Measuring Trees

For this latest project I wanted to explore some of the math involved with drone mapping. I photographed a favorite meadow in Hope Valley with a significant slope to see what measurements I can calculate using the data generated. In my earlier posts I describe how the RGB or color values in an aerial image can be used to quantify or measure vegetation coverage of an area, and in this post I’ll expand on that idea by describing some of the math involved to calculate the heights of trees and shrubs, as well as the slope of a meadow.

Parallax, Binocular Vision, and Photogrammetry

The first important concept to understand is parallax. You experience parallax constantly, whenever you are looking at something with both eyes open. In animals, this type of vision is called binocular vision and it allows our brains to calculate the distance an object is from us based on the discrepancy of what the right eye sees versus what the left eye sees. The image below shows 3 different points, with different angles from the right and left eye.

Drone mapping uses a similar principle, but using the discrepancy in sizes of an object as the drone photographs that object from different locations. By taking photographs of objects from different distances and angles, software can triangulate each point into a 3d point with an x,y, and z coordinate. Using that data, several different map products can be created. I’ll talk about each of them next.

Orthomosaic: This is the composite image which shows the top down view, stitched together from the hundreds of images taken. Each point on the map has a RGB value (red, green, blue). Note the yellow hue from this image, there was considerable smoke from wildfires and I will need to reprocess the orthomosaic after doing batch color correction to the 346 images which make up this map.

DTM: The digital terrain model, or DTM shows the elevations of the terrain, excluding any objects like buildings or trees. This is generated by removing points deemed outliers and averaging the slope to create an even gradient. You’ll notice in the image below that some clumps of shrubs and trees are still visible in the DTM, so it’s not a perfect process.

DSM: The digital surface model shows the absolute heights of each point on the map. Here you’ll see that the tall trees really stand out, while buildings and shrubs are still visible. These heights are still absolute heights calculated using the GPS on the drone as it took images.

Minus: Minus is a function which we teach children at a very young age. In sixth grade math, we use number lines to visualize the difference between two values and then subtract (minus) one value from the other to find the difference. Our GIS software can do the same thing. By subtracting the DTM (digital terrain model) from the DSM (digital surface model), we can find the relative difference between the calculated ground elevation and the calculated height of objects to find their height. Here you’ll see that the trees really stand out and the faint outlines of shrubs and the three buildings.

I’ll write a future post on groundtruthing, or the process of checking the validity of your data with other tools in the field, an important step to ensure any conclusions or decisions you make are based on accurate data. I took some pictures with my phone which I can use to refer back to when looking at the map.

For example, one of the outbuilding skeletons pictured below make a good case study.

Only the timber framing remains. Take note of the clump of trees to the south.

Here we see the outbuilding in the orthomosaic. That blank white area is where the software couldn’t piece the corrugated roof together.

Here we see the height data in the minus layer. The back of the building measures 4.34 meters (14.2 feet). The clump of the trees to the south has a high point of 8.88 meters (29 feet).