REGRESSION ANALYSIS: A METHOD FOR EXTRACTING INFORMATION FROM 
SATELLITE IMAGES 
Michael Wüthrich 
Department of Meteorology and Climatology - University of Basel 
Spalenring 145, CH-4055 Basel, Switzerland 
Commission III 
Abstract 
Regression analysis is used for enhancing spatial res- 
olution of thermal information of à LANDSAT-TM 
5 image. This information layer can be used as an 
input for an urban area classification, which then can 
be used for extracting a functional link between the 
brightness temperatures and urban structures, again 
using the regression model. Finally, a simulation of a 
possible change of urban structures and its impact on 
brightness temperatures (as one important bioclima- 
tological factor) is carried out. 
Keywords: Regression Analysis, Classification, Image 
Analysis, LANDSAT, Thermal, Simulation 
INTRODUCTION 
While experimenting with different classification ap- 
proaches in a selected area! around Basel (Switzer- 
land) in the REKLIP?-project (area = 35000km?), 
the possibilities of including the thermal band 6 of 
LANDSAT-TM (see table 1) for classification pur- 
poses was analysed. One of the problems using this 
band, is the different resolution of thermal informa- 
tion (it contains 16 pixels of the other bands resolu- 
tion; see table 1), which either reduces the resolution 
of the classification or reduces the use of the thermal 
information. As the major interest of the classifica- 
tion was to differ the urban areas, a lot of the seperat- 
ing information can definitely be found in the thermal 
band. 
MULTIPLE LINEAR REGRESSION ANA- 
LYSIS 
The assumption made by a linear regression model is 
that the value for one response variable (y) can be 
  
1x 576km? with the city of Basel in its centre (located in 
the Upper Rhine Valley with the Jura in the south and the 
Black Forest in the north) 
2 REgionales KLImaProjekt: a trinational project between 
Germany, France and Switzerland 
422 
explained by a simple linear function of the k inde- 
pendent variables (21,22,...,24): 
k 
y=co+) cs (1) 
:=l 
The characteristical statistics can be defined and all 
data then standardised to avoid scale dependencies. 
‘The regression values can be received by inverting the 
correlation coefficent matrix: 
Ré = je & = À (2) 
R k * k partial correlation coefficent matrix of 
the k independent variables 
J vektor with the correlation coefficents be- 
tween each independent variable z; and the 
dependent variable y 
c* vektor with the partial regression coefficents 
of the standardised data 
By destandardising the regression coefficents of the 
standardised data the regression results of the raw- 
data can be received: 
k 
== ot Oy = RT 
o; zm c 2 and cq —-g 2,0 (3) 
Using the ordinary least square procedure to deter- 
mine the regression coefficents brings along restric- 
tions which are encapsulated in the Gauss-Markov 
theorem. The multiple linear correlation coefficent 
can be calculated as: 
k 
"mz S oh, (4) 
i=l 
ENHANCING THE SPATIAL RESOLU- 
TION OF THE THERMAL INFORMATION 
OF A LANDSAT-TM 5 IMAGE 
Using additional geographical information, Scherer 
and Parlow (1990) developed a method to enhance 
spatial resolution of NOA A-images. Here the aim was 
  
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