## Variational Space-Time Motion Segmentation (2003)

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Citations: | 27 - 5 self |

### BibTeX

@MISC{Cremers03variationalspace-time,

author = {Daniel Cremers and Stefano Soatto},

title = {Variational Space-Time Motion Segmentation},

year = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

We propose a variational method for segmenting image sequences into spatio-temporal domains of homogeneous motion. To this end, we formulate the problem of motion estimation in the framework of Bayesian inference, using a prior which favors domain boundaries of minimal surface area. We derive a cost functional which depends on a surface in space-time separating a set of motion regions, as well as a set of vectors modeling the motion in each region. We propose a multiphase level set formulation of this functional, in which the surface and the motion regions are represented implicitly by a vector-valued level set function. Joint minimization of the proposed functional results in an eigenvalue problem for the motion model of each region and in a gradient descent evolution for the separating interface. Numerical results on real-world sequences demonstrate that minimization of a single cost functional generates a segmentation of space-time into multiple motion regions.

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Citation Context ... can be applied to the case of segmenting moving objects in video sequences. Many researchers have investigated the problem of motion estimation. Two seminal methods were proposed by Horn and Schunck =-=[7]-=- and by Lucas and Kanade [9]. These methods are based on a least-squares criterion for the optic flow constraint and global or local smoothness assumptions on the estimated flow field. In general, flo... |

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Citation Context ...er vectors modeling the motion in a set of disjoint regions and on a surface separating these regions in the spatio-temporal domain. In Sections 5 and 6, we propose a multiphase level set formulation =-=[3, 18]-=- of this functional. The implicit representation of the separating interface by a vector-valued level set function permits to segment several (possibly multiply connected) motion phases. In Section 7,... |

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Citation Context ... minimizing a single functional, one simultaneously generates a segmentation of the image and an approximation of the gray values in each region. This idea was extended to color and texture images in =-=[23]-=-. In the present paper, we demonstrate that a similar reasoning can be applied to the case of segmenting moving objects in video sequences. Many researchers have investigated the problem of motion est... |

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Citation Context ...er vectors modeling the motion in a set of disjoint regions and on a surface separating these regions in the spatio-temporal domain. In Sections 5 and 6, we propose a multiphase level set formulation =-=[3, 18]-=- of this functional. The implicit representation of the separating interface by a vector-valued level set function permits to segment several (possibly multiply connected) motion phases. In Section 7,... |

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Citation Context ... fields are not smooth. The boundaries of moving objects correspond to discontinuities in the motion field. Such motion discontinuities have been modeled implicitly by non-quadratic robust estimators =-=[1, 10, 8, 21]-=-. Alternatively, it was proposed to separately estimate the motion in disjoint sets and optimize the motion boundaries [14, 19, 22, 2, 13, 5]. In [4], we presented a variational approach called motion... |

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Citation Context ...es have been modeled implicitly by non-quadratic robust estimators [1, 10, 8, 21]. Alternatively, it was proposed to separately estimate the motion in disjoint sets and optimize the motion boundaries =-=[14, 19, 22, 2, 13, 5]-=-. In [4], we presented a variational approach called motion competition which jointly solves the problems of motion estimation and segmentation for two consecutive frames from a sequence in a similar ... |

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Citation Context ...es have been modeled implicitly by non-quadratic robust estimators [1, 10, 8, 21]. Alternatively, it was proposed to separately estimate the motion in disjoint sets and optimize the motion boundaries =-=[14, 19, 22, 2, 13, 5]-=-. In [4], we presented a variational approach called motion competition which jointly solves the problems of motion estimation and segmentation for two consecutive frames from a sequence in a similar ... |

39 |
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Citation Context ...es have been modeled implicitly by non-quadratic robust estimators [1, 10, 8, 21]. Alternatively, it was proposed to separately estimate the motion in disjoint sets and optimize the motion boundaries =-=[14, 19, 22, 2, 13, 5]-=-. In [4], we presented a variational approach called motion competition which jointly solves the problems of motion estimation and segmentation for two consecutive frames from a sequence in a similar ... |

30 |
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Citation Context ... contrast, most alternative approaches to layer extraction perform extensive preprocessing such as local disparity estimation, camera calibration and prior rectification of the individual frames (cf. =-=[17, 15]-=-). Proceedings of the Ninth IEEE International Conference on Computer Vision (ICCV 2003) 2-Volume Set 0-7695-1950-4/03 $17.00 © 2003 IEEEFigure 4. Two motion phases. Motion segmentation of the flower... |

26 | A variational framework for image segmentation combining motion estimation and shape regularization
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Citation Context ...iotemporal gradient is superior to the commonly considered least-squares criterion in the context of motion segmentation. Our approach constitutes a generalization of the motion competition framework =-=[4]-=- to the space-time domain. Based on a few explicitly stated assumptions, we derived a cost functional which depends on the motion parameters for a set of disjoint regions and on a hypersurface separat... |

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