The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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current pyramid, and matching results from current pyramid 
will be used to update terrain range at next lower pyramid. By 
this way, the ambiguity of terrain variation is reduced at each 
pyramid level and search range should be reduced as well and 
converge to a small value, which is a function of terrain slope, 
accuracy, and pixel size. 
If there are no mismatches and blunders, both terrain variation 
and search range will converge through iterations. However, 
mismatch is inevitable in stereo image registration and blunder 
does exist, so search range won’t reduce effectively and may 
ends up too big at low pyramid levels. That is why blunder 
elimination turns to be a very important part of adaptive ATE. 
We developed three blunder elimination techniques: positional 
cross-correlation, PCA-based blunder elimination, and object 
filtering. The first two are applied at the end of matching at 
each pyramid level to suppress mismatches, and object filtering 
is used at final pyramid to eliminate spikes, buildings, and trees 
to produce bare-earth. 
2. BLUNDER ELIMINATION TECHNIQUES 
2.1 Positional Cross-Correlation 
Positional cross-correlation (PCC) measures the consistency of 
relative point locations between two sets of points on image 
space. It is calculated using the following equations: 
coef. (1.00, 0.96) 
coef: (1.00, 0.85) 
Figure 1. Positional correlation coefficients without blunders 
(left, vertex linked by solid lines) and with blunders 
(right, points linked only by dashed lines). Points are 
triangulated in objected space and linked in image 
space to show the displacement 
2.2 PCA-based Blunder Elimination 
This method is based on piecewise smoothness constraint on 
object space. Point cloud in neighbourhood is fitted to a 
principal plane using PCA decomposition (Rao, 1972) and 
points with big distance to this plane are eliminated. Distance 
threshold is dynamically changed with variation of distances. 
Fig. 2 shows an example. 
E({*\-E{xJ){x 2 -E(x 2 )) 
jE((x 1 -E(x i )f-E((x 2 -E(x I )) 1 (1) 
' jE((y t -E(y,))/‘.E[(y 1 -E(,y 1 )) 2 
where, p x is PCC of x coordinates 
P y is PCC of y coordinates 
are image coordinates from set 1 
(x 2 , y 2 ) are image coordinates from set 2 
EQ is an operation to calculate mean value 
Figure 2. Principal plane, blunder points (in red, square-shaped) 
and in-range points (in blue) 
Fig. 1 shows an example: left shows points without blunders 
where PCC is high (1.00, 0.96); right shows points with 
blunders where PCC y is low (0.85). A low PCC normally 
indicates mismatches, which can be identified by iteratively 
eliminating the most-inconsistent pair and re-calculating PCC 
until PCC is big enough. 
This method works for terrain with slopes and also adapts well 
to various natural terrain such as mountains, hills, and flat 
planes. It can normally remove 30% of matches as blunders and 
make terrain estimation reliable for matching at next pyramid 
level. However, this method alone is not suitable for 
metropolitan area where high-rising buildings cause too much 
discontinuity. 
The threshold for PCC is currently practised with empirical 
values. This method can eliminate approximate 5% of matched 
points that are normally big mismatches. 
2.3 Object Filtering 
Blunders that survive above two methods can be further 
eliminated by object filtering. Buildings and trees can be 
filtered as well to generate bare-earth. 
Our object filter is called “ebb process”. It is similar to ebb of 
water: suppose at beginning all buildings and trees are flooded 
with water; as water ebbs away, building/tree tops will first 
come out of water and appear as standalone regions that are 
relatively simple to analysis; and then water level will drop for 
several meters before ground appears. If a region is high and 
small enough before it connects to terrain, it will be classified 
as an object (building, tree, or spike); otherwise, it will be 
merged into terrain. Fig. 3 and 4 show an example. Fig. 3 is a 
DSM together with slope edges that indicate boundaries of 
objects. Fig. 4 shows ebb process while elevation drops from 
278m to 250m.