Reliable, remote measurement of respiration rate is still an unmet need in clinical and home settings. Although the predictive power of respiratory rate for a patient's health status is well-known, this vital sign is often measured inaccurately or not at all. In this paper we propose a camera-based monitoring system to reliably measure respiration rate without any body contact. A computationally efficient algorithm to extract raw breathing signals from the video stream has been developed and implemented. Additionally, a camera offers an easy access to motion information in the analyzed scenes, which significantly improves subsequent breath-to-breath classification. The performance of the sensor system was evaluated using data acquired with healthy volunteers, as well as with a mechanical phantom, under laboratory conditions covering a large range of challenging measurement situations.