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# Lecture-17 - Lecture-17 Mixture of Gaussians Grimson 1...

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1 Lecture-17 Mixture of Gaussians Grimson

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2 Algorithm • Learn background model by watching 30 second video • Detect moving object by measuring deviations from background model, and applying connected component to foreground pixels. • Predict position of a region in the next frame using Kalman filter • Update background and blob statistics Summary • Each pixel is an independent statistical process, which may be combination of several processes. – Swaying branches of tree result in a bimodal behavior of pixel intensity. • The intensity is fit with a mixture of K Gaussians. ) ( ) ( 2 1 1 2 1 2 1 | | ) 2 ( ) Pr( j t j T j t X X K j j m j t e X m m p w - Σ - - = - Σ =
3 Mixture of Gaussians The K distributions are stored in descending order of the term j j s w • Out of “k” distributions, the first B are selected = = = T B K j j b j j b 1 1 min arg w w Learning Background Model • Every new pixel is checked against all existing distributions. The match is the first distribution such that the pixel value lies within 2 standard deviations of mean. •If no match, introduce new distribution.

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4 Updating The mean and s.d. of unmatched distributions remain unchanged. For the matched distributions they are updated as: ) ( ) ( ) 1 ( ) 1 ( , , 2 1 , , 1 , , t j t T t j t t j t j t t j t j X X X m m r s r s r m r m - - + - = + - = - - The weights are adjusted : ) ( ) 1 ( , 1 , , t j t j t j M a w a w + - = - = otherwise 0 matches on distributi if 1 , t j M
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Lecture-17 - Lecture-17 Mixture of Gaussians Grimson 1...

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