along the arcs thus to speed up the procedure. 
2.) Window selection: The predicted point is projected 
into the two images. The coordinates, scales and 
shears are used to select a new subpatch out of the 
image patch in the higher level or to drive the came- 
ras to a new position in the image in order to scan a 
new image patch. 
3.) Matching: The measurement of the node in the measu- 
ring tree uses the matching method preselected for 
this level. The result is a surface point with its 
surface normal, thus a planar approximation of the 
surface within the area of the image patch. 
The change between the levels is controlled by two rules, 
which are applied at each node of the measuring tree: 
1.) Change to the lower level if the current level is not 
the lowest level. This rule ensures that the proce- 
dure tries to measure in the level which gives 
highest accuracy and that it tries to stay there as 
long as possible. This rule leads to a sequential 
procedure in each level. 
2.) Change to the higher level if the predicted subpatch 
is not likely to be fully contained in the image 
patch of the higher level and if the current level is 
not the highest. This rule ensures that the nodes of 
the higher levels are measured before the nodes in 
lower levels and guarantees the prediction to stay 
local. 
At the moment there are no rules which control the change 
of the levels depending on the result of the matching in a 
level, e. g. if the texture or the slope prevents the algo- 
rithms to converge. After various attempts to succeed with 
matching ( e. g. by changing tuning parameters such as win- 
dow size, point density etc.) have failed, the arc is closed 
with a node of degree one (cf. the following section). 
The rules are set up in a way that the number of levels 
needs not to be fixed. Moreover, the operator can define the 
window size to be selected and the matching procedure to be 
used in each level, including manual measuring. 
The arc measuring procedure starts in the highest level 
below the root of the measuring tree. The position and slope 
of the first node in this level are derived from the infor- 
mation of the start node of the arc. Only at the beginning 
of the whole measuring procedure the operator provides the 
measuring tree with this information. Matching and subpatch 
selection are performed until the lowest, the leaf level is 
reached (rule a.). Then, still following rule a., the nodes 
of this level are measured until the image patch of the pa- 
rent of these nodes is left. Now rule b. becomes active and 
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