17.2.4 Optical Flow Field Computation -- Gradient Techniques

Nagel, H.H.[Hans-Hellmut],
Displacement Vectors Derived from Second-Order Intensity Variations in Image Sequences,
CVGIP(21), No. 1, January 1983, pp. 85-117.
WWW Version. Computing the motion of corners by studying the equations for the intensity with respect to time. This gives a closed form solution to the motion problem. Another version is in the Munich paper. This paper shows that the See also Determining Optical Flow. method is a special case of this one. This takes the gradient approaches ( See also Gradient Based Estimation of Disparity. ) to their logical conclusion. BibRef 8301

Nagel, H.H., and Enkelmann, W.,
Investigation of Second Order Greyvalue Variations to Estimate Corner Point Displacements,
ICPR82(768-773). Corner points are computed and a method of computing the displacements is given. This is one step in computing the optic flow. The displacements can be computed directly from the neighborhood averages of the differences (minimize an integral (sum) and force the math through). See also Displacement Vectors Derived from Second-Order Intensity Variations in Image Sequences. for other information. BibRef 8200

Subbarao, M.[Muralidhara],
Interpretation of Image Flow: Rigid Curved Surfaces in Motion,
IJCV(2), No. 1, June 1988, pp. 77-96.
WWW Version. BibRef 8806
Earlier:
Solution and Uniqueness of Image Flow Equations for rigid Curved Surfaces in Motion,
ICCV87(687-692). Similar to the other closed from solution papers. BibRef

Subbarao, M.[Muralidhara],
Interpretation of Image Flow: A Spatio-Temporal Approach,
PAMI(11), No. 3, March 1989, pp. 266-278.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8903
Earlier:
Interpretation of Image Motion Fields: A Spatio-Temporal Approach,
Motion86(157-165). A study of what information is there and how to get it. More equations. BibRef

Subbarao, M.,
Interpretation of Visual Motion: A Computational Study,
Los Altos: Morgan Kaufmann1988. BibRef 8800 Bookfrom his thesis. BibRef

Zhao, W.Z., Qi, F.H., Yang, T.Y.,
Dynamic Estimation of Optical Flow Field Using Objective Functions,
IVC(7), No. 4, November 1989, pp. 259-267.
WWW Version. BibRef 8911

Verri, A., Girosi, F., and Torre, V.,
Differential Techniques for Optical Flow,
JOSA-A(7), No 5, May 1990, pp. 912-922. BibRef 9005

de Micheli, E., Torre, V., and Uras, S.,
The Accuracy of the Computation of Optical Flow and the Recovery of Motion Parameters,
PAMI(15), No. 5, May 1993, pp. 434-447.
IEEE Abstract. IEEE Top Reference.
WWW Version. See also Computational Approach to Motion Perception, A. Produce vector fields and recover motion parameters (time to collision) from reduced images or a single scanline near the FOE. BibRef 9305

Girosi, F., Verri, A., and Torre, V.,
Constraints for the Computation of Optical Flow,
Motion89(116-124). BibRef 8900

Verri, A., Girosi, F., and Torre, V.,
Mathematical Properties of the 2D Motion Field: From Singular Points to Motion Parameters,
Motion89(190-200). BibRef 8900

Schunck, B.G.[Brian],
Robust Estimation of Image Flow,
SPIE(1198), Sensor Fusion II: Human and Machine Strategies, 1989, pp. 116-127. BibRef 8900

Schunck, B.G.[Brian],
Image Flow: Fundamentals and Future Research,
CVPR85(560-571). (GM Research Labs) Invited talk. Discusses the current view of image flow analysis, and some of the past problems. BibRef 8500

Schunck, B.G.,
Image Flow Continuity Equations for Motion and Density,
Motion86(89-94). A continuing attempt to understand flow, either in the image values or in feature density. BibRef 8600

Schunck, B.G.,
The Image Flow Constraint Equation,
CVGIP(35), No. 1, July 1986, pp. 20-46.
WWW Version. BibRef 8607
Earlier:
The Motion Constraint Equation for Optical Flow,
ICPR84(20-22). A cleaner discussion than his earlier papers of the equations, with some discussion of boundaries and discontinuities. BibRef

