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Let be an image of the frame n which is taken at time and the images are taken with the time interval . A pixel value s located at at time is defined as below.
means the pixel value at in the image . A difference image is segmented into two regions according to .
This region consists of the projections of the nodes in and a background.
Moving region consists of three regions; generated moving region , continuous moving region , and vanishing moving region . These three regions are defined below. In the formulations, means union of the projections of all the nodes in the node set onto the image plane.