International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
the terrain. The terrain is thus modelled as pieces of continuous 
parallax curves with upper and lower bounds representing the 
terrain roughness, as shown in Figure 4 (right). 
  
  
oor 
  
  
  
Figure 4. Detection of large parallax outliers by continuity 
verification (left); terrain represented with piece-wise cubic 
curve and upper/lower bound (right) 
For the same matching quality (assuming 1/3 pixel parallax 
accuracy), the 3-D measurement error of a stereo point will be 
proportional to the square of its distance to the camera. For 
example, the uncertainty of point locations derived from 
Navcam images is 3.2m at a range of 50m and 14m at a range 
of 100m, while that for Pancam is 0.86m at 50m and 3.5m at 
100m. At a far range, a very small matching error (less than one 
pixel) can cause a very large measurement error, and introduce 
significant outliers in DEM generation. We therefore apply a 
Delauney triangulation of points in the X-Y plane, then 
backproject the triangular network onto to the image plane, as 
shown in Figure 5. For any matched pair, if its parallax is 
smaller than the true value, the measurement of the point will 
be farther away from the camera than the actual distance (in an 
inverse proportion). Thus surrounding points in the 
triangulation will all be more distant from the current point pair 
and their position in the image should also be higher since they 
are visible. Thus, the backprojected triangulation will form a 
valley. If the parallax is larger than the actual value, a peak will 
be formed. Peaks and valleys are easy to see; all of them can be 
eliminated after several rounds of iteration. 
3.2 Inter-stereo Registration 
Interest points between inter-stereo image pairs are matched by 
backprojecting 3-D interest points from one image to its 
matching pair. Suppose (x0, y0) and (xl, yl) are 2-D 
coordinates of the tie points in images 0 and 1 and the 
backprojected coordinate from 0 to 1 is (xl', yl"). Then the 
dislocation (x1-xl',y1-y1^) is a function of the camera-rotation- 
counting error (d0, dg). The correct match can be found by 
  
Figure 5. Triangulation of points in the X-Y plane (left); 
detection of small parallax outlier by backprojection (right) 
dédg, 
arg max 9 C, |(p, - p;) - / (40,49) (1) 
where (dO, do) arc the camera-rotation-counting errors 
C; is the similarity value between point 0-i and 1-j 
pi is the backprojection of 0-i from image 0 to image 
f(d0, dq) is the pixel dislocation caused by (d0, dq) 
Pairs of interest points corresponding to the final (dO, dq) are 
correct matches of tie points. An example is shown in Figure 6. 
  
Figure 6. Registration of inter-stereo tie points 
3.3  Intensity-Balance 
Panoramic images often come with different levels of 
illumination, as seen in Figure 7 (left). They can be balanced by 
removing the intensity difference among inter-sterco tie points. 
Direct adjustment over a linear model y=a(x+b) will reduce the 
dynamic range during propagation along the image link. Instead, 
a model y=a(x-hy)+b is used to adjust the dynamic range a over 
the zero-mean intensity value (x-by) and then to adjust the mean 
intensity 5. By randomly fixing one image and propagating its 
dynamic range and intensity via tie points, the entire panorama 
can achieve a balanced intensity, as shown in Figure 7 (right). 
1044 
  
34 
Froi 
inte: 
sem 
for 
with 
Fig 
The 
in th 
very 
long 
TIN 
  
Figur 
The 
outpu 
impre 
The | 
point: 
norm; 
travel 
identi