A new algorithm is proposed for novel view generation in one-to-one teleconferencing applications. Given the video streams acquired by two cameras placed on either side of a computer monitor, the proposed algorithm synthesises images from a virtual camera in arbitrary position (typically located within the monitor) to facilitate eye contact. Our technique is based on an improved, dynamic-programming, stereo algorithm for efficient novel-view generation. The two main contributions of this paper are: i) a new type of three-plane graph for dense-stereo dynamic-programming, that encourages correct occlusion labeling; ii) a compact geometric derivation for novel-view synthesis by direct projection of the minimum-cost surface. Furthermore, this paper presents a novel algorithm for the temporal maintenance of a background model to enhance the rendering of occlusions and reduce temporal artefacts (flicker); and a cost aggregation algorithm that acts directly on our three-dimensional matching cost space. Examples are given that demonstrate the robustness of the new algorithm to spatial and temporal artefacts for long stereo video streams. These include demonstrations of synthesis of cyclopean views of extended conversational sequences. We further demonstrate synthesis from a freely translating virtual camera.