Beauchemin, S.S.[Steven S.],
Barron, J.L.[John L.],
The Computation of Optical-Flow,
Surveys(27), No. 3, September 1995, pp. 433-467.
DOI Link Survey, Optic Flow. BibRef 9509
The Perception of the Visual World,
Boston: Houghton Mifflin1955. ?? BibRef 5500 BookBasic perception book where optical flow is formally introduced. BibRef
Optical Motion and Transformations as Stimuli for Visual Perceptions,
PsychR(64), No. 5, 1957, pp. 288-295. BibRef 5700
What Gives Rise to the Perception of Motion?,
PsychR(75), No. 4, 1968, pp. 335-346. BibRef 6800
Limb, J.O., and
Estimating Velocity of Moving Images in Television Signals,
CGIP(4), No. 4, December 1975, pp. 311-327.
Elsevier DOI BibRef 7512
Measuring the Speed of Moving Objects from Television Signals,
Commun(23), No. 4, April 1975, pp. 474-478. Early gradient based method for computation directly from image measurements. The basic results here are that velocity estimates work only for single moving objects. Essentially the subpixel interpolation of the correlation peak in the matchpoint neighborhood. See also Source-Receiver Encoding of Television Signals. BibRef
Cafforio, C., and
Methods for Measuring Small Displacements of Television Images,
IT(22), No. 5 September, 1976, pp. 573-579. BibRef 7609
Tracking Moving Objects in Television Images,
SP(1), 1979, pp. 133-140. BibRef 7900
Remarks on the Differential Method for the Estimation of Movement in Television Images,
SP(4), 1982, pp. 45-52. BibRef 8200
Cafforio, C., and
The Differential Method for Image Motion Estimation,
ISPDSA83(104-124). BibRef 8300
Horn, B.K.P., and
Determining Optical Flow,
AI(17), No. 1-3, August 1981, pp. 185-203.
Elsevier DOI BibRef 8108
Earlier: DARPA81(144-156). BibRef
And: MIT AI Memo-572, April 1980.
WWW Link. Optical Flow. The standard reference for original optical flow equation computations. The exact formulations are not quite right since they only work in special cases. BibRef
Constraints on Optical Flow Computation,
PRIP81(205-210). BibRef 8100
Horn, B.K.P.[Berthold K.P.],
Determining Optical Flow: A Retrospective,
AI(59), No. 1-2, January 1993, pp. 81-87.
Elsevier DOI Original paper important because it started the variational approach to optical flow and other vision problems. BibRef 9301
Experimental Evaluation of Motion Constraint Equations,
CVGIP(54), No. 2, September 1991, pp. 206-214.
Elsevier DOI Evaluate See also Determining Optical Flow. See also Motion Constraint Equation for Optical Flow, The. and See also On a Constraint Equation for the Estimation of Displacement Rates in Image Sequences. constraint equations and conclude that the original was the best for optical flow. BibRef 9109
Longuet-Higgins, H.C., and
The Interpretation of a Moving Retinal Image,
RoyalP(B-208), 1980, pp. 385-397. Optical Flow. An early formulation of the flow pattern with rotation and translation. See also Multiple Interpretations of a Pair of Images of a Surface. BibRef 8000
The Interpretation of Visual Motion,
Cambridge: MIT Press1979. BibRef 7900 Ph.D.Thesis (EE). His thesis as a BibRef Book Relaxation. A network of points are generated for each image with a relaxation based matching scheme applied to find the 1-1 mapping between the views. See also Interpretation of Structure from Motion, The. BibRef
The Optical Flow of Planar Surfaces,
SV(1), 1986, pp. 263-276. BibRef 8600
And: MIT AI Memo-870, December 1985. BibRef
Against Direct Perception,
MIT AI Memo-574, March 1980. BibRef 8003
Hildreth, E.C.[Ellen C.],
Computations Underlying the Measurement of Visual Motion,
AI(23), No. 3, August 1984, pp. 309-354.
Elsevier DOI BibRef 8408
And: IU8799-146). BibRef
And: MIT AI Memo-761, March 1984. BibRef
The Measurement of Visual Motion,
Cambridge: MIT Press1983. BibRef Book BibRef
And: Add A2: Ullman, S.[Shimon], MIT AI Memo-699, December 1982. BibRef
The Computation of the Velocity Field,
RoyalP(B-221), 1984, pp. 189-220. BibRef 8400
And: MIT AI Memo-734, September 1983. See also Computing the Velocity Field along Contours. BibRef
Hildreth, E.C.[Ellen C.],
The Analysis of Visual Motion: From Computational Theory to Neuronal Mechanisms,
MIT AI Memo-919, December 1986.
