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To make the extraction robust, we model also disturbing objects. In the real world, they correspond to medium-sized 
volumes, e.g., cars, or they are vertical linear objects, such as poles and street-lamps. The latter can be modeled at the 
material and geometry level as vertical cylinders, which then appear in the shadow projection at the image level as long 
distinct dark lines. They are like the trunks directed in sun direction and can therefore be mixed up with them. The 
medium-sized volumes often appear as dark blobs disturbing the short dark lines of the branches and the blurred edge of 
the tree crown in shadow projection. To keep the model simple and compact, we decided not to integrate occlusions and 
shadows cast by buildings, though they are necessary in principle. 
3 STRATEGY 
The strategy on top of the model is based on "hypothesize and verify". The focus of attention is laid on objects with 
high contrast to make the extraction as productive as possible. We start with distinct dark lines in sun direction which 
are hypotheses for trunks. After the trunk is verified by integrating more and more evidence, we continue by tracking the 
branches, determination of the outline of the tree, and its classification. 
1. Extraction and Verification of Hypotheses for Trunks 
First, distinct dark lines representing the shadow projections of the trunks are extracted. Knowledge about existing 
objects, e.g., roads or buildings, may help to limit the search space geometrically, speeding up the extraction and 
making it more robust. Since the shadow of the trunk is oriented in sun direction, only these lines are selected and 
combined to form hypotheses for trunks. The direct projection of the tree is used as evidence to verify a hypothesis 
by extracting lines in nadir direction. By intersecting the shadow of the trunk with its direct projection, the position 
of the base of a trunk can be determined more accurately and robustly. If the base is occluded, it might be recovered 
using only this second kind of information. 
2. Tracking of Branches and Determination of the Outline of the Tree 
Starting from a hypothesis for a shadow projection of a trunk, the dark lines representing the branches in shadow 
projection are extracted. It can be seen as a further verification of the hypothesis for the trunk and it is based on the 
knowledge that the branches start at the trunk, branch out and become thiner and thiner. The latter can be used to 
separate trees with overlapping shadow projections. What is more, it can also be employed to separate trees from 
vertical disturbing objects. For this, the structure of the surrounding branches should be investigated. 
By using the end points of the branches together with the fact that the twigs form a blurred edge and the assumption 
that the shape of the tree is more or less compact and symmetric, the outline of the tree can be reconstructed using 
a snake-based approach (Kass et al., 1987). The diameter of the tree crown can be derived directly from the outline. 
The height can be computed from the known sun direction and the shadow outline projected onto a DTM. Based on 
the base of the extracted trunk and a DTM, the 3D position of the base of the trunk can be determined. 
3. Derivation of the Type of the Tree 
The type of the tree is derived by classification based on the shape of the outline, the ratio of the width of the tree 
crown and the height of the tree, and the structure of the branches. Because of the correlation between height and age 
of the tree, one can determine the approximate age of a tree when its type is known (Baumann, 1957, Spurr, 1960, 
Hildebrandt, 1996). 
The proposed strategy has been outlined for a single gray-scale image. We do not use color information, because the 
shadow has no color and the trunk is only weakly colored. In principle, n 7 2 images might be used to find corresponding 
structures of the branches. We have not done this due to the following reasons: Matching the shadow projection results in a 
refined DTM only. In suburban areas roads and other areas can in most cases be represented by plane surfaces sufficiently 
accurately. By matching the direct projection of the branches in two or more images, the 3D branching structure could be 
reconstructed. However, there are not only large problems in line extraction, but above all, the complexity of matching 
these structures is extremely high. The reason for this is that because of the complex distribution of the branches in space, 
their order can change totally in different images. Contrary to this, the information for our application can be derived 
which much less effort from the shadow projection of the tree. 
4 INVESTIGATIONS 
Figure 2 shows a part of an image showing a suburban area of the German town Tamm near Stuttgart. The original color 
image was scanned in black and white at a pixel size of 14 um corresponding to a pixel size of 4.2 cm on the ground at an 
image scale of 1:3000. The image shows a suburban area comprising buildings, roads, and trees. The image was taken on 
March 23. 1995. at about 11 o'clock in the morning. In early spring the deciduous trees are leafless. The shadows of the 
trees are mostly cast on roads and clearly show the structure of the branches. Figure 3a) is a part of Figure 2. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 53