taken by 
ecause of 
0 a forest 
a), using. 
'eometric 
1). 
aspect of 
But this 
itically a 
it change 
ses taken 
such as 
ing pixel 
t of Oran 
ed by the 
e (pinus 
ea While 
measured 
nospheric 
rface 1s 
Lambertian and uniform in rugged terrain, the radiance 
measured by the sensor is : 
PUvcos05TAIUT 
hund s 2 ML (1) 
where : 
Es : sun radiance on the top of the atmosphere 
Tes ,Tev : transmittance in the double path sun-target-satellite 
p : observed target reflectance factor. 
The conversion of the spectral radiance Lsa into a digital 
number DN is expressed as follows: 
La: 7 A.DN * B (2) 
A and B are sensor calibration coefficients or gain and offset 
values of the sensor. 
Then : offset = -A/B & gain G=B. 
The relation between the digital number of an unchangeable 
pixel in the image taken at the time t, and its corresponding 
pixel in the image taken at the time t; in a rugged terrain and 
in similar weather conditions is expressed by : 
  
CN; - CN, - 
ref CN A 
cos Q,. 1 cos 0;, 2 
(3) 
where a and b are coefficients normalisation of DN? with 
respect to DN. 
COS 0; s describes the topographic features of the pixel. 
Using the derived slope and aspectas well as the position of the 
pixel regarding the image geometry and sun position, its 
expression is as follows : 
cosQj, 7 cos0, cosÜ y * sinÜ, sinÜ cos(p, — 9p) (4) 
where 
6, : zenith angle 
0, : slope in degrees 
@s : sun azimuth 
9» : aspect in degrees. 
The topographic and instrumental effects have been corrected 
CN —- off 
COS 
calculating the plans, , of every image. 
is 
To estimate the coefficients a and b of equation (3), some 
surface objects whose reflectances were unchangeable with 
time were selected to determine the regression line by taking 
ground samples into account (See table 1). 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
Table.1. mean and RMS values of the samples 
and the coefficients of normalisation 
  
  
Samplel Sample2 Coef. of 
(sea) (ground) normal. 
Bands DNmean © DNmean o a b 
TM! 7/84" 81-89/>71 7220056 1035.23 1 0:70::521:17 
TM1/93 7862 1.74 161.87 4.30 
TM3/84 1497 0.76 14152 532650827031 
TM3/93. 15.93 1.04 11926 4.51 
TM4 /84- 692 “1.35 1161771 34:49-70 89-> 477 
TM4/93 7.994 196 105.30 4.49 
  
The image of 1984 was corrected and then the image of 1993 
was taken as reference. The coefficients a and b of the linear 
regression (3) were computed to undertake the correction in the 
same conditions as of the image of 1993. 
3.1.1. Results 
The coefficients estimation allowed to get atmospheric 
The normalisation was performed 
comparing reflectances of some samples, corresponding to 
unchangeable objects, taken from the paired images before and 
after normalisation. The results are illustrated in the table 2 : 
comparable 
images. 
Table. 2. mean values before and after atmospheric correction 
  
  
  
TM samplel (sea) sample2 whole image 
band/year ( forest ) 
DNmen 6 *DNmsas ^0 | DNmm 0 
TM1 / 84 82.00 244 8692 431 10545 21.94 
TM1/93ref 79.06 1.93 8148 462 96.11 1522 
TMi /correc : 78.70 + 1.79 8200 3:00 ‘94.939 15,35 
TM3 / 84 1488: 1.51 3156 469 5311. 2840 
TM3/93ref 1640 112 2962 477 46.86 2146 
TM3/correc 1588 131 2957 387 4726 2338 
TM4 / 84 693 208 7485 14.15 81.96 41.23 
TM4/931ef 8.73 : 1.59 71.69 10.36” 66.77: 33:51 
IM4/comec 792 195 6343 1257 74.71 37.13 
  
The quality of the relative atmospheric normalisation of images 
is also pointed out by analysing the coefficients of correlation 
of the paired images (see table 3). 
Table. 3. correlation coefficients 
  
  
band Cor. 
Coef. (1) 
TMI 0.9825 
8d(raw) TM3 0.9921 
93(reference) TM4 0.9869 
TMI 0.9942 
84 (norm.)-93 TM3 0.9923 
TM4 0.9960 
  
3.2. Change detection 
Change detection based on atmospherically corrected images is 
performed by undertaking simple combinations between the 
spectral bands. 
In this study a spectral ratio between comparable images at two 
different dates was calculated. The band TM4 was considered 
because in contains a big deal of information on vegetation. 
677