Developing a seamless merging of real and virtual image streams and 3D models is an active research topic in augmented reality (AR). We propose a method for real-time augmentation of real videos with 2D and 3D objects by addressing the occlusion issue in an unique fashion. For virtual planar objects (such as images), the 2D overlay is automatically overlaid in a planar region selected by the user in the video. The overlay is robust to arbitrary camera motion. Furthermore, a unique background-foreground segmentation algorithm renders this augmented overlay as part of the background if it coincides with foreground objects in the video stream, giving the impression that it is occluded by foreground objects. The proposed technique does not require multiple cameras, camera calibration, use of fiducials, or a structural model of the scene to work. Extending the work further, we propose a novel method of augmentation by using trifocal tensors to augment 3D objects in 3D scenes to similar effect and implement it in real time as a proof of concept. We show several results of the successful working of our algorithm in real-life situations. The technique works on a real-time video from a USB camera, Creative Webcam III, onaPIV1.6GHz system without any special hardware support.