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Advancement in science and technology is playing an increasingly important role in solving difficult cases at present. Thermal cameras can help the police crack difficult cases by capturing the heat trace on the ground left by perpetrators, which cannot be spotted by the naked eye. Therefore, the purpose of this study is to establish a thermalfoot model using thermal imaging system to estimate the departure time. To this end, in the current work, we use a thermal camera to acquire the thermal sequence left on the floor, and convert it into the heat signal via image processing algorithm. We establish the model of thermalfoot print as we observe that the residual temperature would exponentially decrease with the departure time according to Newton's Law of Cooling. The correlation coefficients of 107 thermalfoot models derived from the corresponding 107 heat signals are basically above 0.99. In a validation experiment, a residual analysis is conducted and the residuals between estimated departure time points and ground-truth times are almost within a certain range from -150 s to +150 s. The reverse accuracy of the thermalfoot model for estimating departure time at one-third, one-half, two-thirds, three-fourths, four-fifths, and five-sixths capture time points are 71.96%, 50.47%, 42.06%, 31.78%, 21.70%, and 11.21%, respectively. The results of comparison experiments with two subjective evaluation methods (subjective 1: we directly estimate the departure time according to obtained local curves; subjective 2: we utilize auxiliary means such as a ruler to estimate the departure time based on obtained local curves) further demonstrate the effectiveness of thermalfoot model for detecting the departure time inversely. Experimental results also demonstrated that the thermalfoot model has good performance on the departure time reversal within a short time window someone leaves, whereas it is probably only approximately 15% to accurately determine the departure time via thermalfoot model within a long time window someone leaves. The influence of outliers, ROI (Region of Interest) selection, ROI size, different capture time points and environment temperature on the performance of thermalfoot model on departure time reversal can be explored in the future work. Overall, the thermalfoot model can help the police solve crimes to some extent, which in turn brings more guarantees for people's health, social security, and stability.

Estimating Departure Time Using Thermal Camera and Heat Traces Tracking Technique