. Beijing 2008 
SATELLITE 
data employed 
nth radiometrie 
orms as jagged 
>, the frequency 
only larger than 
integration time, 
the jagged edges 
er, the jitter can 
Is on the whole 
o their original 
bjects shown in 
pixel integration 
can be taken as 
iptions in jitter 
with Beijing-1 
to see if jitter 
hypothesis. As 
>es, the runway 
rty of the jitter, 
as reference for 
red runway is 
centroid of the 
position of the 
ith x y value of 
ted. 
ing the residual 
f relevant lines, 
ig and sampling 
tes to all linear 
refore it can be 
r in Beijing-1 
f pixels on lines 
rome, where (a) 
îe image after 
les 
The International Archives of the Photogrammetry, Remote Sens ing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The achieved displacement from the runway is shown in Figure 
3, the displacement value ranges from -1 to 1, fluctuates with 
the disciplinarian similar to that of a sinusoid, except that the 
frequency and swing is stochastic. Similar conclusion can also 
be drawn from experiments with other linear objects. 
Figure 3. Displacement value of each line 
Uniform are displacements of pixels on the same line, 
manifestation of jitter affiliated to linear objects in different 
directions varies. Hence line jitter performance with image 
containing multi-direction linear objects is simulated as 
validation (Figure 4). Consulting the figure above, period of the 
jitter is set to be 8.3 lines and swing is assumed to be one pixel. 
Displacement value of line i can be calculated with equation 3. 
/(o=i.o*siiA 
O. J 
(3) 
The simulation result explains the variational performance of 
jitter on lines with diversified direction. Jitter shows clearly in 
vertical and near-vertical lines. However, as direction of the 
line approaches horizontal, displacement of pixels on the line is 
somewhat compensated by their tendency. Jitter gradually fades 
away as lines fall horizontal, in horizontal lines jitter can not 
even be seen visually. Performance of jitter in the simulated 
image is the same as that in Beijing-1 panchromatic images. 
It can be concluded from the above analyses that jitter in the 
Beijing-1 panchromatic image can be modelled as varied 
horizontal displacements of the lines. Thus by proper horizontal 
shifting of the lines, jitter in the image can surely be removed. 
The key factor lies in proper assessment of the line 
displacement values. 
4. JITTER REMOVAL 
The adjacent lines in 4-meter resolution image can be 
considered as highly correlated due to the high sampling rate. If 
the lines are shifted, their correlation value degrades. This 
theory fits the correlation of lines in unjittered Beijing-1 
panchromatic image. Figure 5 shows variation of the line 
correlation values against displacement changes between 
adjacent unjittered image lines. In the figure, three groups of 
lines and their correlation variation curves are drawn, showing 
degraded correlation with increasing displacement while the 
absolute displacement value is less than 40. It implies that the 
displacement value can be evaluated by degradation condition 
of the correlation. 
(a) 
(b) 
Figure 4. Jitter simulation with image containing multi 
direction linear objects, where (a) is the original image, (b) is 
the image acquired with line jitter added 
-100 -80 -60 -40 -20 0 20 40 60 80 100 
Line displacement 
Figure 5. Correlation between unjittered adjacent lines 
The jitter in Beijing-1 panchromatic images range from -1 to 1. 
In this range, the correlation distribution is a one-peak curve. 
Figure 6 shows correlation variations of nine groups of jittered 
image lines, the peaks swing from -1 to 1, the displacement 
values with correlation on the peak can be taken as line 
displacement values that can be used to rectify the jitter. 
Therefore, least square fitting of the curves can be used to get 
the displacement values with the highest correlation. 
931