Heeger, D.J.,
Optical Flow Using Spatiotemporal Filters,
IJCV(1), No. 4, January 1988, pp. 279-302).
WWW Version. BibRef 8801
Earlier: ICCV87(181-190). Award, Marr Prize. BibRef
And:
Model for the Extraction of Image Flow,
JOSA-A(2), No. 2, 1987, pp. 1455-1471. BibRef
And:
A Model for the Extraction of Image Flow,
ICCV87(181-190). BibRef
Earlier:
Depth and Flow from Motion Energy,
AAAI-86(657-663). Based on a biological model of motion perception, a set of filters are applied to the image. BibRef

Chen, H.J., Shirai, Y., and Asada, M.,
Obtaining Optical Flow with Multi-Orientation Filters,
CVPR93(736-737).
IEEE Abstract. IEEE Top Reference. BibRef 9300

Weber, J.[Joseph], Malik, J.[Jitendra],
Robust Computation of Optical-Flow in a Multiscale Differential Framework,
IJCV(14), No. 1, January 1995, pp. 67-81.
WWW Version. BibRef 9501
Earlier: ICCV93(12-20).
WWW Version. BibRef
And: UCBCSD-92-709, 1992. First use a set of filters and combine the different estimates. BibRef

Adelson, E.H., and Bergen, J.R.[James R.],
Spatiotemporal Energy Models for the Perception of Motion,
JOSA-A(2), No. 2, 1985, pp. 284-299. BibRef 8500
And:
The Extraction of Spatio-Temporal Energy in Human and Machine Vision,
Motion86(151-155). BibRef

Hadani, I., and Barta, E.,
The Hybrid Constraint Equation for Motion Extraction,
IVC(7), No. 3, August 1989, pp. 217-224.
WWW Version. BibRef 8908

Colombo, C., del Bimbo, A., Santini, S.,
Optical-Flow by Nonlinear Relaxation,
PR(28), No. 7, July 1995, pp. 977-988. BibRef 9507
And:
WWW Version.
Optical-Flow Through Relaxation in the Velocity Space,
PRL(15), No. 4, April 1994, pp. 373-382. BibRef

Taalebinezhaad, M.A.,
Direct Recovery of Motion and Shape in the General Case by Fixation,
PAMI(14), No. 8, August 1992, pp. 847-853.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9208
Earlier: ICCV90(451-455).
WWW Version. BibRef
And: MIT AI Memo-1187, March 1990. BibRef
And:
Partial Implementation of the Fixation Method on Real Images: Direct Recovery of Motion and Shape in the General Case,
CVPR91(400-405).
IEEE Abstract. IEEE Top Reference. BibRef
And:
FIXATION: A Direct Method for Recovery of Motion and Shape in the General Case,
DARPA90(284-291). Gradient approach to OF computation. BibRef

Taalebinezhaad, M.A.[M. Ali],
Robot Motion Vision by Fixation,
MIT AI-TR-1384, September 1992.
WWW Version. BibRef 9209

Taalebinezhaad, M.A.[M. Ali],
Autonomous Fixation,
CVPR92(744-747).
IEEE Abstract. IEEE Top Reference. BibRef 9200
And:
Autonomous Motion Vision,
ICPR92(I:232-235).
WWW Version. BibRef
And:
Towards Autonomous Motion Vision,
MIT AI Memo-1334, April 1992.
WWW Version. BibRef

Taalebinezhaad, M.A.[M. Ali],
Visual Tracking,
MIT AI Memo-1382, October 1992.
WWW Version. BibRef 9210

Efstratiadis, S.N., Katsaggelos, A.K.,
Nonstationary AR modeling and constrained recursive estimation of the displacement field,
CirSysVideo(2), No. 4, December 1992, pp. 334-346.
IEEE Top Reference. 0206 BibRef

Brailean, J.C., Katsaggelos, A.K.,
A Recursive Nonstationary Map Displacement Vector Field Estimation Algorithm,
IP(4), No. 4, April 1995, pp. 416-429.
WWW Version. BibRef 9504
And:
Noise robust spatial gradient estimation for use in displacement estimation,
ICIP95(I: 211-214).
WWW Version. 9510 BibRef

