## Performance of optical flow techniques (1994)

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Venue: | INTERNATIONAL JOURNAL OF COMPUTER VISION |

Citations: | 1055 - 32 self |

### BibTeX

@ARTICLE{Barron94performanceof,

author = {J. L. Barron and D. J. Fleet and S. S. Beauchemin},

title = {Performance of optical flow techniques},

journal = {INTERNATIONAL JOURNAL OF COMPUTER VISION},

year = {1994},

volume = {12},

pages = {43--77}

}

### Years of Citing Articles

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### Abstract

While different optical flow techniques continue to appear, there has been a lack of quantitative evaluation of existing methods. For a common set of real and synthetic image sequences, we report the results of a number of regularly cited optical flow techniques, including instances of differential, matching, energy-based and phase-based methods. Our comparisons are primarily empirical, and concentrate on the accuracy, reliability and density of the velocity measurements; they show that performance can differ significantly among the techniques we implemented.

### Citations

1985 | T.: An iterative image registration technique with an application to stereo vision. International joint conference on artificial intelligence 3 - LUCAS, KANADE - 1981 |

1747 | Determining optical flow - HORN, SCHUNCK - 1981 |

1406 | Robot vision - Horn - 1986 |

1021 | The laplacian pyramid as a compact image code
- Burt, Adelson
- 1983
(Show Context)
Citation Context ... matching strategy. The Laplacian 3 In the original paper [57] the authors used standard deviations of 5 in space and 1 frame in time.sBarron, Fleet and Beauchemin IJCV 12:1, pp43-77, 1994 10 pyramid =-=[13]-=- allows the computation of large displacements between frames and helps to enhance image structure, such as edges, that is often thought to be important. We begin at the coarsest level where displacem... |

854 | Theory of edge detection
- Marr, Hildreth
(Show Context)
Citation Context ...et and Jepson [20, 23]. Waxman, Wu and Bergholm Waxman, Wu and Bergholm [61] apply spatiotemporal lters to binary edge maps to track edges in real-time. Edge maps E(x� t), based on DOG zero-crossings =-=[42]-=-, are smoothed with a Gaussian lter to create a convected activation pro le A(x� t): A(x� t) = G(x�t� x� y� t) E(x� t) : (2.29) Level contours of A(x� t) are then tracked using di erential methods. Ho... |

596 | Spatiotemporal energy models for the perception of motion.” J Opt Soc Am
- Adelson, Bergen
- 1985
(Show Context)
Citation Context ...echniques is based on the output energy of velocity-tuned lters [2, 7, 11, 27, 30, 34]. These are also called frequency-based methods owing to the design of velocity-tuned lters in the Fourier domain =-=[1, 23, 49, 59]-=-. The Fourier transform of a translating 2-d pattern (2.1) is ^I(k� !) = ^ I 0(k) (! + v T k) � (2.25) where ^ I 0(k) istheFourier transform of I(x� 0), (k) is a Dirac delta function, ! denotes tempor... |

452 |
computational framework and an algorithm for the measurement of visual motion
- Anandan, “A
- 1989
(Show Context)
Citation Context ...11 In what follows we summarize our main results, concentrating on the techniques that produced reasonably good results, namely, those of Fleet and Jepson [20, 23], Lucas and Kanade [41, 40], Anandan =-=[5, 6]-=-, Uras et al. [57] and Singh [54, 55]. Further quantitative details on the con dence measures can be found in [9]. With respect to rst-order di erential methods, there are several points of interest. ... |

298 | A.: Computation of component image velocity from local phase information - FLEET, JEPSON - 1990 |

216 |
An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences
- Nagel, Enkelmann
- 1986
(Show Context)
Citation Context ...cessfully [60, 20]. The second approach uses global smoothness constraints (regularization) in which thevelocity eld is de ned implicitly in terms of the minimum of a functional de ned over the image =-=[32, 43, 44, 46]-=-. Of course, one requirement of di erential techniques is that I(x� t)must be di erentiable. This implies that temporal smoothing at the sensors is needed to avoid aliasing and that numerical di erent... |

178 | Probability distributions of optical flow - Simoncelli, Adelson, et al. |

171 |
Model of human visual-motion sensing
- Watson, Ahumada, et al.
- 1985
(Show Context)
Citation Context ...echniques is based on the output energy of velocity-tuned lters [2, 7, 11, 27, 30, 34]. These are also called frequency-based methods owing to the design of velocity-tuned lters in the Fourier domain =-=[1, 23, 49, 59]-=-. The Fourier transform of a translating 2-d pattern (2.1) is ^I(k� !) = ^ I 0(k) (! + v T k) � (2.25) where ^ I 0(k) istheFourier transform of I(x� 0), (k) is a Dirac delta function, ! denotes tempor... |

