of Video Image Sequences Using Point and Line Correspondences: Comment,
PR(28), No. 2, February 1995, pp. 283-292.
Elsevier DOI 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 DOI Reduce the problem to finding triangles, with known angles, on a sphere. Three images. BibRef 9903

Avidan, S.[Shai], Shashua, A.[Amnon],
PAMI(23), No. 1, January 2001, pp. 73-77.
IEEE DOI 0101
BibRef
Earlier: ECCV98(I: 124).
Springer DOI 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 DOI 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

Shashua, A., Avidan, S.,
The Rank 4 Constraint in Multiple (over 3) View Geometry,
ECCV96(II:196-206).
Springer DOI 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

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. 0307
BibRef
Earlier: CVPR00(II: 607-614).
IEEE DOI 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 0605
Reconstruction from 4 points in 3 or more calibrated images. BibRef

Chuang, T.Y., Rottensteiner, F., Heipke, C.,
Relative Pose Estimation Using Image Feature Triplets,
PIA15(39-45).
relative pose estimation from image point and line triplets. BibRef

Stewenius, H.[Henrik], Åström, K.[Kalle],
Structure and Motion Problems for Multiple Rigidly Moving Cameras,
ECCV04(Vol III: 252-263).
Springer DOI 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 Translation on the floor and rotation about its axis. 5 features in 3 frames. BibRef 9900

Chapter on Motion -- Feature-Based, Long Range, Motion and Structure Estimates, Tracking, Surveillance, Activities continues in
Motion Estimates Using 4 Frames .

Last update:May 18, 2019 at 16:15:50