## A Probabilistic Background Model for Tracking (2000)

Citations: | 53 - 1 self |

### BibTeX

@INPROCEEDINGS{Rittscher00aprobabilistic,

author = {J. Rittscher and J. Kato and S. Joga and A. Blake},

title = {A Probabilistic Background Model for Tracking},

booktitle = {},

year = {2000},

pages = {336--350}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new probabilistic background model based on a Hidden Markov Model is presented. The hidden states of the model enable discrimination between foreground, background and shadow. This model functions as a low level process for a car tracker. A particle filter is employed as a stochastic filter for the car tracker. The use of a particle filter allows the incorporation of the information from the low level process via importance sampling. A novel observation density for the particle filter which models the statistical dependence of neighboring pixels based on a Markov random field is presented. The effectiveness of both the low level process and the observation likelihood are demonstrated.

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Citation Context ... inferred to be in a foreground region it is expected to be within a foreground region for some time. An suitable model to impose such temporal continuity constraints is the Hidden Markov Model (HMM) =-=[14]-=-. The grey-value intensities over time for one specific pixel location is to be modelled as a single HMM, independent of the neighbouring pixels. This is Fig. 1. A traffic surveillance example. This i... |

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Citation Context ...t in this case the measurements Z cannot be assumed to be independent (also see [19]). These conditions lead us to model the likelihood (6) as a conditioned Markov random field (MRF) (see for example =-=[5, 21]-=-). In Gibbs form an MRF can be written as P (Z|X ; #) = exp(-H # (Z, X)) # Z # #Z exp(-H # (Z # , X)) . (7) The denominator of the fraction is known as the partition function of the MRF. The difficult... |

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Citation Context ...ained that it is not possible to approximate the observation likelihood (7). It is therefore necessary to find a simpler model. It is known that under certain conditions the pseudolikelihood function =-=[1, 21]-=-, defined as # s#S p(z s |z S\s ; #) (9) can be used for parameter estimation instead of the Maximum Likelihood approach based on the MRF (7). It can be shown [21] that estimators obtained by maximizi... |

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Citation Context ...nd model is introduced in section 2. In addition to the low level process it is necessary to build a high level process that can track the vehicles. Probabilistic trackers based on a particle filters =-=[7]-=- are known to be robust and can be extended to tracking multiple objects [11]. The benefit of using a particle filter is that the tracker can recover from failures [7]. But very importantly the use of... |

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Citation Context ...ficult. As simple background subtraction or inter-frame differencing schemes are known to perform poorly a number of researchers have addressed the problem of finding a probabilistic background model =-=[6, 17, 10, 13, 20]-=-. Haritaoglu et al. [6] only learn the minimal and maximal grey-value intensity for every pixel location. The special case of a video camera mounted on a pan-tilt head is investigated in [17]. Here a ... |

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Citation Context ... distribution for the previous time-step t - 1 is effectively used as a prior for time t. It is very difficult to fuse two sources of prior information. However, importance sampling, as introduced in =-=[8]-=-, can be used to incorporate the information obtained from the low level process. Instead of applying the original algorithm an importance sampling scheme which is linear in time [16] is used here. Th... |

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Citation Context ... is necessary to build a high level process that can track the vehicles. Probabilistic trackers based on a particle filters [7] are known to be robust and can be extended to tracking multiple objects =-=[11]-=-. The benefit of using a particle filter is that the tracker can recover from failures [7]. But very importantly the use of a particle filter also allows a way to utilise the information of the low le... |

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Citation Context ...t in this case the measurements Z cannot be assumed to be independent (also see [19]). These conditions lead us to model the likelihood (6) as a conditioned Markov random field (MRF) (see for example =-=[5, 21]-=-). In Gibbs form an MRF can be written as P (Z|X ; #) = exp(-H # (Z, X)) # Z # #Z exp(-H # (Z # , X)) . (7) The denominator of the fraction is known as the partition function of the MRF. The difficult... |

