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# Lecture-14 - Change Detection Skin Detection Color Tracking...

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1 Change Detection, Skin Detection, Color Tracking Lecture-14 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 µ µ π ω Σ = Σ =
3 Summary Where X=[R,G,B] T , is a 3x 1 mean vector, is a 3x3 covariance matrix. The method assumes that RGB color channels are independent and have the same variance . In this case = I. Where I is a 3x3 unit matrix. 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. •Another way of measuring distance from a Gaussian distribution is the Mahalanobis distance i.e the match is the distribution with M-distance less than a threshold ) ( ) ( 1 j t j T j t X X d µ µ Σ =

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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 µ µ ρ σ ρ σ ρ µ ρ µ + = + = • The weights are adjusted: ) ( ) 1 ( , 1 , , t j t j t j M α ω α ω + = = otherwise 0 matches
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