### Citations

2401 | Determining optical flow
- Horn, Schunck
- 1981
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Citation Context ...on (small squares denote the associated velocities) for the iteration number 1, 3, 5 and 10, for the 2 points marked in the figure on the left. The pseudocolor scale for the range in the alpha values =-=[0,1]-=- is shown to the right-hand side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Optical flow in real scene (single motion case). (a) One frame of the coastgu... |

1320 | Performance of optic flow techniques
- Barron, Fleet, et al.
- 1994
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Citation Context ... also called optical flow. Such a craze for optical flow is notably due by the number of applications that require some motion estimation to perform their tasks. We refer the reader to [6], [7], [2], =-=[8]-=- for some reviews on this topic. Although less models are proposed concerning multiple motions, it is our conviction that considering more complex stimuli will also bring some new solutions and ideas ... |

667 |
The robust estimation of multiple motions: parametric and piecewise-smooth flow fields
- Black, Anandan
- 1996
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Citation Context ...tered in the image plane/volume and are associated with different layers at different positions. We will now describe a few of these approaches. In the robust statistics approach of Black and Anandan =-=[27]-=-, the transparency is treated through a segmentation approach. The image plane is assumed to be partitioned into regions, each but one corresponding to a parametric motion model u = u(a), a being the ... |

268 | On the unification of line processes, outlier rejection, and robust statistics with applications to early vision
- Black, Rangarajan
- 1996
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Citation Context ...rm and the attach term introduces a motion model competition mechanism. A. Attach Term In order to compute the presence of the i-th model, we use an approach related with the outlier rejection method =-=[36]-=- and with the EM formulation [31], [32], [33], [30]. Remind that function d(f,r,ui) is close to zero when the velocity ui explains correctly the motion at position r, and is a positive large value oth... |

243 | Computing Occluding and Transparent Motions
- Irani, Rousso, et al.
- 1994
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Citation Context ...erpretation, including multiresolution pyramid effects, is provided. In particular a “dominant velocity extraction” mechanism is explained, and the latter is used by Irani and Peleg in [12] (see also =-=[13]-=-). Starting from the linear superposition principle, Shizawa and Mase explore in a series of papers [14], [15], [4] a frequency domain, total least squares formulation of the multiple motion problems.... |

224 | Motion analysis for image enhancement resolution, occlusion, and transparency
- Irani, Peleg
- 1993
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Citation Context ...ency domain interpretation, including multiresolution pyramid effects, is provided. In particular a “dominant velocity extraction” mechanism is explained, and the latter is used by Irani and Peleg in =-=[12]-=- (see also [13]). Starting from the linear superposition principle, Shizawa and Mase explore in a series of papers [14], [15], [4] a frequency domain, total least squares formulation of the multiple m... |

212 |
Multidimensional orientation estimation with applications to texture analysis and optical flow
- Bigun, Granlund, et al.
- 1991
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Citation Context ...tion is given as the (an) eigenvector corresponding to the smallest eigenvalue of the 3 × 3 symmetric, positive (semi-)definite matrix � A = ωω t | ˆ f(ω) 2 |dω which is a Structure Tensor (see [16], =-=[17]-=-, [18] for instance). For the recovery of n motions at a given location, the linear, first order, constraint (4) is replaced by a n-th order, n-th multilinear one obtained by “cascading” the linear fi... |

175 | A unified mixture framework for motion segmentation: incorporating spatial coherence and estimating the number of models,”
- Weiss, Adelson
- 1996
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Citation Context ...e which layer is more likely to belong to a region. Although the method captures the changes in illumination, it does not allow to compute the optical flow of moving transparencies. Weiss and Adelson =-=[32]-=- and recently Rivera et al. [33] proposed EM-based approaches for computing different layered motion models in an image sequence and its segmentation based on these models. They use as prior knowledge... |

158 | Mixture models for optical flow computation, in:
- Black
- 1993
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Citation Context ...g patterns, through the ways these patterns are recovered, via a nulling process similar to the one of [10]. Mixture models for multiple motion computation have been introduced by Jepson and Black in =-=[28]-=-, [29]. A parametric layered flow model is considered. One assumes that the motion can be explained by up to N parametric motion fields with parameter vectors �an. As input, one uses motion vector con... |

