## Recursive Filters for Optical Flow (1995)

Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Citations: | 38 - 1 self |

### BibTeX

@ARTICLE{Fleet95recursivefilters,

author = {David J. Fleet and Keith Langley},

title = {Recursive Filters for Optical Flow},

journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},

year = {1995},

volume = {17},

pages = {61--67}

}

### Years of Citing Articles

### OpenURL

### Abstract

: Working toward ecient (real-time) implementations of optical ow methods, we have applied simple recursive lters to achieve temporal smoothing and dierentiation of image intensity, and to compute 2d ow from component velocity constraints using spatiotemporal least-squares minimization. Accuracy in simulation is similar to that obtained in the study by Barron et al. [3], while requiring much less storage, less computation, and shorter delays. 1 Introduction Many methods exist for computing optic ow, but few currently run at frame rates on reasonably priced, conventional hardware. The goal of this paper is to outline simplications to a successful gradient-based approach that reduce computational expense with little degradation in accuracy. Our specic concerns include temporal smoothing and dierentiation of image intensity, and temporal integration of component velocity constraints to solve for 2d velocity. More generally, we are working toward ecient implementations of dierent...

### Citations

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

579 | Hierarchical model-based motion estimation - Bergen, Anandan, et al. - 1992 |

412 |
Fourier Transform and Its Applications
- Bracewell
- 1986
(Show Context)
Citation Context ... computed as R(x; t) = E(t) [B(x) I(x; t)], and we may examine its spatial and temporal components independently. The class of temporalslters we consider is derived from the truncated exponential [6, 7]: E(t) H(t) e t = ( exp[ t] ; t 0 0 ; ts0 (6) where H(t) is a Heaviside step function. Equation (6) is a low-pass causalslter where 1 , the time constant, determines the duration of tempo... |

298 |
A.: Computation of component image velocity from local phase information
- FLEET, JEPSON
- 1990
(Show Context)
Citation Context ...ral delay. Low-pass prelters are required by dierential techniques for reliable numerical dierentiation, while band-passslters are an essential ingredient of energybased and phase-based approaches [1,=-= 2, 8, 9, 11, 12]-=-. Despite the use of separableslters and reasonably ecient implementations, theslters are a major computational burden of these methods. We concentrate on gradient-based methods here because of their ... |

109 | Robust dynamic motion estimation over time
- Black, Anandan
- 1991
(Show Context)
Citation Context ...raints near the centre of the neighbourhood. The constant model for v, and the support W (x; t), re ect assumptions of spatial and temporal coherence (or smoothness) in the local behaviour of v (e.g. =-=[5, 22, 23]-=-). The minimization in (3) leads to a linear system WAv = Wb, the solution of which is given by v = [A T WA] 1 A T Wb ; (4) where, for n points (x i ; t i ) 2sA = [rI(x 1 ; t 1 ); :::; rI(x n ; t n )]... |

97 |
Measurement of Image Velocity
- Fleet
- 1992
(Show Context)
Citation Context ...ral delay. Low-pass prelters are required by dierential techniques for reliable numerical dierentiation, while band-passslters are an essential ingredient of energybased and phase-based approaches [1,=-= 2, 8, 9, 11, 12]-=-. Despite the use of separableslters and reasonably ecient implementations, theslters are a major computational burden of these methods. We concentrate on gradient-based methods here because of their ... |

92 |
V.: A computational approach to motion perception
- Uras, Girosi, et al.
- 1988
(Show Context)
Citation Context ...s in v(x; t), and therefore further constraints are necessary to solve for both. Three possibilities are well-known: (i) to use higher-order derivatives with additional conservation assumptions (e.g. =-=[10, 24]-=-); (ii) to impose global smoothness constraints (regularization) on the velocityseld (e.g. [13, 20]); and (iii) to impose a parametric model (e.g. constant or linear variation) on the velocityseld loc... |

52 |
The extraction of spatiotemporal energy in human and machine vision
- Adelson, Bergen
- 1986
(Show Context)
Citation Context ...ral delay. Low-pass prelters are required by dierential techniques for reliable numerical dierentiation, while band-passslters are an essential ingredient of energybased and phase-based approaches [1,=-= 2, 8, 9, 11, 12]-=-. Despite the use of separableslters and reasonably ecient implementations, theslters are a major computational burden of these methods. We concentrate on gradient-based methods here because of their ... |

39 |
Determining Optical
- Horn, Schunck
- 1981
(Show Context)
Citation Context ...s are well-known: (i) to use higher-order derivatives with additional conservation assumptions (e.g. [10, 24]); (ii) to impose global smoothness constraints (regularization) on the velocityseld (e.g. =-=[13, 20]-=-); and (iii) to impose a parametric model (e.g. constant or linear variation) on the velocityseld locally (e.g. [1, 4, 9, 17, 21, 22]). The latter approach is adopted here, based on its performance in... |

