 So, in this talk, I'm going to discuss about using multi-camera system to measure the three-dimensional motion of the birth in the field. So in this talk, I'm going to show you that by improving the measurement accuracy, we are able to measure both, not only the body motion, but also the wing motion of the birth in the field. And this work is a collaboration work between three different universities. And it is sponsored by Human Frontery Science Program. So using multi-camera system to track the motion of the birth has been used in many years. But the problem is that the distance between camera is relatively shorter compared to the distance of the birth to the camera. And as a result, the image measurement accuracy in the direction perpendicular to the image plan is relatively low. So in most previous work, people have just treated the birth as a single point. They are not able to measure the wing motion. So the purpose of our study is that we are going to develop a system that is able to overcome the distance barrier between the cameras so that we are able to improve the measurement accuracy in all three directions. And I'm going to show you that by doing this, how we can measure both the body motion and the wing motion. So this is our simple experiment setup. So because if you want to work in the field, it's very important to make the system very portable. So we actually apply the USB cameras. So those cameras can be both powered and controlled through a single laptop. So we're using four cameras. Each two camera is controlled by one laptop. And in this experiment setup, the camera is looking into the sky. And the birth is flying at a height about 50 meters height. So we set our cameras at the distance into 50 to 60 meters. But in some other system, when the birth is flying even higher, we are able to extend the distance even further. And so as you see here, this is a sample image. We capture from the image when the birth is flying through the cameras. So from these images, you could see that the shape of the birth is clearly distinguishable. So we are able to measure both the body and the location of the wing. And this is how we set up the camera in the field. So the birth species we're interested in is the Jack-Tor and the Rook. Both the birth species belong to Carvold family. So they are social animals. So during the daytime there, they will spend the time in the town to find the food. And in the late afternoon there, the birds were gathering together and flying towards the trees where they spent the night. So the flying path of the birth is very predictable. So we could set up the cameras in the farm just above the flying, just below the flight path to capture the motion of the birds. And so one very important problem is how do you solve the optical occlusion problem. So because the birds, they have very high collared motion and they may fly very close to each other. So you may have some situation when two birds, they form an overlap image on camera one. So as you heard in yesterday morning's talk, they have developed some global optimization work to solve the occlusion problem. But here, since we can take advantage of the larger distance between cameras. So even if you have overlap image on camera one, because the other camera has very different viewing angle, so the birds will not form overlap image on camera two. So we can take advantage of that to develop a simple algorithm to solve the occlusion problem. So first of all, we just follow the simple one-to-one match, just like for each detect the birds on camera one to find the matched one on camera two and to detect the birds. So after this step, you may see that there's still one bird that is missing. You haven't used that information. So we could do additional steps, like searching the unmatched birds from the first one to find the unmatched birds. So we could recover the missing birds. And then by combining these two steps, we're able to recover all the birds. And then we can track them in time to find the trajectory. And so as I mentioned that we are able to measure the shape of the birds. So now I'm going to show you how we can measure both body and wing motion. So initially, we just detect the center of the birds, just based on the center of the shape. So that 2D location is coupled with both body and wing motion. So if you're using this 2D location to calculate the 3D trajectory, you will find out that the trajectory have this wave package, have this high frequency wing motion. So then we can set a cut off, because the body motion has a very relatively low frequency. However, the wing motion is a very high frequency. You could set a cut off frequency to gather the body motion, and then you can subtract the body motion from this hole and to gather the wing motion. Now you may ask the question, whether this body motion really captures the center of the birds? So we could project the 3D location back to the camera to see whether this really captures the center of the body. So yes, we do. We're really able to capture the center of the body. And now, since we calculated the wing motion, we could do a continuous wave wave transform to gather the time dependent wing bead frequency. So as you can see here, we clearly distinguish that the flapping motion, during the flapping motion, the wing bead frequency is about 5 hertz, and then the birds start to decrease height into the gliding mode, where the wing bead frequency is zero. So by doing this, we are able to measure along the 3D trajectory, we are able to measure the wing bead frequency, the time dependent wing bead frequency. And here I'm showing you a sample data with 15 jackdolls flying through the tracking volume. So you saw that for each trajectory, we were able to measure the varying of the shape. So I'm going to show you that because most early work about the birds, about the collective motion of birds, they only depending on the position of velocity. So here, since the wing motion is something which the birds could control, directly control in response to environmental stimulate. So this may help, using wing motion may help us to better understand how the birds is response to other environmental stimulate. So the first thing we can use the wing motion is to classify the trajectory into different flying modes. So we have, so in this plot, I'm plotting some simple trajectory, the changing of height as they traveling around. So we can look, and the color is colored by the wing bead frequency. So we found that the birds can have three flapping modes. So by depending on the changing of height, they could fly horizontally without changing height or clamping or diving. And the birds can also like, has none flapping region, which can also decreasing height or increasing height. For each flying mode, we are able to calculate the flying speed and the wing bead frequency. And the second thing is that we are able to maybe investigate a little bit about the wing aerodynamics in the field. Because people have studied the wing aerodynamics in the laboratory, such as put the birds in the wind tunnel to study how the force is generated on the wing. And they found out that as you increase, after you increase the speed above 10 meters per second, if you keep increasing the speed, they found out that the birds has to flap the wing much faster. That is because above 10 meters per second, if you keep increasing speed, the drag on the wing is become higher and higher. So the power is also increased. So the birds has to flap the wing much faster. But however, such kind of experiment has never been