*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

*Dubé, D.[Daniel]*,
*Mitiche, A.[Amar]*,

**The incremental rigidity scheme for structure from motion:
The line-based formulation**,

*ECCV90*(292-296).

Springer DOI
**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 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.*,
*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.

DOI Link
**9708**

BibRef

Earlier:

**Motion and Structure from Multiple Frame Correspondence**,

*ATT*11256-900706.01TM, 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.[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

*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.

DOI Link
**9708**

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

*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.

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**

*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 DOI
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 Illinois*Use 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.

Elsevier DOI
BibRef
**9206**

Earlier:
*BMVC91*(xx-yy).

PDF File.
**9109**

See also Computer Algorithm for Reconstructing a Scene from Two Projections, A.
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]*,

**Threading Fundamental Matrices**,

*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

*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 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
BibRef
**9500**

*Shashua, A.*,

**Trilinearity in Visual Recognition by Alignment**,

*ECCV94*(A:479-484).

Springer DOI
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.
**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

DOI Link

relative pose estimation from image point and line triplets. BibRef

*Schindler, G.[Grant]*,
*Krishnamurthy, P.[Panchapagesan]*,
*Dellaert, F.[Frank]*,

**Line-Based Structure from Motion for Urban Environments**,

*3DPVT06*(846-853).

IEEE DOI
**0606**

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
**0606**

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**

*Quan, L.[Long]*,
*Lhuillier, M.*,

**Structure from motion from three affine views**,

*ICPR02*(IV: 1-6).

IEEE DOI
**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 DOI
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).

Springer DOI
**9909**

BibRef

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

Motion Estimates Using 4 Frames .

Last update:Jun 1, 2023 at 10:05:03