This contribution examines the problem of linking two remote rooms into one shared teleconference space using augmented reality (AR). Previous work in remote collaboration focusses either on the display of data and participants or on the interactions required to complete a given task. The surroundings are usually either disregarded entirely or one room is chosen as the "hosting" room which serves as the reference space. In this paper, we aim to integrate the two surrounding physical spaces of the users into the virtual conference space. We approach this problem using techniques borrowed from computational geometric analysis, from computer graphics and from 2D image processing. Our goal is to provide a thorough discussion of the problem and to describe an approach to creating consensus realities for use in AR videoconferencing.