Statistical Properties and Control Algorithms of Recursive Quantile Estimators

Möller, Eva; Grieszbach, G.; Schack, Bärbel; Witte, Herbert

doi:10.1002/1521-4036(200010)42:6<729::aid-bimj729>3.0.co;2-w

Cited by 7 publications

(3 citation statements)

References 10 publications

(16 reference statements)

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“…Möller et al shows [11] how to estimates quantiles recursively, and proves that it will converge under very general assumptions on the input data. They use a control sequence c t = max(c 0 /t, c min ), where constant c 0 is a starting value that is typically chosen a few times larger than the maximum intensity value.…”

Section: A Recursive Quantile Estimationmentioning

confidence: 99%

“…This is because it is based on the EM-algorithm, which is a local optimisation algorithm that can get stuck in a local maxima. The convergence properties of the recursive quantile estimator are investigated in [11] and it is shown to converge under some very general assumptions on the input sequence. The result is also tabulated in Table I.…”

Section: B Simulationsmentioning

confidence: 99%

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Bayesian Formulation of Image Patch Matching Using Cross-correlation

Ardö

Ågström

2011

J Math Imaging Vis

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Abstract-A classical solution for matching two image patches is to use the cross-correlation coefficient. This works well if there is a lot of structure within the patches, but not so well if the patches are close to uniform. This means that some patches are matched with more confidence than others. By estimating this uncertainty more weight can be put on the confident matches than those that are more uncertain. In this paper we present a system that can learn the distribution of the correlation coefficient from a video sequence of an empty scene. No manual annotation of the video is needed. Two distributions functions are learned for two different cases: i) the correlation between an estimated background image and the current frame showing that background and ii) the correlation between an estimated background image and an unrelated patch.Using these two distributions the patch matching problem is formulated as a binary classification problem and the probability of two patches matching is derived. The model depends on the signal to noise ratio. The noise level is reasonably invariant over time, while the signal level, represented by the amount of structure in the patch or it's spatial variance, has to be measured for every frame.A common application where this is useful is feature point matching between different images. Another application is background/foreground segmentation. In this paper it is shown how the theory can be used to implement a very fast background/foreground segmentation by transforming the calculations to the DCT-domain and processing a motion JPEG stream without uncompressing it. This allows the algorithm to be embedded on a 150MHz ARM based network camera. It is also suggested to use recursive quantile estimation to estimate the background model. This gives very accurate background models even if there is a lot of foreground present during the initialisation of the model.

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Section: A Recursive Quantile Estimationmentioning

confidence: 99%

Section: B Simulationsmentioning

confidence: 99%

Bayesian Formulation of Image Patch Matching Using Cross-correlation

Ardö

Ågström

2011

J Math Imaging Vis

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show abstract

“…However, convergence might be extremely slow for certain distributions. Therefore, techniques to choose a suitable sequence c t f g t¼0;1;... ; for instance based on an estimation of the probability density function of the sampled random variable, are proposed in Möller et al (2000); Grieszbach and Schack (1993).…”

Section: Related Workmentioning

confidence: 99%

Incremental quantile estimation

Tschumitschew

Klawonn

2010

Evolving Systems

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Quantiles play an important role in data analysis. On-line estimation of quantiles for streaming datai.e.data arriving step by step over time-especially with devices with limited memory and computation capacity like electronic control units is not as simple as incremental or recursive estimation of characteristics like the mean (expected value) or the variance. In this paper, we propose an algorithm for incremental quantile estimation that overcomes restrictions of previously described techniques. We also develop a statistical test for our algorithm to detect changes, so that the on-line estimation of the quantiles can be carried out in an adaptive or evolving manner. Besides a statistical analysis of our algorithm, we also provide experimental results comparing our algorithm with a recursive quantile estimation technique which is restricted to continuous random variables.

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Incremental Statistical Measures

Tschumitschew

Klawonn

2012

Learning in Non-Stationary Environments

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Statistical Properties and Control Algorithms of Recursive Quantile Estimators

Cited by 7 publications

References 10 publications

Bayesian Formulation of Image Patch Matching Using Cross-correlation

Bayesian Formulation of Image Patch Matching Using Cross-correlation

Incremental quantile estimation

Incremental Statistical Measures

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