challenge for the matching algorithm compared to the indoor
scene. The selected frames are representative of occlusions
and aspect changes of camera motion in day and night condi-
tions. Table 3 shows statistics of the results from the corre-
sponding frames in Figure 11.
According to Table 3, the average precision of focal length
is 0.03 mm, while the precision of the angles is under 1/30 of
a degree. In comparison to the indoor dataset, the uncertain-
ties of the parameters are higher. This can be attributed to
the poor image coverage of the wireframe model lines during
instances where the camera viewing perspective forces the
prospective matching to take place in a small portion of the
image space. It is assumed that the lack of matching features
in these “control free” image areas increases the level of
uncertainty for the estimated parameters. Both RMSE
v
and
σ
v
have an overall error of less than three pixels.
Photogrammetric space resection has been used to obtain
the reference camera parameters for all 144 frames of the out-
door dataset. The corresponding six image-to-3
D
CAD
model
points have been manually acquired. Figure 12 shows the dif-
ference between reference parameters and
LR-RANSAC
-derived
parameters. The mean errors are: -0.01 mm for focal length,
-0.17° for omega, -0.004° for phi, and 0.06° for kappa. These
values tend to zero, thus suggesting lack of bias. The mean
absolute errors for parameters are: 0.07 mm for focal length,
0.28° for omega, 0.19° for phi, and 0.30° for kappa.
Comparison of LR-RANSAC with Sequential Relative Angular Orientation
An alternative to applying wireframe to image matching for
each individual frame is sequential relative angular orienta-
tion (
SRO
) between the highly overlapping image frames. It is
based on “open traverse” geometry for the determination of
absolute (world) camera angular parameters for each sequen-
tial frame based on an initial absolutely oriented frame of the
image sequence. Anchored by frame
t-1
, whose image to world
camera parameters are known, the focal length and relative
angles between frame
t-1
and frame
t
are estimated. The relative
angles are estimated using the standard collinearity math-
ematical model. The
SIFT
algorithm (Lowe, 2004) and
RANSAC
are used to robustly establish matched feature points between
image pairs. Figure 13 shows the behavior of rotation param-
eters automatically generated by
LR-RANSAC
versus absolute
Figure 10. Camera parameter errors using LR-RANSAC for the Indoor Scene Sequence: (a) Focal length error (mm), (b) Omega error (de-
grees), (c) Phi error (degrees), and (d) Kappa error (degrees).
T
able
2. I
ndoor
S
cene
: E
stimated
V
alues
at
V
arious
F
rames
across
I
mage
S
equence
LR-RANSAC based camera parameters
frame f(mm)
ω
°
φ
°
κ
°
σ
f
(mm)
σ
ω
°
σ
φ
°
σ
κ
°
RMSE
v
(pix)
σ
v
(pix)
13
21.7
-9.9
-1.2
-1.1
0.06
0.0013 0.0008 0.0012
0.19
0.20
31
21.1
-3.3
-1.9
-1.1
0.13
0.0028 0.0018 0.0052
0.66
0.70
41
21.7
-3.5
3.2
-0.77
0.01
0.0001 0.0001 0.0003
0.05
0.05
50
21.7
-2.9
-4.9
-1.4
0.24
0.0110 0.0091 0.0094
1.33
1.42
67
21.6
-3.9
-0.5
-1.1
0.09
0.0021 0.0017 0.0034
0.64
0.67
80
21.9
-0.7
-0.9
-1.1
0.24
0.0057 0.0043 0.0101
1.67
1.57
90
21.1
-9.9
3.8
-0.5
0.13
0.0023 0.0016 0.0051
0.50
0.53
94
22.1
-9.5
5.5
-0.2
0.32
0.0030 0.0024 0.0122
0.68
0.73
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
November 2015
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