In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). 1APRS. Vol. XXXVIII. Pan ЗА - Saint-Mandé, France. September 1-3. 2010 
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of datasets and every method has advantages and drawbacks 
with results depending on the selected thresholds and the 
expected fraction of outliers among the observations. Until 
now, the user has to manually select the outlier rejection 
method but a criterion for automatic switching on the basis of 
the detected characteristics is under development. 
Figure 2. The flowchart of the implemented method. The 
symbol indicates optional functions or data. 
After the image pair matching for all possible combinations, the 
found stereo pairs are concatenated according to the network 
geometry. Different strategies can be followed: 
- ordered image sequences (Figure 4 and 5): as the overlapping 
is guaranteed between consecutives images, the whole sequence 
is divided into /7-2 triplets. If I is a generic image, each triplet 7) 
is made up with the images {/,, /,+i, /,+2}. For each triplet 7) a 
pair-wise matching between the couples of images C, = {/,, /, +] } 
and C/-{/,+], /,+2} is carried out in order to determine a set of 
homologous features. Correspondences of the couple C/= {/,-, 
/,+2} are determined from the points of the images 7, +1 which 
also appear on the images 7, and 4+ 2 . After the single triplet 
matching, the image coordinates of consecutives triplets are 
compared in order to determine correspondences in the whole 
sequence. The triplet T, and the next one T i+l = {7, +] , /, +2 , /¡+3} 
share two images and their tie points can be transferred with a 
simple comparison based on the value of the image coordinates. 
In addition, for closed sequences an additional triplet T a ={I„. 1, 
/„, /)} is added to match first and last images. This method has a 
linear computational cost O(n) with respect to the number of 
images, with a significant advantage in terms of CPU time. 
- unordered sets of images (Figure 6): this is the general case, 
where it is necessary to check all possible image pair 
combinations to determine the ones sharing sufficient 
correspondences. Therefore each image must be compared with 
all the others, leading to a high computational cost 0(n 2 ). For 
this reason, the use of a visibility map (which can be 
automatically estimated) is recommended. 
2.3 Image coordinates refinement 
After the concatenation step, the precision of the image 
coordinates can be improved with a Least Squares Matching 
refining (LSM; Grün, 1985). Although an orientation with SIFT 
or SURF features can produce sub-pixel results, the refinement 
with LSM gives better results (Table 2). The use of LSM allows 
the analysis of low resolution images with SIFT and SURF (by 
using a coarse-to-fme approach). This limits the number of 
extracted features and speeds up the comparison of the 
descriptors. These features are then projected onto the original 
images by considering the applied compression factor and 
become good approximations for the LSM refining. In the case 
of widely separated and convergent images, the descriptor 
values can be used as initial approximation of the LSM 
parameters (Remondino and Ressl, 2006). 
Casel 
(1936*1296 px) 
Case 2 
(2816*2112 px) 
RMS 
# 
(Го 
RMS 
# 
SIFT alone 
0.54 
0.36 
87 
1.21 
0.86 
793 
SIFT+LSM 
0.33 
0.22 
68 
0.86 
0.61 
784 
SURF alone 
0.86 
0.58 
137 
0.47 
0.33 
104 
SURF+LSM 
0.51 
0.34 
104 
0.35 
0.24 
95 
Table 2. Orientation results in terms of a 0 , RMS (both in pixels) 
and number of final 3D points with the SIFT and SURF 
operators, coupled with an image location improvement (LSM). 
6 images - 2816*2112 (px) 
Object size: ¡.2*1*1 (m) 
С-- 
SIFT+LSM 
FAST+LSM 
#3D points 
1181 
541 
On (px) 
0.42 
0.28 
m _ -vT 
RMS (px) 
0.43 
0.32 
Л J i 
o x (mm) 
0.27 
0.13 
<7 V (mm) 
0.39 
0.24 
4 Jr Ì l 
<7. (mm) 
0.65 
0.33 
ННИННИ 
Table 3. Comparison between feature- and comer-based 
orientation procedures with a LSM refining. 
As the precision of the computed object coordinates improves 
with the number of images where the same point is visible, an 
additional matching procedure based on the FAST operator 
(Rosten and Drummond, 2006) was added. FAST demonstrated 
to quickly extract a large number of comers under a higher 
repeatability compared to SIFT and SURF, with also a better 
distribution in the images and a higher accuracy of the final 
sparse geometry (Jazayeri and Fraser, 2008). According to these 
considerations, the FAST operator was included in the pipeline