We propose an interface achieved using surrounding stereo cameras as a method of independently recognizing the intentional arm-pointing gestures of several users. The stereo cameras provide depth information maps in real time with resulting robustness against the influence of changes in lighting and users' clothing. Utilizing this, we developed a method capable of sensing intentional arm-pointing gestures that ignored unconscious arm-pointing gestures. This interface does not depend on the user's position, direction, or posture. We placed four stereo cameras in four corners of the ceiling and used this method in various lighting environments. We evaluated the arm-pointing gestures of seven subjects at multiple points and obtained reliable accuracy. Furthermore, we applied this method to the arm-pointing gesture interface of home electronics appliances using Bluetooth.