We propose a novel method that localizes the thermal footprint of the facial and ophthalmic arterial-venous complexes in the periorbital area. This footprint is used to extract the mean thermal signal over time (periorbital signal), which is a correlate of the blood supply to the ocular muscle. Previous work demonstrated that the periorbital signal is associated to autonomic responses and it changes significantly upon the onset of instantaneous stress. The present method enables accurate and consistent extraction of this signal. It aims to replace the heuristic segmentation approach that has been used in stress quantification thus far. Applications in computational psychology and particularly in deception detection are the first to benefit from this new technology. We tested the method on thermal videos of 39 subjects who faced stressful interrogation for a mock crime. The results show that the proposed approach has improved the deception classification success rate to 82%, which is 20% higher compared to the previous approach.