169 | Passive Navigation
- Bruss, Horn
- 1983
(Show Context)
Citation Context ...normal velocity since there is growing interest in the use of normal velocity, thereby side-stepping some of the assumptions inherent incurrent methods for integrating measurements to nd 2-d velocity =-=[3, 4, 10, 16, 33, 47]-=-. We have used both real and synthetic image sequences to test the techniques. In both cases however, we have chosen sequences that are not severely corrupted by spatial or temporal aliasing. This ena... |

145 | Optical flow using spatiotemporal filters - Heeger - 1987 |

144 |
Velocity determination in scenes containing several moving objects
- C, Thompson
- 1979
(Show Context)
Citation Context ...rom spatiotemporal derivatives of image intensity or ltered versions of the image (using low-pass or band-pass lters). The rst instances used rst-order derivatives and were based on image translation =-=[19, 32, 43]-=-, i.e. I(x� t) = I(x ; v t� 0) � (2.1) where v =(u� v) T . From a Taylor expansion of (2.1) [32] or more generally from an assumption that intensity is conserved, dI(x� t)=dt =0,thegradient constraint... |

135 | On the estimation of optical flow: Relations between different approaches and some new results - Nagel - 1987 |

130 | Model for the extraction of image flow - Heeger - 1987 |

111 |
Displacement vectors derived from second-order intensity variations in image sequences
- Nagel
- 1983
(Show Context)
Citation Context ...rom spatiotemporal derivatives of image intensity or ltered versions of the image (using low-pass or band-pass lters). The rst instances used rst-order derivatives and were based on image translation =-=[19, 32, 43]-=-, i.e. I(x� t) = I(x ; v t� 0) � (2.1) where v =(u� v) T . From a Taylor expansion of (2.1) [32] or more generally from an assumption that intensity is conserved, dI(x� t)=dt =0,thegradient constraint... |

98 |
Rotationally invariant image operators
- Beaudet
- 1978
(Show Context)
Citation Context ...nts are then computed by nding the minimum of a quadratic approximation to the SSD surface (about the minimum SSD value found with integer displacements d). As suggested by Anandan, Beaudet operators =-=[12]-=- were used to estimate the quadratic surface parameters. Con dence measures, cmin and cmax, are derived from the principle curvatures, Cmin and Cmax, oftheSSDsurface at the minimum: cmax = Cmax k 1 + ... |

97 |
Measurement of Image Velocity
- Fleet
- 1992
(Show Context)
Citation Context ...-based techniques, namely those of Horn and Schunck [32], Lucas and Kanade [40, 41], Uras et al. [57], Nagel [44], Anandan [5, 6], Singh [54, 55], Heeger [30], Waxman et al. [61] and Fleet and Jepson =-=[20, 23]-=-. Despite their di erences, many of these techniques can be viewed conceptually in terms of three stages of processing: 1. pre ltering or smoothing with low-pass/band-pass lters in order to extract si... |

92 |
V.: A computational approach to motion perception
- Uras, Girosi, et al.
- 1988
(Show Context)
Citation Context ...ne techniques including instances of di erential methods, region-based matching, energy-based and phase-based techniques, namely those of Horn and Schunck [32], Lucas and Kanade [40, 41], Uras et al. =-=[57]-=-, Nagel [44], Anandan [5, 6], Singh [54, 55], Heeger [30], Waxman et al. [61] and Fleet and Jepson [20, 23]. Despite their di erences, many of these techniques can be viewed conceptually in terms of t... |

78 | Optical flow estimation: an error analysis of gradient-based methods with local optimization - Kearney, Thompson, et al. |

76 |
Determining optical ow
- Horn, Schunk
- 1981
(Show Context)
Citation Context ...rage relative errors of 10%{20%, and average angular errors of 7 {12 in the best cases. More recently, Willick andYang [62] have examined the merits of the gradient constraint usedby Horn and Schunck =-=[32]-=- compared to the constraints suggested by Schunck [50, 51] and Nagel [45]. Of these three, they argue that the original gradient constraint is superior. This paper reports a comparison of widely cited... |

71 | Stability of phase information - Fleet, Jepson - 1993 |

69 | A model for the estimate of local image velocity by cells in the visual cortex - Grzywacz, Yuille - 1990 |

