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- Lindström, Johan, et al.
(författare)
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Background and Foreground Modeling Using an Online EM Algorithm
- 2006
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Ingår i: IEEE International Workshop on Visual Surveillance. ; VS2006, s. 9-16
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Konferensbidrag (refereegranskat)abstract
- A novel approach to background/foreground segmentation using an online EM algorithm is presented. The method models each layer as a Gaussian mixture, with local, per pixel, parameters for the background layer and global parameters for the foreground layer, utilising information from the entire scene when estimating the foreground. Additionally, the online EM algorithm uses a progressive learning rate where the relative update speed of each Gaussian component depends on how often the component has been observed. It is shown that the progressive learning rate follows naturally from introduction of a forgetting factor in the log-likelihood. To reduce the number of mixture components similar foreground components are merged using a method based on the Kullback-Leibler distance. A bias is introduced in the variance estimates to avoid the known problem of singularities in the log-likelihood of Gaussian mixtures when the variance tends to zero. To allow a decoupling of the learning rate of the Gaussian components and the speed at which stationary objects are incorporated into the background a CUSUM detector is used instead of the prevailing method that uses the ratio of prior probability to standard deviation. The algorithm is scale invariant and its properties on gray-scale and RGB videos, as well as on output from an edge detector, is compared to that of another algorithm. Especially for the edge detector video performance increases dramatically.
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| 2. |
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| 3. |
- Åberg, Sofia, et al.
(författare)
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An image warping approach to spatio-temporal modelling
- 2005
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Ingår i: Environmetrics. - : Wiley. - 1099-095X .- 1180-4009. ; 16:8, s. 833-848
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Tidskriftsartikel (refereegranskat)abstract
- In this article we present a spatio-temporal dynamic model that can be realized using image warping. Image warping is a non-linear deformation which maps every point in one image plane to a point in another image plane. Using thin-plate splines, these deformations are defined by how a small set of points is mapped, making the method computationally tractable. In our case the dynamics of the process is modelled by thin-plate spline deformations and how they vary in time. Thus we make no assumption of stationarity in time. Finding the deformation between two images in the space-time series is a trade-off between a good match of the images and, a smooth, physically plausible, deformation. This is formulated as a penalized likelihood problem, where the likelihood measures how good the match is and the penalty comes from a prior model on the deformation. The dynamic model we suggest can be used to make forecasts and also to estimate the uncertainties associated with these. An introduction to image warping and thin-plate splines is given as well as an application where the methodology is applied to the problem of nowcasting radar precipitation.
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