# Detection and Model of Thermal Traces Left after Aggressive Behavior of Laboratory Rodents
## 4 Results
### Temporal Analysis  
Figure 10 shows two simulated images with traces and the results of Harris detector. The simulated trace was superimposed on the simulated shape during simulated motion of two objects, therefore sometimes the trace was covered by the body of the other individual. A small proportion (7.6%) of all simulated trace sequences had only one measurement per process (the trace was visible for only one frame during whole process) and were therefore excluded from further analysis. Nearly one-fifth (18.9%) of cooling and 9.4% of heating processes achieved negative coefficient of determination value, indicating poor fitting of the data to the model. In fact, a negative result was often caused by one wrong measurement and/or a small number of all measurements (see Figure 11b cooling). The average length ratio LR for the rest of measurements was 0.44 \(\pm\) 0.12 and 0.47 \(\pm\) 0.25.  
Figure 8: Multiple comparisons of (**a**) R score for the temperature and the trace size, (**b**) ranking for trace and the filter size. T stands for temperature, S for the trace size and F for the filter size.  
Figure 10: The results of [PERSON] corner detector (**b**,**d**) on the simulated images (**a**,**c**) in the (**a**,**b**) 7 th and (**c**,**d**) 19 th frame of simulation. The trace is marked with a red rectangle and the detected corners are marked with red crosses.  
Figure 9: The results of [PERSON] corner detector on the real images with simulated saliva trace of size (**a**) 2 pixels and (**c**) 3 pixels. The trace is marked with a black rectangle. Panels (**b**,**d**) are the detected corners are marked with red crosses.  
The mean values of coefficient of determination (\(R^{2}\)) between the observations and simulated values for the rest of traces was 0.87 \(\pm\) 0.22 for cooling and 0.81 \(\pm\) 0.23 for heating processes.  
The effect of the trace length on the \(R^{2}\) value was calculated using the correlation coefficient, which was equal to 0.15 for cooling and 0.08 for heating. The scatter plots for both processes are presented in Figure 12.  
Figure 11 shows some curves fitted to the corners detected by the [PERSON] algorithm. Black circles denote detected corners, and the blue dashed line is the curve best fitted to the observed corners. The red solid line presents the simulated (modeled) curve. The coefficient of determination presented for each process measures the quality of fitting the temperature of detected corners to the simulated data. We have chosen one example of a good fit (Figure 11a) and one example of a poor fitting (Figure 11b).  
A visualization of summary statistics for the R score and the ranking grouped by the simulation frame number are presented in Figure 13 as a box plot. The bottom and the top of each box are the 25 th and 75 th percentiles of the sample, respectively. The red line inside each box is the sample median. The whiskers extend to the adjacent values, which correspond to approximately \(\pm\)2.7\(\sigma\). Observations beyond the whisker length are outliers marked as a red \(+\) sign only in Figure 13b. Outliers for R score were omitted in Figure 13a so as not to clutter the image.  
Figure 11: Fitting examples of cooling (**top graph**) and heating (**bottom graph**) for four different traces: (**a**) with high value of \(R^{2}\) for both processes: 1 and 0.99, respectively, (**b**) with negative value for cooling (\(R^{2}=-1.14\)) and positive for heating (\(R^{2}=0.81\)).  
Figure 12: Scatter plots of trace length (LR) effect on the \(R^{2}\) value for (**a**) cooling and (**b**) heating processes.