120 
4. EXPERIMENTAL RESULTS 
4.1 Required Texture 
Correlation inherently needs a spatial greylevel variance (texture). In case of low texture, wrong correlation results are 
obtained: 
e correlation methods working on highpass filtered images produce low correlation values in low textured regions, 
because the "texture" introduced by noise, which is different in both pictures, outperforms the real texture. 
e correlation methods working directly on intensity images tend to yield high correlation values even when the patterns 
do not really match. 
In order to test if the correlation measure at a specific point is reliable and to specially treat regions with low texture, 
we must have an adequate texture measure and we must know the minimal tolerable texture. We correlated images 
of patterns with different texture intensities at various differential disparities. These experiments showed the necessary 
texture intensity to discriminate corresponding regions from regions with differential disparity. The mean standard 
deviation in a 7x7 neighbourhood was used as measure for texture and the results are presented as a function of this 
local standard deviation. For corresponding regions the correlation value is low for low texture and reaches its maximal 
level at a local standard deviation of 8. 
In a next step we calculated the segmentation error when distinguishing a region of good correspondence from another 
region with nonzero disparity. The threshold was chosen at the intersection point of the two histograms. Figure 3 shows 
the segmentation error for three differential disparities (0.9, 1.8, 3.5 pxl) as a function of the local standard deviation. 
The figure shows that a texture measure of 8 is sufficient. Figure 4 shows the detection rate in function of the distance 
from the separation surface (= differential disparity) for various correlation methods (Nishihara: kernel size 7x7 and 
bandlimit w = 2,3, 5; Sobel: kernel sizes 5,7,9). 
4.2 Texture Measure 
Analysis of the local variance is a good basis for texture measure. However, the variance var has quadratic terms and 
depends on the mean value y: 1 2 1 
= — I(m,n) — ith = — I(m, 5 
var=— 3 (I(mn)-p)’ with p=— 3 I(mm) (5) 
i,j=1..m,n $,2z1..m,n 
therefore the calculation of the local variance requires a lot of hardware resources. Various gradient-operators, which 
' are easier to calculate, were tested to get texture information. Summing up, the mean value of the gradient operators 
are a linear function of the local standard deviation, but the variance of the local standard deviation is smaller than 
the variance of the gradient operators and therefore results in better segmentation. Table 2 shows the linear factor 
between the mean value of the local standard deviation and the gradient operators, the relative standard deviation of 
the operators and the segmentation error when discriminating textures with different texture intensities. 
In order to illustrate the abstract texture intensities, the local variances of some sample surfaces were measured: 
  
  
  
  
    
    
  
  
  
  
  
  
  
  
Surface type mean value relative std. dev. Surface type mean value relative std. dev. 
White paper 1.7 0.2 Light jeans tissue 8.8 0.17 
Brown paper 3.0 0.2 Human hand 7.4 0.3 
Dark jeans tissue 5.6 0.15 Carpet 18.0 0.15 
0.4 1 : : 
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0.3 : Fb. 5 MA : 
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: 11]: t > 
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2 i t RE : : AE Nish w=2, Sobel 7x7 
2 0.2 i SOS Mense quss ique Gs ; aie : access p “Li Nish wed; Sobel 5x8 
A Seat. i ik... oe NSN ere ; 
o : 0.47 ; 7-3 > er ? 
0.155 AL HEN : 
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0.1} : 
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0.05 1 O.1F-- f m a. u^ Bb Nereessasassauusamusasssneeneeeusédeseces wir 3 
MN : uem as ee ; Tt. 
0 Q — 1 t . 
0 5 10 15 20 25 30 -30 -20 -10 0 ; 10 
Texture strength (standard deviation) Distance from separation surface [mm] 
Figure 3: Segmentation error as function of texture Figure 4: Detection rate in function of distance for several 
intensity correlation methods and kernel sizes 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995