I’m a recovering scientist managing a remote sensing group at the NOAA Coastal Services Center. In my spare time, when I’m not torturing staff, I try to fit in some technical work on lidar processing and distribution.
Submitted by Kirk Waters on February 20, 2012
Zombies and lidar - Oh My!
A frequent question we hear is, "What can you see with lidar?" Since not all lidar is created equal, it might be easier to look at it from another direction, one which I'm sure is often on people's minds. That is, "What lidar specifications would be good enough to detect zombies?" Given the recent warnings from the CDC about preparedness for a zombie apocalypse, there is a clear need to get a head start in zombie detection.
The first thing we need to know is how big zombies are. Luckily, we have a very good notion of the source of zombies. They tend to be the same size as your typical human, though they may be missing some parts, so we'll trim our size estimates a little. Zombies are also expected to stoop a bit, so while their height will be lessened, their footprint from a nadir perspective may be a little larger. For the purposes of this exercise, I'll modify the human body dimensions found online, though I won't claim to know anything about the statistical validity of the measurements. We'll put our zombie dimensions as 5' tall (shorter than 5'9" average due to the stooping), 1'4" wide (reduced to account for potential arm loss), and 2' deep (increased to account for forward stoop and frequently outstretched arms). For non-U.S. citizens and the more scientifically minded, that's 1.52m x 0.41m x 0.61m.
Clearly the zombie is not a nice sphere where it wouldn't matter which angle we were coming from. Since the zombie is at its most dangerous in the mostly upright form, we'll use that position. The zombies that have had the misfortune of losing the use or existence of their legs will not be considered, though they would probably be a wider target for an aerial survey. The case of the prone zombie will be considered later.
From the nadir view, the zombie presents an odd ellipse shaped target that I'll approximate as a 25 cm radius circle. From an object detection point of view, we need to figure out if we're covering the ground adequately with laser pulses to get a reasonable return from an object that size. The size of a lidar pulse on the ground varies a bit, but a typical spot might be around the size of a small pizza box for those in the US. To make the math easier, I'll us a somewhat large spot size that matches the size of our zombie at 25 cm radius.
The lidar system is looking for energy coming back from the laser pulse exceeding some threshold and the amount that comes back from our zombie will depend on how much of the pulse hits the zombie (note that it is eye-safe, so no zombies are harmed) and how well the zombie reflects light directly back to the source. All this is pretty variable and individual zombie dependent, but if 50% of the spot hits the zombie, we're very likely to get enough energy back to consider it a return. Note that this is for a fairly fresh zombie and older zombies may be less reflective - more research is needed. After doing a little circle intersection math, we find that if the center of our lidar spot is within 20 cm of the center of our zombie, we'll get a return. Every lidar point we put randomly within the square meter containing the zombie has a 12.5% chance of hitting him/her/it with enough light to be detected by our system.
Looked at another way, we have an 87.5% chance of missing the zombie. Every laser pulse we send into that square meter has the same 87.5% chance to miss. So, what point density do we need to make sure we hit? Well, you can never be 100% sure in a case like this if the point placement is random and we aren't systematically painting the area. However, if we had a point density of 8 points per square meter, we would have only a 34% chance to miss or 66% chance to detect the zombie. If we need to detect every zombie, this might be a problem. If we're trying to detect that there are lots of zombies, we might not even need this density. Most people can run away from one zombie (remember, fitness is important) and the real trouble is when we have enough zombies to be a zombie apocalypse.
We only considered the nadir view. Most of the time the lidar system will be scanning off-nadir and we'll be looking for the zombie at an angle. This actually helps us because the zombie has some height and his effective size perpendicular to the laser beam is bigger. It would be a little easier without the stoop, but that's the nature of zombies. You can't have everything. It gets a little more complicated though because the height you get for that lidar return is just as likely to be from the zombie's knee - if he still has one - as from his head. Since you're looking for things that are around five feet or a meter and half tall, you might not realize the return from a knee is really a zombie.
The next problem we have is with terrain. The individual photons in a lidar pulse aren't going to penetrate something like a leaf or a tree. However, a lidar pulse is made up of a LOT of photons and some of them may have a path between the leaves. If you were in a forest and looked up, you might be able to see some sky depending on how thick the forest canopy is. Any place you could see the sky, is a path that lidar could get through to the ground and detect a zombie (for safety, you should not stand where the zombie is). Similar to our discussion above on detecting a zombie in open areas, the denser the forest, the more lidar pulses you'll need per square meter to increase your odds of getting through the leaves to the ground or zombie.
Finally, we'll consider the prone zombie. Generally a prone zombie is not as dangerous since lying on the ground gives them much lower mobility. While they present a larger target and may not require the sampling density, we do have to consider our measurement accuracy. They obviously don't have the stoop and outstretched arms that led us to use a larger thickness than their former human selves. Instead, a zombie would more closely resemble the nine-inch (~23 cm) thickness of the average person. It is possible that various differences in zombie bodies (blood pooling, spinal curvature, the occasional protruding axe) may increase this to an even one foot (30.5 cm). Just like any other measurement device, lidar has some degree of error and that error will determine whether or not you can confidently see the height bump of a prone zombie. How much error depends on a lot of factors - everything from the GPS satellite positions to the aircraft turbulence to the ground spacing of GPS base stations. The amount of error you can allow to detect those zombies also depends on how confident you want to be that you saw them or more importantly, that you didn't miss them. To generate one-foot contours following the U.S. National Map Accuracy Standards, you'd need lidar data that had an accuracy of about 9.25 cm RMSE or 18.5 cm at 95% confidence. Luckily, this is possible with today's technology as long as attention is paid to flight parameters and data quality.
I believe I see some zombies heading my way, though it is possible they are co-workers, so I'd better finish this up. It does appear that lidar is adequate in detecting zombies if sufficient point density and accuracy are maintained. Processing could still be somewhat complicated and is best left for another day. Luckily the typical zombie is a relatively opaque target and likely to give more consistent returns than something like a small bush. There are other aspects of zombie detection that we haven't hit, such as the effect of laser pulse length on detection in shallow water (the submerged zombie problem). That will have to wait for another day. By the way, in case you were wondering why imagery wouldn't be a better choice for zombie detection, lasers work perfectly well at night and we all know that's when zombies come out to play.