WWW Link. BibRef 8612
Mitiche, A., and
A Computational Analysis of Time-Varying Images,
HPRIP86(311-332). Survey, Motion. Motion, Survey. BibRef 8600
Derivation of Optical Flow Using a Spatiotemporal-Frequency Approach,
CVGIP(38), No. 1, April 1987, pp. 29-65.
Elsevier DOI Survey, Motion. Motion, Survey. The approach includes Hildreth and Schunck. The paper has a nice survey of techniques and a lot of equations. There may be something here if you want optical flow. BibRef 8704
A Theory for Invariant Object Recognition in the Frontoparallel Plane,
PAMI(6), No. 3, May 1984, pp. 325-331. BibRef 8405
A Paradigm for Invariant Object Recognition of Brightness, Optical Flow and Binocular Disparity Images,
PRL(1), No. 1, October 1982, pp. 61-68. BibRef
On the Estimation of Optical Flow: Relations between Different Approaches and Some New Results,
AI(33), No. 3, November 1987, pp. 299-324.
Elsevier DOI Optical Flow. A unifying approach to optical flow. Nagel ( See also Displacement Vectors Derived from Second-Order Intensity Variations in Image Sequences. ), Haralick-Lee ( See also Facet Approach to Optic Flow, The. ), Tretiak-Pastor ( See also Velocity Estimation from Image Sequences with Second Order Differential Operators. ), Hildreth ( See also Computations Underlying the Measurement of Visual Motion. ). BibRef 8711
Toet, A., and
Displacement Estimates Through Adaptive Affinities,
PAMI(12), No. 7, July 1990, pp. 658-663.
IEEE DOI Replace iterative approach of See also On the Estimation of Optical Flow: Relations between Different Approaches and Some New Results. with a noniterative scheme. BibRef 9007
Motion Fields Are Hardly Ever Ambiguous,
IJCV(1), No. 3, October 1987, pp. 239-258.
Springer DOI The cases where a flow field can be ambiguous are difficult to construct and thus are not a major concern for the solution. BibRef 8710
Critical Surface Pairs and Triplets,
IJCV(3), No. 4, November 1989, pp. 293-312.
Springer DOI Where can the field have multiple interpretations. At most, for a curved surface, it is three interpretations. BibRef 8911
Multiple Interpretations of the Shape and Motion of Objects from Two Perspective Images,
PAMI(12), No. 11, November 1990, pp. 1025-1039.
IEEE DOI BibRef 9011
Ambiguities of a Motion Field,
And: MIT AI Memo-940, January 1987. Cases with ambiguous perspective motion fields are limited with know flow for all points on the surface. BibRef
Singh, A., and
Image-Flow Computation: An Estimation-Theoretic Framework and a Unified Perspective,
CVGIP(56), No. 2, September 1992, pp. 152-177.
Elsevier DOI Two categories: conservation information and neighborhood information. BibRef 9209
Incremental Estimation of Image-Flow Using a Kalman Filter,
JVCIR(3), 1992, pp. 39-57. BibRef 9200
Earlier: Motion91(36-43). BibRef
An Estimation-Theoretic Framework for Image-Flow Computation,
IEEE DOI BibRef 9000
And: DARPA90(314-328). Kalman Filter. Generate the depths from a spatio-temporal sequence. BibRef
Image-Flow Computation: An Estimation-Theoretic Framework, Unification and Integration,
MVA(4), 1991, pp. 55. BibRef 9100
Robust Computation of Image-Motion and Scene Depth,
CRA91(2730-2737). BibRef 9100
Optic Flow Computation: A Unified Perspective,
IEEE_Press1990. BibRef 9000
And: From the thesis:
Image-Flow Computation: Estimation-Theoretic Framework, Unification and Integration,
Ph.D.Thesis (CS), Columbia, Univ., May 1990. BibRef
Estimation Of Motion Vectors And Their Application To Scene Retrieval,
MVA(7), No. 3, 1994, pp. 199-208. BibRef 9400
Fitzpatrick, J.M.[J. Michael],
The Existence of Geometrical Density-Image Transformations Corresponding to Object Motion,
CVGIP(44), No. 2, November 1988, pp. 155-174.
Elsevier DOI Geometrical image transformation is identical to change in density image produced by motion of the object. (Primarily medical imagery.) BibRef 8811
Fitzpatrick, J.M.[J. Michael],
A Method for Calculating Velocity in Time Dependent Images Based on the Continuity Equation,
CVPR85(78-81). (Vanderbilt Univ.) CT or X-ray data is preferred, more equations than results. BibRef 8500
Sozou, P.D., and
New Perspectives on Optical-Flow,
PR(26), No. 8, August 1993, pp. 1125-1136.
Elsevier DOI Non-uniform medium. Refractive index changes the computation. BibRef 9308
Motion Constraint Equations Based on Constant Image Irradiance,
IVC(11), No. 9, November 1993, pp. 577-587.
