1. A computer-implemented process for allowing a local user of a local mobile device to participate in a video conference session with a remote user of a remote mobile device, wherein the local and remote mobile devices are interconnected by a network, and the local mobile device comprises a local display screen, a front video capture device that is pointed toward the local user and captures live video of the local user, and a rear video capture device that is pointed away from the local user and captures live video of a scene that is in front of the local user, comprising: using the local mobile device to perform the following process actions: receiving live video over the network from the remote mobile device; displaying the received live video on the local display screen; upon the local user selecting either the live video of the local user, or the live video of the scene that is in front of the local user, transmitting the selected live video over the network to the remote mobile device; resizing the selected live video as necessary to fit within an inset sector on the local display screen; and displaying the resized selected live video within the inset sector; and whenever the local user makes a first digital annotation on the received live video, displaying the first digital annotation on top of the received live video, recognizing and tracking objects that exist in the received live video, and anchoring the first digital annotation to said objects, wherein said anchoring allows the first digital annotation to track said objects and maintain its orientation relative to said objects if said objects move.