How large are Troisdorf's trees in three dimensions?

Victoria Luise Pissulla’s master’s thesis estimated the height and crown volume of 70,438 detected crowns in Troisdorf’s settlement area. Explore the recorded results below.

What this page shows

The colour-only Mask R-CNN detection model outlined the tree crowns. LiDAR points within each outline were then used to estimate height and volume. This page presents the recorded estimates; it does not calculate new volumes.

From the settlement study area to individual crowns

The original analysis covered approximately 29 km² of settlement areas in Troisdorf, delineated from ATKIS Basis-DLM. The maps locate the study area and show the distribution of recorded crown footprints. The ten red rectangles are the evaluation patches used for the later height-input detection comparison; they are not the extent of the volume analysis.

Troisdorf city boundary in orange and settlement study areas in yellow on an orthophoto. — Municipal boundary (orange) and settlement study areas (yellow). Select the map to open it at full size.

Geographic overview of the 70,438 recorded crown polygons in green and the ten detection evaluation patches outlined in red. — Green: recorded crown polygons. Red: ten evaluation patches. North up, EPSG:25832. The display extent follows the recorded crown distribution; the settlement study areas are shown in the adjacent map. Select the map to open it at full size.

Below, individual point clouds show how a geometric crown envelope was estimated. The later 250 m grid map summarises these same recorded crowns by neighbourhood-sized cells. Detection accuracy was evaluated on the ten test patches; it was not measured for all 70,438 town-wide crowns.

From orthophoto to crown volume

1 · Detect the crownThe Mask R-CNN model outlines each crown in the 2024 orthophoto.

2 · Extract the pointsLiDAR points inside the crown and a 0.5 m buffer form its point cloud.

3 · Measure the heightHighest minus lowest point of the tree's point cloud.

4 · Estimate volumeAn alpha shape encloses the points; the enclosed space is the crown-volume estimate.

Schematic drawings. The thesis used an alpha shape with α = 0.25. The result is a geometric envelope of the points, not wood volume. The original method is preserved in the thesis notebook.

How the alpha setting changes the crown envelope

An alpha shape fits a geometric envelope to selected points. Its form depends on the parameter and the available points. These original examples show why the geometric definition matters when interpreting a volume estimate.

Two triangular alpha-shape crown envelopes shown with height axes: alpha 0.25 on the left and alpha 0.5 on the right. — **A volume estimate depends on its geometric definition.** Original crown examples with alpha = 0.25 in (a) and alpha = 0.5 in (b). The surface encloses space around the points. It does not measure the solid wood contained in the tree.

Point density and point selection also affect the result. These illustrations explain the method; they do not validate the volumes against field measurements.

Look at a tree

Six of the 70,438 delivered point clouds. Drag to turn the tree; the green line is the crown outline found in the aerial photo, drawn at ground level. Colours show height above the terrain. The values are the recorded thesis results.

0 m

Results for all trees

Median crown area is about 18 m² and median height 6.4 m. The charts use logarithmic axes so small and large values remain visible.

Volume classes

Relationships between area, height and volume

Area, height and volume

Larger and taller crowns tend to have larger recorded volumes. Correlation describes this relationship; it does not establish volume accuracy.

Pearson r near 1 indicates a strong positive linear relationship. The notebook recalculates these values.

Tree crowns across Troisdorf

Each square below is a 250 m × 250 m aggregation cell, not an image pixel or an individual tree. Its colour summarises the recorded crowns whose locations fall in that cell: count, median crown volume, or median height. Hover over a cell for its values. Red rectangles locate the ten detection evaluation patches shown in the overview above. Uncoloured space is not evidence that there are no trees there.

Recorded crowns in a 250 m grid

Orthophoto of Troisdorf with the municipal boundary in orange and the settlement study areas in yellow, providing geographic context for the adjacent 250 m grid. — Troisdorf municipal boundary (orange) and settlement study areas (yellow). The adjacent grid summarises the recorded crown locations across these settlement areas. Both maps face north, at different display extents and scales. Select this map to inspect the boundary, aerial imagery and legend at full size.

Each grid cell represents 6.25 hectares. The colours describe recorded crown counts or median estimates within a cell. The grid provides a two-dimensional geographic summary of the three-dimensional crown analysis. The red outlines locate the ten small detection evaluation patches.

Comparison with the municipal tree register

The register is a comparison source, not exact ground truth. Its crown areas are derived from diameters; observations have different dates, and several registered trees can match one merged crown. Only aggregate values are shown.

What the results mean, and the data

Limits

Volumes are exploratory geometric estimates; they were not validated against field measurements and do not measure wood volume, biomass or carbon.
Automatic detection can miss, split or merge crowns.
LiDAR (March 2022) and imagery (August 2024) differ in date and season. Other objects within a buffered crown can affect estimates.
833 crowns have recorded zero volume; most contain fewer than four LiDAR points.

Data and code

Sources

Orthophotos: Geobasis NRW, InVeKoS DOP, August 2024, ground sampling distance 20 cm.
LiDAR point clouds: Geobasis NRW, March 2022, 4–10 points per m².
Tree register: Stadt Troisdorf.

For geographic inspection, open the QGIS project and select 08_Whole_Settlement_Crown_Volume. See the GIS guide.