Brailean, J.C., Katsaggelos, A.,
Recursive MAP Displacement Field Estimation and Its Applications,
ICIP96(I: 917-920).
WWW Version. BibRef 9600

Tistarelli, M.,
Multiple Constraints to Compute Optical-Flow,
PAMI(18), No. 12, December 1996, pp. 1243-1250.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9701Differential constraints correspond to feature tracking. Considers multiple points and a constant acceleration motion model. BibRef

Tistarelli, M.,
Computation of Optical Flow and Its Derivatives from Local Differential Constraints,
SCV95(19-24).
IEEE Top Reference. U. of Genoa. BibRef 9500

Tistarelli, M.[Massimo],
Computation of Coherent Optical Flow by Using Multiple Constraints,
ICCV95(263-268).
WWW Version.
WWW Version. BibRef 9500
Earlier:
Multiple Constraints for Optical Flow,
ECCV94(A:61-70).
WWW Version. BibRef

Bainbridge-Smith, A., Lane, R.G.,
Determining Optical-Flow Using a Differential Method,
IVC(15), No. 1, January 1997, pp. 11-22.
WWW Version. 9702 BibRef

Brandt, J.W.,
Improved Accuracy in Gradient Based Optical Flow Estimation,
IJCV(25), No. 1, October 1997, pp. 5-22.
WWW Version. 9710 BibRef
Earlier:
Finite-differencing errors in gradient-based optical flow estimation,
ICIP94(II: 775-779).
WWW Version. 9411 BibRef

Elad, M., Feuer, A.,
Recursive Optical Flow Estimation: Adaptive Filtering Approach,
JVCIR(9), 1998, pp. 119-138. BibRef 9800

Christmas, W.J.,
Filtering Requirements for Gradient-Based Optical Flow Measurement,
IP(9), No. 10, October 2000, pp. 1817-1820.
WWW Version. 0010 BibRef
Earlier:
Spatial Filtering Requirements for Gradient-based Optical Flow Measurement,
BMVC98(xx-yy). BibRef

Lai, S.H.[Shang-Hong], Vemuri, B.C.[Baba C.],
Reliable and Efficient Computation of Optical Flow,
IJCV(29), No. 2, August-September 1998, pp. 87-105.
WWW Version. 0010 BibRef

Lai, S.H., Vemuri, B.C.,
Robust and Efficient Algorithms for Optical Flow Computation,
SCV95(455-460).
IEEE Top Reference. University of Florida. A gradient-based approach and a SSD approach. BibRef 9500

Simoncelli, E.P.,
Bayesian Multi-scale Differential Optical Flow,
HCVA99(II: 397-422). Coarse to fine, Kalman Filter.
HTML Version. BibRef 9900
Earlier: WIMSP93(128-129). BibRef
Coarse-to-fine Estimation of Visual Motion,

Postscript Version. BibRef

Nestares, O., Navarro, R.,
Probabilistic estimation of optical flow in multiple band-pass directional channels,
IVC(19), No. 6, April 2001, pp. 339-351.
WWW Version. 0105 BibRef

Haussecker, H.W.[Horst W.], Fleet, D.J.[David J.],
Computing Optical Flow with Physical Models of Brightness Variation,
PAMI(23), No. 6, June 2001, pp. 661-673.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0106 BibRef
Earlier: CVPR00(II: 760-767).
IEEE Abstract. IEEE Top Reference.
WWW Version. 0005Do not rely on brightness constancy. Use a model of how it will vary. BibRef

Haussecker, H.W.[Horst W.],
Simultaneous Estimation of Optical Flow and Heat Transport in Infrared Image Sequences,
CVBVS00(85).
WWW Version. 0006 BibRef

Gautama, T., van Hulle, M.M.[Marc M.], M. (2002).
A Phase-based Approach to the Estimation of the Optical Flow Field Using Spatial Filtering,
TNN(13), No. 5, 2002, pp. 1127-1136. BibRef 0200

Arredondo, M.A., Lebart, K., Lane, D.,
Optical flow using textures,
PRL(25), No. 4, March 2004, pp. 449-457.
WWW Version. 0402Combine results of texture and intensity. BibRef

Burgi, P.Y.[Pierre-Yves],
Motion estimation based on the direction of intensity gradient,
IVC(22), No. 8, August 2004, pp. 637-653.
WWW Version. 0405 BibRef

