Statistical analysis of a change detector based on image modeling of difference picture

A statistical analysis of a change detector for motion detection based on image modeling of a difference picture is presented. The approach is founded upon the fact that complete silhouettes of moving objects can be segmented at each frame time using a change detector based on image modeling of the difference picture. The change detection problem can be treated as a signal detection problem in which very little is known about the signal to be detected. The exact modeling of the background event is necessary for a robust change detector which can adapt to changing environments. The governing statistics for change measures, which have a form of sum of squares of the difference picture, can be inferred from the assumed Gaussian distribution of the stationary background in the difference picture and are used for calculation of the adaptive decision threshold for the change detector. It is shown that the adaptive decision threshold derived from the change measure minimizes the total probability of error as measured in false alarms and missed detections. Experimental results that support the underlying statistical analysis are presented