## 4 Application examples  
### Termite head-banging experiment  
A typical application of the described image pattern tracking algorithm is to quantitatively investigate the termite head-banging behavior, which induces sound waves that can be used to detect and identify different termites behind the wall. Head-banging in termite soldiers in response to some disturbance is well known [13-15]. The head-banging movements of termites can be captured with a standard (PAL/NTCS) video system, i.e. 25/30 full frames or 50/60 interlaced frames per second. However, a high-speed imaging system is required to map the details of the head-banging movement, because the head-banging period is around 30 ms that cannot be resolved with standard video systems. In the present work a head-banging behavior is resolved with more than 300 frames at 10,000 fps by using a Photron's ultra APX high-speed imaging system, so that the temporally dependent termite head displacement, instantaneous velocity and acceleration can be determined. Image frames of 256\(\times\)256 were taken with a scale of 0.04 mm/pixel. Some sample images obtained in this experiment are given in Fig. 1. During the tracking, image patterns were chosen on the termite head in size of 24\(\times\)24 pixels, i.e. 0.96\(\times\)0.96 mm\({}^{2}\). The physical coordinate origin is set to the image pattern position in the first frame.  
In order to determine the optimal image pattern tracking freedom limit, the first 225 frames in the termite head-banging recording group are selected for a multi-pass tracking test. At the 225 th frame (i.e. t=22.4 ms), the termite head falls almost to the same position as in the 1 st frame, so that the image pattern in these two frames are very similar. That allows a reliable tracking of the last (i.e. in the 225 th frame) image pattern back to the first frame, so that the accumulated tracking bias can reasonably be determined. The accumulated tracking bias distribution on the tracking freedom limit for the test case is given in Fig. 9, and it is shown that the minimal tracking bias can be obtained with _L_=5.  
The image pattern tracking results, i.e. the time histories of the termite head position in a 33-ms head-banging period, are given in Fig. 10 for a tracking freedom limit of 5. It is shown that the termite raises its head slowly in 15 ms to accumulate potential energy, and then releases the potential energy quickly in 8 ms by moving the head down until it strikes the substrate. Then the termite head passively rebounds up and down (striking the substrate) again for several more times until the energy is completely released. The main head-bang is completed in 24 ms with a rising magnitude of 1.67 mm, and the following secondary head bangs have a much smaller magnitude (\(\approx\) 0.2 mm) and shorter period (\(\approx\) 5 ms). The time histories of the termite head velocity are determined with the image pattern displacement and time interval, and the results are given in Fig. 11. The figure shows that the maximal velocity in the head raising period is 0.2 m/s at t =8 ms, and the maximal velocity in the head falling period is 0.34 m/s at t =21 ms.  
As shown in Fig. 12, the acceleration time histories of the tracked termite head can further be computed according to the velocity time histories shown in Fig. 11. The total acceleration (i.e. \"a\" in Fig. 12) has a high peak of 362 m/s\({}^{2}\) at the main head-bang, i.e. at t =22.8 ms. The corresponding striking force of the termite head with known weight (mass) of 1.37 mg is estimated as 0.5 mN. Note that the support force of the termite neck and the gravity should also be considered when using the estimated striking force value. It should also be mentioned that the measured valuables are twodimensional in the camera focus plane. The out of plane component, i.e. in z-direction, cannot be determined with the described image pattern tracking system.