Elad, M.[Michael], Teo, P.[Patrick], Hel-Or, Y.[Yacov],
On the Design of Filters for Gradient-Based Motion Estimation,
JMIV(23), No. 3, November 2005, pp. 345-365.
WWW Version. 0510 BibRef
Earlier:
Optimal Filters for Gradient-based Motion Estimation,
ICCV99(559-565).
WWW Version. BibRef

Lu, Q.H.[Qing-Hua], Zhang, X.M.[Xian-Min],
Robust multiscale algorithms for gradient-based motion estimation,
IJIST(17), No. 6, 2007, pp. 333-340.
WWW Version. 0804 BibRef

Wietzke, L.[Lennart], Sommer, G.[Gerald],
The Conformal Monogenic Signal,
DAGM08(xx-yy).
WWW Version. 0806 BibRef

Wietzke, L.[Lennart], Sommer, G.[Gerald], Schmaltz, C.[Christian], Weickert, J.[Joachim],
Differential Geometry of Monogenic Signal Representations,
RobVis08(454-465).
WWW Version. 0802 BibRef

Zang, D.[Di], Wietzke, L.[Lennart], Schmaltz, C.[Christian], Sommer, G.[Gerald],
Dense Optical Flow Estimation from the Monogenic Curvature Tensor,
SSVM07(239-250).
WWW Version. 0705 BibRef

Koeser, K.[Kevin], Perwass, C.[Christian], Sommer, G.[Gerald],
Dense Optic Flow with a Bayesian Occlusion Model,
SCVMA04(127-139).
WWW Version. 0405 BibRef

Guo, X.X.[Xiao-Xin], Xu, Z.W.[Zhi-Wen], Feng, Y.[Yueping], Wang, Y.[Yunxiao], Wang, Z.[Zhengxuan],
Optical Flow Computation with Fourth Order Partial Differential Equations,
SSPR06(279-286).
WWW Version. 0608 BibRef

Lee, T.[Teahyung], Anderson, D.V.,
Checkerboard-Type Filtering for a Low-Power Gradient-Based Optical Flow Estimation System,
ICIP06(3285-3288). 0610
WWW Version. BibRef

Salgado, A., Sanchez, J.,
A Temporal Regularizer for Large Optical Flow Estimation,
ICIP06(1233-1236). 0610
WWW Version. BibRef

van de Weijer, J., Gevers, T.,
Robust optical flow from photometric invariants,
ICIP04(III: 1835-1838).
WWW Version. 0505 See also Edge and Corner Detection by Photometric Quasi-Invariants. BibRef

Sun, S., Haynor, D., Kim, Y.,
Motion Estimation Based on Optical Flow with Adaptive Gradients,
ICIP00(Vol I: 852-855).
IEEE Abstract. IEEE Top Reference. 0008 BibRef

Ng, L.,
Selecting the Neighbourhood Size, Shape, Weights and Model Order in Optical Flow Estimation,
ICIP00(Vol III: 600-603).
IEEE Abstract. IEEE Top Reference. 0008 BibRef

Ohta, N.[Naoya],
Optical flow detection using a general noise model for gradient constraint,
CAIP97(669-676).
WWW Version. 9709 BibRef

Niessen, W.J., Duncan, J.S., Florack, L.M.J., ter Haar Romeny, B.M., Viergever, M.A.,
Spatiotemporal Operators and Optic Flow,
PBMCV95(SESSION 3) BibRef 9500

Jiang, M., Wu, Z.Q., Wu, Y.S.,
Recursively Estimating Optical Flow from a Noisy Image Sequence,
ICPR88(II: 888-890).
WWW Version.
IEEE Top Reference. BibRef 8800

Liu, W., Liu, J., Wan, F.,
The Theorem Analysis on Optical Flow Estimation from Three Frames of Image Sequences,
ICPR88(II: 1103-1105).
WWW Version.
IEEE Top Reference. BibRef 8800

Tretiak, O.J., Pastor, L.,
Velocity Estimation from Image Sequences with Second Order Differential Operators,
ICPR84(16-19). BibRef 8400

Chapter on Optical Flow Field Computations and Use continues in
Optical Flow for Simple Motions .