32 |
A fast subspace algorithm for recovering rigid motion
- Jepson, Heeger
- 1991
(Show Context)
Citation Context ...oes however helpsll in small holes where aperture problem occurs in textured patches. This may be important for egomotion methods that require densesow (e.g., the convolution form of subspace methods =-=[1-=-5]). Finally, Figure 5 shows thesowselds computed from the synthetic sequences using a third-order prelter with 1 1 = 1:25, the quantitative results for which are given in the second row of Table 3. ... |

31 | Adaptive multidimensional filtering
- Haglund
- 1992
(Show Context)
Citation Context |

22 |
Performance of optical techniques
- Barron, Fleet, et al.
- 1994
(Show Context)
Citation Context ...e intensity, and to compute 2dsow from component velocity constraints using spatiotemporal least-squares minimization. Accuracy in simulation is similar to that obtained in the study by Barron et al. =-=[3]-=-, while requiring much less storage, less computation, and shorter delays. 1 Introduction Many methods exist for computing opticsow, but few currently run at frame rates on reasonably priced, conventi... |

10 |
A model and tracking algorithm for a class of video targets
- Schalkoff, McVey
- 1982
(Show Context)
Citation Context ...impose global smoothness constraints (regularization) on the velocityseld (e.g. [13, 20]); and (iii) to impose a parametric model (e.g. constant or linear variation) on the velocityseld locally (e.g. =-=[1, 4, 9, 17, 21, 22]-=-). The latter approach is adopted here, based on its performance in [3]: we compute velocity using a weighted least-squaresst of localsrst-order constraints (1) to a constant model for v(x; t) in each... |

8 |
On the hierarchical construction of orientation and velocity selective filters
- Fleet, Jepson
- 1985
(Show Context)
Citation Context ... computed as R(x; t) = E(t) [B(x) I(x; t)], and we may examine its spatial and temporal components independently. The class of temporalslters we consider is derived from the truncated exponential [6, 7]: E(t) H(t) e t = ( exp[ t] ; t 0 0 ; ts0 (6) where H(t) is a Heaviside step function. Equation (6) is a low-pass causalslter where 1 , the time constant, determines the duration of tempo... |

7 |
On the estimation of optical relations between dierent approaches and some new results
- Nagel
- 1987
(Show Context)
Citation Context ...s are well-known: (i) to use higher-order derivatives with additional conservation assumptions (e.g. [10, 24]); (ii) to impose global smoothness constraints (regularization) on the velocityseld (e.g. =-=[13, 20]-=-); and (iii) to impose a parametric model (e.g. constant or linear variation) on the velocityseld locally (e.g. [1, 4, 9, 17, 21, 22]). The latter approach is adopted here, based on its performance in... |

6 |
Probability distributions of optical
- Simoncelli, Adelson, et al.
- 1991
(Show Context)
Citation Context ...impose global smoothness constraints (regularization) on the velocityseld (e.g. [13, 20]); and (iii) to impose a parametric model (e.g. constant or linear variation) on the velocityseld locally (e.g. =-=[1, 4, 9, 17, 21, 22]-=-). The latter approach is adopted here, based on its performance in [3]: we compute velocity using a weighted least-squaresst of localsrst-order constraints (1) to a constant model for v(x; t) in each... |

5 |
Optical using spatiotemporal
- Heeger
- 1987
(Show Context)
Citation Context |

2 |
Estimation of velocity, acceleration and disparity in time sequences
- L, Knutsson, et al.
- 1991
(Show Context)
Citation Context |

2 | Incremental estimation of image- using a kalman - Singh - 1991 |

1 | Constraints for the computation of optical - A, Torre - 1989 |

1 |
Analysis of fundamental image operations
- Karabassis, Spetsakis
- 1993
(Show Context)
Citation Context ...me ^ D(!), our measure of error is E(!) = ^ D(!) i !s: (19) Table 1 gives the convolution masks for several common FIRslters for numerical dierentiation, and their respective transfer functions (see [=-=1-=-6] for more details). It also gives a RMS measure of error, computed as the integral of E(!) 2 over radian frequencies 0 ! 1:0 (the lowest third of the frequency spectrum). With all these schemes, a... |

1 |
Optical estimation: An error analysis of gradient-based methods with local optimization
- Kearney, Thompson, et al.
- 1987
(Show Context)
Citation Context ...impose global smoothness constraints (regularization) on the velocityseld (e.g. [13, 20]); and (iii) to impose a parametric model (e.g. constant or linear variation) on the velocityseld locally (e.g. =-=[1, 4, 9, 17, 21, 22]-=-). The latter approach is adopted here, based on its performance in [3]: we compute velocity using a weighted least-squaresst of localsrst-order constraints (1) to a constant model for v(x; t) in each... |

1 |
Recursive for phase-based optical
- Langley, Fleet
- 1992
(Show Context)
Citation Context ...ering and dierentiation, with small storage requirements and shorter delays. These low-passslters are also readily generalized to band-passslters, and are therefore applicable to phase-based methods [=-=18]-=-. We also examine a simple form of recursion in solving for opticalsow from normal velocity constraints. 1 Published in IEEE Trans. PAMI, 17(1): 61-67, 1995 1 2 Local Gradient-Based Method Gradient-ba... |