100 |
A feature based correspondence algorithm for image matching.
- Forstner
- 1986
(Show Context)
Citation Context ...e solution is given as the (an) eigenvector corresponding to the smallest eigenvalue of the 3 × 3 symmetric, positive (semi-)definite matrix � A = ωω t | ˆ f(ω) 2 |dω which is a Structure Tensor (see =-=[16]-=-, [17], [18] for instance). For the recovery of n motions at a given location, the linear, first order, constraint (4) is replaced by a n-th order, n-th multilinear one obtained by “cascading” the lin... |

74 | Skin and Bones: Multilayer, locally affine, optical flow and regularaization with transparency.
- Ju, Black, et al.
- 1996
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Citation Context ... (�cr|r, (�ai)i=1...N, (αi)i=0...N) = αipi(�cr|r,�ai). The problem is then to compute the best mixture and motion parameters (αi, �ai)i. This is usually done using EM-like algorithms. Ju, Black et al =-=[30]-=- proposed the “Skin and Bones” model, in which multi-layered affine models are defined on small rectangular patches of the image (bones), then an ownership field defines the likelihood that each pixel... |

72 | Robustly estimating changes in image appearance,”
- Black, Fleet, et al.
- 2000
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Citation Context ...rk using an EM-algorithm. An interpatch regularization (skin) term introduces a regularization effect in the model parameters estimation. Another layered representation is proposed by Black et al. in =-=[31]-=-. In that approach, they consider that multiple motions may appear due to occlusions and limited forms of transparency. The method introduces models for illumination changes and specular reflections, ... |

61 | Computing optical flow via variational techniques.
- Aubert, Deriche, et al.
- 1999
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Citation Context ...s roughly horizontally to the left, while the foreground object, a coastguard boat, moves roughly to the right. For comparison purposes some results computed with standard variational approaches [1], =-=[2]-=- are displayed. Figure 4 (b) shows the flow corresponding to the most probable velocity at every position. The orientation of the solution is color-coded: the color associated to a each orientation is... |

57 | Recovering motion fields: An evaluation of eight optical flow algorithms.
- GALVIN, MCCANE, et al.
- 1998
(Show Context)
Citation Context ...stimation, also called optical flow. Such a craze for optical flow is notably due by the number of applications that require some motion estimation to perform their tasks. We refer the reader to [6], =-=[7]-=-, [2], [8] for some reviews on this topic. Although less models are proposed concerning multiple motions, it is our conviction that considering more complex stimuli will also bring some new solutions ... |

57 |
Simultaneous multiple optical flow estimation
- Shizawa, Mase
- 1990
(Show Context)
Citation Context ...extraction” mechanism is explained, and the latter is used by Irani and Peleg in [12] (see also [13]). Starting from the linear superposition principle, Shizawa and Mase explore in a series of papers =-=[14]-=-, [15], [4] a frequency domain, total least squares formulation of the multiple motion problems. They start from the single motion case, the OFC constraint equation (2) is replaced by the spatiotempor... |

56 | A unified computational theory for motion transparency and motion boundaries based on eigenergy analysis, in: - Shizawa, Mase - 1991 |

50 | Computing two motions from three frames
- Bergen, Burt, et al.
- 1990
(Show Context)
Citation Context ...e [9] where intensity addition is replaced by an operation with similar formal algebraic properties such as multiplication in reflection. A simple superposition model was introduced by Burt et al. in =-=[10]-=- for the case of two motions. The observed image sequence f is assumed to come from the combination f = P1 ⊕ P2 of two moving patterns P1 and P2 with respective motions u1 and u2, such that brightness... |

43 |
Mechanisms for Isolating Component Patterns in the Sequential Analysis of Multiple Motion
- Burt, Hingorani, et al.
- 1991
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Citation Context ... to form the difference pattern D1 and get a new estimate of u1 from it. This process is iterated until convergence. A more thorough study and extension of this idea is proposed in a subsequent paper =-=[11]-=-, where a frequency domain interpretation, including multiresolution pyramid effects, is provided. In particular a “dominant velocity extraction” mechanism is explained, and the latter is used by Iran... |