performed, it's very hard to conform in the field. But here, since we can measure the wing bead frequency, so we are able to conform whether this experiment is true in the field, whether it's really happening in the field. So we plot the wing bead frequency as a function of the flying speed. We indeed conform that as you increase in the flying speed, the wing bead frequency also increase. The second thing is that we are able to tell us the response time between a pair of birds. So we found a pair of birds. So you have these two trajectory. The birds A, first of all, clamping and then diving. Then the birds B just follow the path of the bird A. So you may ask, what's the response time? What's the time lag between B and A? So in the previous work, people have determined the delay time based on the acceleration of velocity correlation. So from here, if you plot the acceleration, you could look at the peak location of the when the birds have the highest radial acceleration to determine the delay time. And in both methods, that tells you a delay time about 0.3 seconds. But however, the velocity and the acceleration is the consequence of how the birds changes the wing motion or changes the body posture. So this is a consequence of how the birds change in the wing motion. It may not tell you how fast they respond. So here, because we are able to measure the wing motion, so we could directly measure how fast they respond. So from here, you could see that the red one, if you look very carefully, you'll find that the bird A stops the flap as a wing. But however, the bird B has to finish a whole wing bead cycle, then stops the wing motion. So the delay time is, if you look at the wing bead frequency, it also tells you that the delay time is about one wing bead cycle. So the first of all, the delay time is about 0.3 seconds. They all match with each other. This is a good news. The more important thing is that maybe it tells you that how fast a bird can respond to its neighborhood. It depends on how fast it could flap its wing. If the bird has higher wing bead frequency, it may indicate that the bird could respond faster. So the third thing you can ask is, where the flying group could save energy? So in this well-organized group formed by Snow Geese, some people have shown that the birds in the behind could actually take advantage of the upward wing motion generated by the birds in the front to save energy. However, in this randomly organized group, whether the birds could save energy or not. This is questionable. And we could actually check that. So we plot the wing bead frequency as a function of local density. So local density is calculated by how many neighborhood birds around me. So we found out, as you increase in the local density, like if you have more birds around me, the wing bead frequency also increase. However, the flying speed doesn't increase. So it may indicate that flying in group may not save energy for this randomly organized group. Now we can move on to ask the question, why flying in group couldn't save energy in this randomly organized group? So we calculated the acceleration as a function of local density. And we found out that as you increase in local density, the acceleration has also to increase. That means we could decouple the acceleration in the direction that along the flying direction and in the direction normal to the flying direction. And we found out most of the acceleration is due to the acceleration normal to your flight direction. That means the birds in more dense group has to make more turns to avoid collision into some other birds. So that maybe tells you why flying in group in this randomly organized group doesn't save energy. Maybe also cause increase energy. And the last thing we can use the wing bead frequency is that as I told you before, we have two different bird species. One is jactal, another is rook. If you just look very carefully along how the bird shape looks like, maybe it's a little hard to determine which one is which. Now, because since we can measure the wing bead frequency, maybe we could be using the wing bead frequency to identify the birds. So we did some more experiment to measure some pairs of isolated jactals and rooks. We identified that indeed the rooks and the jactals have different wing bead frequency. So this may indicate that we may able to using the wing bead frequency to identify the birds in this flock. So now I'm going to move forward like we also have some data with flock with about more than 200 birds. So this is around the x1 is around the flying direction and the x3 is the gravity direction. And we saw that the birds as they fly traveling around the distribution is not homogeneous. Instead, they form some subgroups around the flying direction. You saw that the subgroup 1 or subgroup 2. And the subgroups, they are connected by some birds located in between. So you may ask the question, whether this is two subgroups, they are interacting with each other or not. So we actually performed the correlation and analyze to look at the correlation of the velocity fluctuation. So in this plot, we plot the velocity fluctuation subgroup 1 or subgroup 2, or you could do the analyze for the entire group. And in this plot, you show that the blue one is corresponding to this blue curve. You could say that as you increase the subgroup size, the correlation length also increase. And the more interesting is that if you treat the two subgroups as a whole, the correlation length even increase much larger than the subgroup size. So it may tell you that the two subgroups is really interactive with each other. So the next step we are going to do is we are trying to understand how does the information transfer from the first group to the second group. So this is what we are going to do in the future. And the second, so this is a very special case for the car world family, because you will always see a pair of birds flying very close to each other. That is because in this car world family, this pair of birds, they have a very long time social relationship. This pair of birds maybe come from the same family, which is a father and a mother. So you may ask the question, maybe the pair of birds have much stronger interaction within the pairs compared to the rest of the group. And such a kind of heterogeneity, how this heterogeneity will affect the global structure or local interaction is questionable. So this is also the second direction we are going to do. And we have performed some preliminary analysis. You could look at the first neighborhood relatively positioned, like surrounding me. So if the theta is 90 degrees, it means it's on my side. If it's 0 or 180 degrees, it's in my front or back. So you could say that for some birds, which is a pair, so the distribution is more anthropic. So the more anthropic the distribution is, it means that you have much stronger interaction. So we really confirm that the pair of birds has much stronger interaction compared to the birds that is not a pair. And the next thing we are going to do is we are trying to find out whether this local heterogeneity interaction will affect the global structure. And so I put the conclusion here that we develop a portable system that is able to measure both body and wing motion. And I show you that if we're using the wing motion, we are able to better characterize the birds' behavior in the nature. And then I also show you some heterogeneity effect on the global behavior. With that, I'd like to thank all for your attention. And I'd like to take any question you might have. Any questions?