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Citation Context ...ficult. As simple background subtraction or inter-frame differencing schemes are known to perform poorly a number of researchers have addressed the problem of finding a probabilistic background model =-=[6, 17, 10, 13, 20]-=-. Haritaoglu et al. [6] only learn the minimal and maximal grey-value intensity for every pixel location. The special case of a video camera mounted on a pan-tilt head is investigated in [17]. Here a ... |

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Citation Context ...by employing a Markov random field it is possible to model these statistical dependencies. Such a car tracking system has to be able to compete with existing traffic monitoring systems. Beymer et al. =-=[2]-=- built an very robust car tracker. Their tracking approach is based on feature points and works in most illumination conditions. The disadvantage of the system is that it is necessary to run a complex... |

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Citation Context ...ssion or observation probability for each state p f (z), p b (z) and p s (z). The set of parameters defining the HMM model will be abbreviated as # := (A, #, p f , p s , p b ). Standard texts include =-=[14, 9]-=-. Based on the intensity histograms of figure 2 the emission models of the background and shadow regions are modelled as Gaussian densities. Since very little about the distribution of the colours of ... |

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Citation Context ...ficult. As simple background subtraction or inter-frame differencing schemes are known to perform poorly a number of researchers have addressed the problem of finding a probabilistic background model =-=[6, 17, 10, 13, 20]-=-. Haritaoglu et al. [6] only learn the minimal and maximal grey-value intensity for every pixel location. The special case of a video camera mounted on a pan-tilt head is investigated in [17]. Here a ... |

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Citation Context ...ut the shape of the cars. By modelling cars as rectangular regions it would be possible to infer about their size and allow classification into basic categories. Koller et al. [10] as well as Ferrier =-=[4]-=- et al. already demonstrated applications of contour tracking to traffic surveillance. [10] extracts a contour extraction from features computed from inter-frame difference images as well as the grey ... |

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Citation Context ... as introduced in [8], can be used to incorporate the information obtained from the low level process. Instead of applying the original algorithm an importance sampling scheme which is linear in time =-=[16]-=- is used here. The importance function itself is generated by fitting a rectangle with parameters X I to the pixels which are classified as foreground pixels (see figure 5) and using a normal distribu... |

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Citation Context |

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Citation Context ...ity images themselves. In the case of extreme lighting conditions as shown in figure 1 this system is likely to get distracted. Approaches which model vehicles as three dimensional wire frame objects =-=[18, 12, 15]-=- are of course less sensitive to extreme lighting conditions. The main drawback of modelling vehicles as three dimensional objects is that the tracking is computationally expensive. The challenge is t... |

10 | Penalized pseudolikelihood inference in spatial interaction models with covariates. The Scandinavian
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Citation Context ...s of statistical properties with maximum likelihood estimators. Although some authors state that when the variables are weakly correlated, the pseudolikehood is a good approximation to the likelihood =-=[3]-=- it seems to be an open problem under which conditions precisely it can be used as an approximation to the likelihood function. In section 3.2 it will also become clear why the pseudolikehood method c... |

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Citation Context ...ity images themselves. In the case of extreme lighting conditions as shown in figure 1 this system is likely to get distracted. Approaches which model vehicles as three dimensional wire frame objects =-=[18, 12, 15]-=- are of course less sensitive to extreme lighting conditions. The main drawback of modelling vehicles as three dimensional objects is that the tracking is computationally expensive. The challenge is t... |

1 |
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Citation Context ...ity images themselves. In the case of extreme lighting conditions as shown in figure 1 this system is likely to get distracted. Approaches which model vehicles as three dimensional wire frame objects =-=[18, 12, 15]-=- are of course less sensitive to extreme lighting conditions. The main drawback of modelling vehicles as three dimensional objects is that the tracking is computationally expensive. The challenge is t... |

1 |
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Citation Context ...tlines of the cars as a perspectively distorted rectangle which will be parameterised by the state vector X . In order to track cars robustly it is not sufficient to take edge measurements as in [7]. =-=[19]-=- showed that detection of the background aids finding the foreground object. The problem is that in this case the measurements Z cannot be assumed to be independent (also see [19]). These conditions l... |