31 | Separating transparent layers through layer information exchange
- Sarel, Irani
- 2004
(Show Context)
Citation Context ...ly important one of layer recovery, at the exception of [21], [22]. We mention here the work of Toro et al. [34] where the knowlegde of motion is fundamental, as opposed to to work of Sarel and Irani =-=[35]-=-, where such a separation is performed by optimizing some correlation measures. Also non mentioned here are the perceptual/neurophysiological aspects of transparency. III. PROBLEM STATEMENT: FROM LOCA... |

27 | Temporal dynamics of motion integration for the initiation of tracking eye movements at ultra-short latencies
- Masson, Rybarczyk, et al.
- 2000
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Citation Context ...c sequence that consists of an oblique bar translating in the horizontal direction (Figure 3). Interestingly, some psychophysics studies show how motion integration is performed in tracking tasks. In =-=[38]-=- is shown that the eyes will first follow the normal direction of the bar, according to 1D motion detectors. Then, after few milliseconds, there is a correction of the pursuit toward the horizontal di... |

25 |
Visualization and Processing of Tensor Fields
- Weickert, Hagen
- 2006
(Show Context)
Citation Context ...s given as the (an) eigenvector corresponding to the smallest eigenvalue of the 3 × 3 symmetric, positive (semi-)definite matrix � A = ωω t | ˆ f(ω) 2 |dω which is a Structure Tensor (see [16], [17], =-=[18]-=- for instance). For the recovery of n motions at a given location, the linear, first order, constraint (4) is replaced by a n-th order, n-th multilinear one obtained by “cascading” the linear first or... |

23 | Separation of transparent motion into layers using velocity-tuned mechanisms
- Darrell, Simoncelli
- 1993
(Show Context)
Citation Context ...used by Liu et al. in [23] with Hermite polynomial based differentiation filters and specific checks for the presence of single or multiple motions. Darell and Simoncelly “dualize” this constraint in =-=[24]-=- in order to construct some Fourier “donuts” used to respond to one or more velocities. The 2-folds optical flow constraint is used in the present work, in order to build local multiple motions “probe... |

21 |
Superposition in a class of nonlinear systems
- Oppenheim
- 1964
(Show Context)
Citation Context ...le motions, especially in the case of transparency. Transparency can be modeled as a superposition of moving layers, a linear superposition meaning addition of layer intensities, or a generalized one =-=[9]-=- where intensity addition is replaced by an operation with similar formal algebraic properties such as multiplication in reflection. A simple superposition model was introduced by Burt et al. in [10] ... |

18 |
Decoupling fourier components of dynamic image sequences: a theory of signal separation, image segmentation and opical flow estimation,
- Vernon
- 1998
(Show Context)
Citation Context ...ach have proposed an algebraic framework based on homogeneous parts of symmetric algebras in [20]. The very algebraic nature of the motion constraint in frequency domain has lead Vernon to propose in =-=[21]-=- an algorithm for the decoupling of moving patterns, for both transparency and occlusion models. An algorithm for the specific problem of reflections is proposed by Zou and Kambhamettu in [22]. The no... |

13 | Multiresolution parametric estimation of transparent motions
- Auvray, Bouthemy, et al.
- 2005
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Citation Context ...m a N-th order Taylor expansion around velocity values. A multi-resolution non linear least squares estimation is performed, using a Levenberg-Marquardt algorithm. Recently, Auvray et al. proposed in =-=[26]-=- an algorithm based on equation (7). The method is also multi-resolution, uses a simplex algorithm for its initialization and adds a postprocessing step, especially efficient when the two velocities a... |

9 |
A Robust Multiscale B-Spline Function Decomposition for Estimating Motion Transparency
- Pingault, Bruno, et al.
- 2003
(Show Context)
Citation Context ...he use of a field of binary indicator variables) and complex (due to a statistical confidence test used to discern the number of motions at each pixel). Starting with equation (7), Pingault et al. in =-=[25]-=- perform a N-th order Taylor expansion around velocity values. A multi-resolution non linear least squares estimation is performed, using a Levenberg-Marquardt algorithm. Recently, Auvray et al. propo... |

9 | Entropy controlled gauss-markov random measure field models for early vision - Rivera, Ocegeda, et al. - 2005 |

