Video sequences captured over a long range through the turbulent atmosphere contain some degree of atmospheric turbulence degradation (ATD). Stabilization of the geometric distortions present in video sequences containing ATD and containing objects undergoing real motion is a challenging task. This is due to the difficulty of discriminating which part of visible motion is real motion and which part is caused by ATD warping. Due to this, most stabilization techniques applied to ATD sequences distort real motion in the sequence. We propose a method to classify foreground regions in ATD video sequences. This classification is used to stabilize the background of the scene while preserving objects undergoing real motion by compositing them back into the sequence. A hand-annotated dataset of three ATD sequences is produced with which the performance of this approach can be quantitatively measured and compared against the current state of the art.