Elsevier DOI BibRef 9311
Image-Processing: Flows under Min/Max Curvature and Mean-Curvature,
GMIP(58), No. 2, March 1996, pp. 127-141. Level Set Methods. BibRef 9603
Flows under Min/Max Curvature Flow and Mean Curvature: Applications in Image Processing,
Springer DOI Image enhancement, noise suppression. BibRef 9600
A Computer Vision Approach to Air-Flow Analysis,
PRL(17), No. 4, April 4 1996, pp. 369-385. 9605
A Motion Constraint Equation under Space-Varying or Time-Varying Illumination,
PRL(5), 1987, pp. 203-205. BibRef 8700
Second-Order Motion Perception in the Peripheral Visual-Field,
JOSA-A(14), No. 7, July 1997, pp. 1385-1392. 9708
Directions of Motion Fields Are Hardly Ever Ambiguous,
IJCV(26), No. 1, January 1998, pp. 5-24.
DOI Link 9804
Springer DOI BibRef
And: UMDTR3501, 1995.
WWW Link. BibRef
Anisotropies in Visual Motion Perception: A Fresh Look,
JOSA-A(15), No. 8, August 1998, pp. 2003-2011. 9808
Continuous Time Matching Constraints for Image Streams,
IJCV(28), No. 1, June 1998, pp. 85-96.
DOI Link 9807
Multilinear constraints for optical flow. See also Simplifications of Multilinear Forms for Sequences of Images. BibRef
On convergence of the Horn and Schunck optical-flow estimation method,
IP(13), No. 6, June 2004, pp. 848-852.
IEEE DOI 0406
See also Determining Optical Flow. Analyze the equations to prove convergence via both the Jacobi and the Gauss-Seidel methods. BibRef
Disambiguating Visual Motion by Form-Motion Interaction: A Computational Model,
IJCV(72), No. 1, April 2007, pp. 27-45.
Springer DOI 0001
Neural Mechanisms of Visual Flow Integration and Segregation: Insights from the Pinna-Brelstaff Illusion and Variations of It,
Springer DOI 0303
Computational model of neural mechanisms for visual flow. BibRef
Integration of Multiple Temporal and Spatial Scales for Robust Optic Flow Estimation in a Biologically Inspired Algorithm,
Springer DOI 0708
Optic Flow Integration at Multiple Spatial Frequencies: Neural Mechanism and Algorithm,
Springer DOI 0611
A Fast Biologically Inspired Algorithm for Recurrent Motion Estimation,
PAMI(29), No. 2, February 2007, pp. 246-260.
IEEE DOI 0701
Sparse coding framework to implement the method. BibRef
Sánchez Pérez, J.[Javier],
Horn-Schunck Optical Flow with a Multi-Scale Strategy,
IPOL(2012), No. 2012, pp. xx-yy.
DOI Link 1309
Code, Optical Flow. See also Determining Optical Flow. BibRef
Le Tarnec, L.,
A Proof of Convergence of the Horn-Schunck Optical Flow Algorithm in Arbitrary Dimension,
SIIMS(7), No. 1, 2014, pp. 277-293.
DOI Link 1404
See also Determining Optical Flow. BibRef
Optical flow modeling and computation: A survey,
CVIU(134), No. 1, 2015, pp. 1-21.
Elsevier DOI 1504
Survey, Optical Flow. Optical flow BibRef
A Variational Aggregation Framework for Patch-Based Optical Flow Estimation,
JMIV(56), No. 2, October 2016, pp. 280-299.
Springer DOI 1609
Sparse Aggregation Framework for Optical Flow Estimation,
Springer DOI 1506
Sahl, F.Z.[Farisi Zeyad],
Adaptive dual fractional-order variational optical flow model for motion estimation,
IET-CV(13), No. 3, April 2019, pp. 277-284.
DOI Link 1904
Revisiting Horn and Schunck: Interpretation as Gauss-newton Optimisation,
HTML Version. 1009
See also Determining Optical Flow. BibRef
Govindu, V.M.[Venu Madhav],
Revisiting the Brightness Constraint: Probabilistic Formulation and Algorithms,
Springer DOI 0608
Spatio-Temporal Approaches to Computation of Optical Flow,
HTML Version. 0209
Optical Flow Estimation Using Forward-backward Constraint Equation,
ICIP00(Vol II: 578-581).
IEEE DOI 0008
Re-examining the Optical Flow Constraint: A New Optical Flow Algorithm with Outlier rejection,
IEEE Abstract. BibRef 9900
Van Gool, L.J., and
Towards a General Framework for Feature Extraction,
IEEE DOI Merge optical flow and recognition. BibRef 9200
Chapter on Optical Flow Field Computations and Use continues in
Optical Flow Field Computation and Analysis .