8 |
A Theory of Multiple Orientation Estimation
- Mühlich, Aach
- 2006
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Citation Context ...mplicated for higher orders. Very recently, Mota et al. have extended these ideas in [19] and Mühlich and Aach have proposed an algebraic framework based on homogeneous parts of symmetric algebras in =-=[20]-=-. The very algebraic nature of the motion constraint in frequency domain has lead Vernon to propose in [21] an algorithm for the decoupling of moving patterns, for both transparency and occlusion mode... |

7 | Estimation of multiple motions by block matching
- Stuke, Aach, et al.
- 2003
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Citation Context .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5 First row: performance of the two local motion estimators. (a) noise-free frame. (b) Nonregularized velocities for =-=[3]-=- distance (SNR=30) and (c) for [4] distance. Second and third rows: Our results for different amounts of Gaussian noise, as input we used [3] distance. Figures (d)-(f) velocity fields and Figures (g)-... |

6 | Divide-and-Conquer Strategies for Estimating Multiple Transparent Motions
- Mota, Stuke, et al.
(Show Context)
Citation Context ...velocities. A closed-form formula for that decomposition is provided in the case n = 2, but becomes rapidly more complicated for higher orders. Very recently, Mota et al. have extended these ideas in =-=[19]-=- and Mühlich and Aach have proposed an algebraic framework based on homogeneous parts of symmetric algebras in [20]. The very algebraic nature of the motion constraint in frequency domain has lead Ver... |

5 |
Multiple-motion-estimation by block matching using MRF
- Stuke, Aach, et al.
- 2004
(Show Context)
Citation Context ...gures (g)-(i) number of motions per pixel: in (g),(h) white = 2 velocities, and black = 1 velocity. In Figure (i) white = 3 velocities, gray = 2 and black = 1. Last row: the Gibbs Sampler (GS) scheme =-=[5]-=-: (j) results in noise-free sequence and (k) in a noise-corrupted one (SNR=30). (l) same than (d), but sampled for comparison with (j) and (k). . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |

5 | Spatio-temporal filters for transparent motion segmentation
- Liu, Hong, et al.
- 1995
(Show Context)
Citation Context ... optical flow constraint equation as introduced by Shizawa and Mase in [15]: � v 1 ∂ 1 + v ∂x1 2 ∂ 1 + ∂x2 ∂ �� v ∂t 1 ∂ 2 + v ∂x1 2 ∂ 2 + ∂x2 ∂ � f(x,t) = 0 (6) ∂t This form is used by Liu et al. in =-=[23]-=- with Hermite polynomial based differentiation filters and specific checks for the presence of single or multiple motions. Darell and Simoncelly “dualize” this constraint in [24] in order to construct... |

3 |
Brain nerve boundless estimation by restoring and filtering intra-voxel information in DT-MRI
- Ramirez-Manzanares, Rivera
- 2003
(Show Context)
Citation Context ...nes α(s) in its neighborhood, Nr. Given that our indicator variables are real valued, we can use differentiable potentials with the well-known algorithmic advantages. We use the approach presented in =-=[37]-=- for achieving such a regularization, i.e. a directional one. Therefore the smoothing process is controlled by directional fixed weights, wi(r,s) = (s − r)T Īi (s − r) �s − r� 4 , generated from the i... |

2 |
Separation of Reflection by Fourier Decoupling
- Zhou, Kambhamettu
- 2004
(Show Context)
Citation Context ...pose in [21] an algorithm for the decoupling of moving patterns, for both transparency and occlusion models. An algorithm for the specific problem of reflections is proposed by Zou and Kambhamettu in =-=[22]-=-. The non homogeneous form (with u3 i = 1) of equation (5) provides the 2-folds optical flow constraint equation as introduced by Shizawa and Mase in [15]: � v 1 ∂ 1 + v ∂x1 2 ∂ 1 + ∂x2 ∂ �� v ∂t 1 ∂ ... |

2 |
Using known motion fields for image separation
- Toro, Owens, et al.
- 2003
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Citation Context ...n optical flow recovery and does not include some of the related questions, and the especially important one of layer recovery, at the exception of [21], [22]. We mention here the work of Toro et al. =-=[34]-=- where the knowlegde of motion is fundamental, as opposed to to work of Sarel and Irani [35], where such a separation is performed by optimizing some correlation measures. Also non mentioned here are ... |

1 | Estimation du flot optique en présence de discontinuités: une revue - Orkisz, Clarysse - 1996 |