68 |
Measuring visual motion from image sequences
- Anandan
- 1987
(Show Context)
Citation Context ...stances of di erential methods, region-based matching, energy-based and phase-based techniques, namely those of Horn and Schunck [32], Lucas and Kanade [40, 41], Uras et al. [57], Nagel [44], Anandan =-=[5, 6]-=-, Singh [54, 55], Heeger [30], Waxman et al. [61] and Fleet and Jepson [20, 23]. Despite their di erences, many of these techniques can be viewed conceptually in terms of three stages of processing: 1... |

67 |
Surface orientation and time to contact from image divergence and deformation
- Cipolla, Blake
- 1992
(Show Context)
Citation Context ...normal velocity since there is growing interest in the use of normal velocity, thereby side-stepping some of the assumptions inherent incurrent methods for integrating measurements to nd 2-d velocity =-=[3, 4, 10, 16, 33, 47]-=-. We have used both real and synthetic image sequences to test the techniques. In both cases however, we have chosen sequences that are not severely corrupted by spatial or temporal aliasing. This ena... |

67 | Optic flow computation: a unified perspective - Singh - 1991 |

61 | Distributed Representation and Analysis of Visual Motion - Simoncelli - 1993 |

52 |
The extraction of spatiotemporal energy in human and machine vision
- Adelson, Bergen
- 1986
(Show Context)
Citation Context ...ions. Results from both the original and our modi ed method are reported below.sBarron, Fleet and Beauchemin IJCV 12:1, pp43-77, 1994 6 Lucas and Kanade Following Lucas and Kanade [41, 40] and others =-=[2, 37, 52, 53]-=-, we implemented a weighted least-squares (LS) t of local rst-order constraints (2.2) to a constant model for v in each small spatial neighbourhood by minimizing X x2 W 2 (x)[rI(x� t) v + It(x� t)] 2 ... |

50 |
Performance of optical ow techniques
- Barron, Fleet, et al.
- 1992
(Show Context)
Citation Context ... 0:21 26.8% Table 4.4: Summary of the Translating Tree 2D Velocity Results. ing the testing of these gradient-based methods and some changes that occurred since we reported our preliminary results in =-=[8, 9]-=-. Our initial implementation quantized the Gaussian smoothed image sequence with 8-bit/pixel for storage, prior to the subsequent gradient computation and least-squares minimization, causing relativel... |

48 |
An estimation-theoretic framework for image-flow computation
- Singh
- 1990
(Show Context)
Citation Context ...erential methods, region-based matching, energy-based and phase-based techniques, namely those of Horn and Schunck [32], Lucas and Kanade [40, 41], Uras et al. [57], Nagel [44], Anandan [5, 6], Singh =-=[54, 55]-=-, Heeger [30], Waxman et al. [61] and Fleet and Jepson [20, 23]. Despite their di erences, many of these techniques can be viewed conceptually in terms of three stages of processing: 1. pre ltering or... |

44 | Against quantitative optic flow - Verri, Poggio - 1987 |

40 | Generalized image matching by the method of differences - Lucas - 1984 |

39 |
Velocity estimation from image sequences with second order differential operators
- O, Pastor
- 1984
(Show Context)
Citation Context ...y to solve for both components of v.sBarron, Fleet and Beauchemin IJCV 12:1, pp43-77, 1994 4 Second-order di erential methods use second-order derivatives (the Hessian of I) to constrain 2-d velocity =-=[43, 44, 56, 57]-=-: 2 4 Ixx(x� t) Iyx(x� t) Ixy(x� t) Iyy(x� t) 3 5 0 @ v 1 v 2 1 A + 0 @ Itx(x� t) Ity(x� t) 1 A = 0 @ 0 0 1 A : (2.4) Equation (2.4) can be derived from (2.1) or from the conservation of rI(x� t), drI... |

38 |
Multidimensional orientation estimation with applications to texture analysis and optical flow
- Bign, Granlund, et al.
- 1991
(Show Context)
Citation Context ...rom step 1 (2.19), with a threshold based on the largest eigenvalue of Sc (2.20). 2.3 Energy-Based Methods A third class of optical ow techniques is based on the output energy of velocity-tuned lters =-=[2, 7, 11, 27, 30, 34]-=-. These are also called frequency-based methods owing to the design of velocity-tuned lters in the Fourier domain [1, 23, 49, 59]. The Fourier transform of a translating 2-d pattern (2.1) is ^I(k� !) ... |

37 | The computation of the velocity field - Hildreth - 1984 |

34 |
On a constraint equation for the estimation of displacement rates in image sequences
- Nagel
- 1989
(Show Context)
Citation Context ...he best cases. More recently, Willick andYang [62] have examined the merits of the gradient constraint usedby Horn and Schunck [32] compared to the constraints suggested by Schunck [50, 51] and Nagel =-=[45]-=-. Of these three, they argue that the original gradient constraint is superior. This paper reports a comparison of widely cited optical ow methods. We implemented nine techniques including instances o... |

