Change detection generally is the difference between images. The differences or changes could be due to moving objects or a variation of illumination. In general the goal is to extract only changes due to moving object that occur int eh scene, and to ignore changes due to illumination. A requirement is that the detection has to be performed in real-time. The proposed change detection approach relies on a model assigning a vector to every pixel of the reference and the current image. Based on this model, linear independence is used to describe an operator for change detection. This previously published operator is based on the variance. The improved linear independence model consists in redefining the change detection operator to fulfill the real-time requirement and to improve the object detection performance. This model has been applied to surveillance and compared to the variance based linear independence detector. The operator proved to be robust to background and illumination changes and in the same time it detected object changes.