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tlons, 
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ched 
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or in 
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imes, 
pixel 
fos Ve) 
correspond to pixel displacements in the current camera frame’s 
full-seize pyramid level. The determinant of the warping matrix 
can decide the level of the image pyramid. 
The position and pose updates are computed iteratively by 
minimizing a robust objective function of the re-projection error. 
lun? 
Ep... pu.4:79,)- el 
(3) 
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22e, —#(p,.a,)} +(v, -v(p..a,)] 
X = arg min Tonle], | (4) 
Oy 
Tukey bi-weight objective function Obj(, o-..) is applied as a 
robust objective function and x is a set of parameters. Iteration 
of reweighted least squares method is used to allow the M- 
estimator to converge. 
3.1.2 Feature Points Mapping: Once camera position and 
pose are estimated, three dimensional coordinates of the feature 
points are mapped. First of all, an initial map is built based on 
intersection (Stewenius et al., 2006). For the optimization of 
intersection, RANSAC algorithm (Fischler and Bolles, 1981) is 
applied. Here, the scale and coordinate systems are arbitrary, 
not set as real scale and world coordinates. 
After that, the map continuously refined and expanded, while 
key frames are added by the above camera tracking. The key 
frames are recognized when number of frames exceeds a certain 
frames from previous key frame. With the added key frames, 
the bundle adjustment is applied for improving the accuracy 
(Triggs et al., 2000). In order to solve the bundle adjustment 
problem, Levenberg-Marquardt method (Hartley and Zisserman, 
2004) is applied. The objective function E is approximated by 
the following formula 
  
E(x+6x)= E(x)+ g Sc OX HOY (5) 
(H — A1 )éx =g (6) 
where g= dE (gradient) 
dx |, 
Hs dE (Hessian) 
dx? x 
  
À = dumping factor 
There are two types of the bundle adjustment: full bundle 
adjustment and local bundle adjustment. The local bundle 
adjustment uses only some recent key frames. The full bundle 
adjustment is more accurate than the local bundle adjustment, 
but computational load is more expensive. The local bundle 
adjustment method will be discussed later. 
3.2 Investigation of the SLAM Applicability in Outdoor 
Environment 
We investigated the applicability in outdoor environment by 
comparing the feature points tracking in indoor and outdoor 
environments. Table 1 shows comparison of the results of 
feature points tracking during one minute. 
Table 1. Comparison of the results of feature points tracking 
  
  
  
  
  
  
  
  
  
  
indoor outdoor 
initial number of feature points 1036 290 
0 (fine) 600-840 | 150-250 
number of feature points | 1 40-300 0 
in image pyramid level 2 15-70 0 
3 (coarse) 5-50 0 
final number of feature points 2650 289 
number of key frames 14 26 
  
  
  
The tracked feature points successfully were greatly reduced 
compared with application in indoor environment. Since 
objects in the scene were very far, feature points extraction 
provided worse performance. Additionally, images features for 
tracking changed drastically with tiny camera moving. Asa 
result, the estimated coordinate system tilted and three 
dimensional models arranged inappropriately (Figure 2). 
  
Figure 2. Inappropriately model arrangement 
4. IMPROVEMENT OF SLAM METHOD 
According to the experimental result, the method is improved 
by introducing auxiliary information. One is simple markers as 
the auxiliary information, another is GPS. 
4.1 Marker-Based Approach 
One of approaches for improvement of the method is 
introduction of simple markers on ground as auxiliary 
information. ARToolKit (Kato and Billinghurst, 1999) is a 
famous software library of marker-based approach. The 
marker-based approach calculates the real camera position and 
orientation relative to physical markers in real time. The marker 
is defined as two dimensional code patterns (Figure 3), and it 
makes recognition easier. 
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