Robust Hierarchical motion estimation |

Description |

The estimator we have devolopped is a trade-off between methods based on global parameterized flow models and local dense optic flow estimators. The method relies on an adaptive multigrid minimization approach. In addition to accelerated convergence toward good estimates, it allows to mix different parameterizations of the estimate relative to adaptive partitions of the image. This last feature is of particular interest for sequences involving fluid dynamical phenomena such as in meteorological images. Coherent dynamical structures of interest such as vortices are then well described by global linear parametric motions, whereas less coherent non-linear portions of motion are captured by non-parametric dense estimation. The performances of the resulting algorithms are demonstrated in the difficult context of a non-convex energy. Experimental results obtained for real world sequences and for the yosemite synthetic sequence are presented below.

Results |

We presents here results obtained for a difficult sequence showing a smoke diffusing in front a camera.

Smoke sequence | Final estimation grids | Estimated vector fields |
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The table below gathers the results obtained on the basis of Barron
et. al criterion ("*performance of optical flow techniques" IJCV vol. 12 1994*), for the cropped Yosemite sequence (without the sky). This criterion represents a discrepancy between the estimated flow field and the actual one.

Model |
Regular grids |
Adaptive grids |

Affine | moy= 2.33, sigma= 2.12, tps = 43s | moy= 2.19, sigma= 1.95, tps= 44s |

Translationnel | moy= 1.86, sigma= 1.32, tps = 74s | moy= 3.29, sigma= 2.64, tps= 63s |

Mixed Affine +Translationnal | moy= 1.80, sigma= 1.35, tps = 123s | moy= 1.87, sigma= 1.50, tps= 94s |

Results obtained with other methods are recalled below:

Estimateur |
Résultats |
Références |

Szeliski et Coughlan |
moy= 2.45 sigma= 3.05 | "Hierarchical spline based image registration". CVPR'94 |

Black et Anandan |
moy= 4.46 sigma= 4.21 | "Robust incremental optical flow", CVPR'92 |

Black |
moy= 3.52 sigma= 3.25 | "Recursive non linear estimation of discontinuous flow field", ECCV'94 |

Black et Jepson |
moy= 2.29 sigma= 2.25 | "Estimating optical flow in segmented images using variable-order parametric models with local deformations", PAMI vol.
18, 1996 |

Ju, Black et Jepson |
moy= 2.16 sigma= 2.0 | "Skin and bones: multi-layer locally affine, optical flow and regularization with transparency", CVPR'96 |

Lai et Vemuri |
moy= 1.99 sigma= 1.41 | "Reliable and efficient computation of optical flow", IJCV 29(2) 1998 |

Références |

- E. Mémin et P. Pérez.
**A multigrid approach for hierarchical motion estimation.**Int. Conf on Computer Vision, ICCV'98, pages 933-938, Bombay ,India, 1998. (postscript) - E. Mémin et P. Pérez.
**Dense estimation and object-based segmentation of the optical flow.**IEEE Trans. Image Processing, 7(5):703-719, 1998. (postscript) - E. Mémin et P. Pérez.
**Hierarchical estimation and segmentation of dense motion fields.**submitted to Int. Journ of Comp. Vision. (postscript)