Breathing can be measured in a non-contact method using a thermal camera. The objective of this study investigates non-contact breathing measurements using thermal cameras, which have previously been limited to measuring the nostril only from the front where it is clearly visible. The previous method is challenging to use for other angles and frontal views, where the nostril is not well-represented. In this paper, we defined a new region called the breathing-associated-facial-region (BAFR) that reflects the physiological characteristics of breathing, and extract breathing signals from views of 45 and 90 degrees, including the frontal view where the nostril is not clearly visible. Experiments were conducted on fifteen healthy subjects in different views, including frontal with and without nostril, 45-degree, and 90-degree views. A thermal camera (A655sc model, FLIR systems) was used for non-contact measurement, and biopac (MP150, Biopac-systems-Inc) was used as a chest breathing reference. The results showed that the proposed algorithm could extract stable breathing signals at various angles and views, achieving an average breathing cycle accuracy of 90.9% when applied compared to 65.6% without proposed algorithm. The average correlation value increases from 0.587 to 0.885. The proposed algorithm can be monitored in a variety of environments and extract the BAFR at diverse angles and views.