Screening systems for infectious diseases based on fever have been implemented at international airports to prevent the spread of infection for over a decade. Currently, only Infrared Thermography (IRT) is used for screening and measuring facial skin temperature, which is one of clinical indicators of potential infection. Aiming at higher accuracy in screening, our group adopted heart rate (HR) and respiration rate (RR) for the first time as the new screening parameters. In our previous study, we proposed a screening system based on dual image sensors, which include IRT and a charged-coupled devices (CCD) camera. The sensors can measure three vital signs simultaneously, namely HR, RR, and facial skin temperature. For the measurement of RR in this system, stability and swiftness must be applied for application in airports. In this study, we introduce feature matching and multiple signal classification (MUSIC) algorithm in this system. Feature matching between thermal images and RGB images captured by a CCD camera and IRT, respectively, is used to detect the nose and mouth in IRT, which helps extract respiration signals corresponding to airflow from breathing. In addition, the MUSIC algorithm improves the accuracy of RR frequency estimations in limited time respiration signal and achieves swiftness. The proposed method improves stability by simultaneously detecting the nose and mouth in thermal images, and enhances the accuracy of estimated RR using the MUSIC algorithm. By using this system, we evaluate the accuracy of the estimated vital signs. The performance of this screening system was evaluated using data obtained from 12 influenza patients and 13 healthy subjects at a clinical facility in Fukushima, Japan.