31 | Adaptive multidimensional filtering
- Haglund
- 1992
(Show Context)
Citation Context ...rom step 1 (2.19), with a threshold based on the largest eigenvalue of Sc (2.20). 2.3 Energy-Based Methods A third class of optical ow techniques is based on the output energy of velocity-tuned lters =-=[2, 7, 11, 27, 30, 34]-=-. These are also called frequency-based methods owing to the design of velocity-tuned lters in the Fourier domain [1, 23, 49, 59]. The Fourier transform of a translating 2-d pattern (2.1) is ^I(k� !) ... |

29 |
Subspace methods for recovering rigid motion
- Heeger, Jepson
- 1992
(Show Context)
Citation Context ...ure require that velocity measurements be accurate and dense, providing a close approximation to the 2-d motion eld. Current techniques require that relative errors in the optical ow be less than 10% =-=[10, 36]-=-. Verri and Poggio [58] have suggested that accurate estimates of the 2-d motion eld are generally inaccessible due to inherent di erences between the 2-d motion eld and intensity variations, while ot... |

25 | Multi-resolution flow through motion analysis - Burt - 1984 |

23 |
Direct processing of curvilinear sensor motion from a sequence of perspective images
- Aloimonas, Brown
(Show Context)
Citation Context ...normal velocity since there is growing interest in the use of normal velocity, thereby side-stepping some of the assumptions inherent incurrent methods for integrating measurements to nd 2-d velocity =-=[3, 4, 10, 16, 33, 47]-=-. We have used both real and synthetic image sequences to test the techniques. In both cases however, we have chosen sequences that are not severely corrupted by spatial or temporal aliasing. This ena... |

21 | Analysis of differential and matching methods for optical flow - Little, Verri - 1989 |

18 | Convected activation profiles and receptive fields for real time measurement of short range visual motion - AM, Wu, et al. - 1988 |

17 |
Optical ow using spatiotemporal lters
- Heeger
- 1988
(Show Context)
Citation Context ... region-based matching, energy-based and phase-based techniques, namely those of Horn and Schunck [32], Lucas and Kanade [40, 41], Uras et al. [57], Nagel [44], Anandan [5, 6], Singh [54, 55], Heeger =-=[30]-=-, Waxman et al. [61] and Fleet and Jepson [20, 23]. Despite their di erences, many of these techniques can be viewed conceptually in terms of three stages of processing: 1. pre ltering or smoothing wi... |

17 |
Contour evolution, neighbourhood deformation and global image flow: Planar surfaces in motion
- Waxman, Wohn
- 1985
(Show Context)
Citation Context ... accomplish this: The rst method ts the measurements in each neighbourhood to a local model for 2-d velocity (e.g. a low-order polynomial model), using least-squares minimization or a Hough transform =-=[19, 37, 41, 54, 60]-=-. Usually v(x) is taken to be constant, although linear models for v(x) have been used successfully [60, 20]. The second approach uses global smoothness constraints (regularization) in which theveloci... |

15 |
Active egomotion estimation: A qualitative approach
- Aloimonos, Duric
- 1992
(Show Context)
Citation Context ... Poggio [58] have suggested that accurate estimates of the 2-d motion eld are generally inaccessible due to inherent di erences between the 2-d motion eld and intensity variations, while others (e.g. =-=[4]-=-) argue that the measurement of optical ow is an ill-posed problem. For these reasons it has been suggested that only qualitative information can be extracted. Many methods for computing optical ow ha... |

15 | Computation of optic flow from the motion of edge features in image squcnces - Buxton, Buxton - 1985 |

15 | Parallel optical flow using local voting - Little, Bulthoff, et al. - 1988 |

14 |
Probability distributions of optical ow
- Simoncelli, Adelson, et al.
- 1991
(Show Context)
Citation Context ...ions. Results from both the original and our modi ed method are reported below.sBarron, Fleet and Beauchemin IJCV 12:1, pp43-77, 1994 6 Lucas and Kanade Following Lucas and Kanade [41, 40] and others =-=[2, 37, 52, 53]-=-, we implemented a weighted least-squares (LS) t of local rst-order constraints (2.2) to a constant model for v in each small spatial neighbourhood by minimizing X x2 W 2 (x)[rI(x� t) v + It(x� t)] 2 ... |

14 | The motion constraint equation for the optical flow - Schunck - 1984 |