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Since radiometry variations in two images cannot be compared, 
because of the difference between captors responses, cqrrelation 
is done in gradient images (see Figure 4). Correlation scores on 
15x15 windows present various aspects (see Figure 5). Some 
edges and multiple peaks appear. They should be filtered to keep 
only unique sharp peaks. 
  
       
Figure 5: Correlation windows on gradient images on Harris 
edges. 
This approach is fully automatic and leads to comparable results 
to interactive points matching. 
4.3 Segments extraction 
3D segments : Segments extraction in peint cloud is fulfilled 
by planes intersection. Planes are extracted using region growing 
in the range image. Seeds are chosen by click into the retro- 
diffusion image overlayed by range image. They could also be 
chosen at random, or on a regular grid, on the same scheme as 
for points. Single value decomposition on the 3D points set leads 
to plane’s parameters. For the growing process, an aggregation 
criterion is put on distance to the plane, which removes outliers. 
This threshold t is set according to the noise of measure(l = 30). 
Noise on data is integrated so on by robust estimate on numerous 
points. 
2D segments : We are using Canny-Deriche edge detector (De- 
riche, 1987). So, we are handling the alpha parameter and a 
compromise between localization and sensitivity to noise. Then, 
comes a hysteresis threshold, chaining and pixel chains polygo- 
nisation by split and merge algorithm. At last, to increase edge 
localization quality, a subpixelar estimate on the pixel chains is 
performed by least-square fitting. 
  
Figure 6: Repartition of the segments. 
At the moment, segments matching is interactive. Automation 
should be easy, since we can predict segments’ position in image 
with a simple projection from approximate pose estimate. 
1133 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
5 STATISTICS 
The approach presented in this paper uses rigorous least-squares 
adjustment at three stages : edge fitting, plane fitting and global 
system minimization. For each case, residuals are normalized. 
This representation allows error propagation and thus, assessment 
of the quality of pose results. 
The covariance matrix on pose parameters results from propa- 
gation of the covariance matrix of the observations, which can 
be determined by propagation of the variance of the measures. 
Formalization of error propagation for linear and non-linear sys- 
tems is described by Hartley and Zisserman (Hartley and Zisser- 
man, 2000). For more details about uncertainty propagation, see 
(Fórstner, 2004) for single view geometry and (Jung and Boldo, 
2004), where the same mathematical model is studied for bundle 
adjustment. Therefore, error propagation has been used at three 
stages of our study. 
5.1 Primitives consistency. 
Error propagation needs prior estimation of error for observations 
on each primitive. 
Points 
e Two cases have been tested to find 2D points. 
— Points are plotted into digital images. Here, we con- 
sider that accuracy is ranging about 1 pixel. 
— Points are extracted by Harris detector. Since detec- 
tion is followed by correlation, this method provides 
subpixelar accuracy on localization. 
If targets have been placed into the scene, their center would 
be recovered with a precision from 0.1 to 0.01 pixel (de- 
pending on the image quality). 
e 3D points have direct relation with laser scanner measure. 
We are using scanner with range measure standard deviation 
of 6 mm. As we perform multiple-shots measures, standard 
deviation is reduced : 0, = 01/ Vv (n) For instance, we use 
four measures for each points. This leads to c4 = 3 mm. 
In first approximation, we consider homogeneous standard 
deviation around point. 
Segments As linear features come from least-square estimate, 
we can predict their respective variance from the variance of data 
measures. 
e 2D segments are fitted on edge points detected by the 
Canny-Deriche operator. The line parameters are re- 
trieved by regression (Taillandier and Deriche, 2002). The 
variance-covariance matrix of these parameters are esti- 
mated from variance on pixels, which depends on signal to 
noise ratio in image. 
e 3D Segments Assuming that range measures follow a Gaus- 
sian law, the forward error propagation frame enables to cal- 
culate the variance-covariance matrix of the parameters of 
the normal to the plane. We may then spread variance to 
cross product, considering the Jacobian matrix of the appli- 
cation. This part of our work is still under development. 
5,2 Pose quality evaluation 
In this paragraph, uncertainty on location and orientation has 
been investigated for pose analysis. 
Experiments have been performed on sets of 15 segments and 15 
points. 20 random sampling/trials of n segments amongst 15 have 
been proceeded. We have also randomly sampled 3 and 12 points 
amongst 15 points. Configuration with 3 points corresponds to 
the minimum number of points needed for space resection.