RECTIFICATION OF AIRCRAFT THEMATIC MAPPER IMAGERY 
M J Smith lecturer, V Veronese Research Student and P M Mather Professor 
University of Nottingham, England 
ISPRS Commission IV 
ABSTRACT: 
Digital imagery acquired from aircraft contains 
instability and variation in viewing geometry. 
collinearity equations and using a digital elevation model. 
significant geometric errors resulting from platform 
This paper proposes a correction method based on the 
Results are presented for a test site in 
Southern Spain to demonstrate the technique in comparison with traditional methods based on a polynomial 
fits 
KEYWORDS: 
1. INTRODUCTION 
A Daedalus AADS 1268 Airborne Thematic Mapper (ATM) 
flight. was. carried: out iby. the - UK ‚Natural 
Environment Research Council (NERC) on May 16, 1989 
over the Antequera Valley, Andalusia, Spain. The 
survey was flown at a height of approximately 3000m 
in a SE-NW direction, with a path width of 
approximately 4.6 Km (716 pixels) and over a 
distance of 33 Km (5699 scan lines). It covers à 
flat area of intensive agriculture lying between 
two upland regions which form the hills around 
Antequera and the Sierra del Humilladero. 
A portion of the image, 1000 scan lines and 716 
pixels in size, was selected for a project which 
has the aim: of investigating. methods: of 
incorporating cartographic information to improve 
land-cover classification. The selected area 
includes a hilly area to the south and a flat area 
to the north. The hilly area is covered by 
scrubland variably intermixed with bare soil and 
rock outcrops, pines and fields in which olives and 
fruits are the main crops. The flat area in the 
north is occupied by fields of mainly cereal crop. 
In between in the central area is the town of 
Antequera. The terrain height range over the image 
area is from approximately 428 m to 755 m. 
A reasonably good registration of the digitally 
transformed map and the image is an essential 
prerequisite for the achievement of the aims of the 
project. Initially geometric correction of the 
image was carried out by traditional polynomial 
techniques. Results from this technique were not 
as good as expected and an alternative technique 
was investigated. The method suggested here is 
general in its application and may be applicable to 
other systems. 
2. TRADITIONAL POLYNOMIAL TECHNIQUES FOR THE 
RECTIFICATION OF IMAGES 
2.1 Introduction 
The sources of geometric error in satellite imagery 
are mainly due to instrument error, panoramic 
distortion, : Earth rotation and platform 
instability. Instrument errors include distortions 
in the optical system, nonlinearity of the scanning 
mechanism and non-uniform sampling rates. The 
panoramic distortion is a function of the angular 
field of view of the sensor. Earth rotation 
velocity varies with latitude and has the effect of 
skewing the image. The platform instability 
includes variation in altitude and attitude. 
Mather (1987), describes two methods for geometric 
correction of remotely sensed images with a narrow- 
angular field of view: the orbital geometry method 
and the map-based method. The first is based on 
the knowledge of the orbit of the satellite, the 
Earth's rotation and the along-scan and across-scan 
sampling rate. It is useful only when the desired 
accuracy is not high, or where sensor resolution is 
15 
Rectification, Registration, Remote Sensing. 
low, or when suitable maps of the area are not 
available. Otherwise, the second method, based on 
ground control points, is preferable. 
The map-based geometric correction is accomplished 
by transforming the image point coordinates on to 
corresponding ground control point coordinates 
selected from a map or other source. 
2.2 Form and Application of the Polynomials 
Let (x,y) be the grid coordinates of a point on the 
map and (c,r) be the row and pixel coordinates of 
the corresponding point in the image. For the 
transformation from (x,y) to (c,r) and vice versa, 
a polynomial relationship is established. 
The form of the polynomial should describe the 
transformtion. of. coordinates including any 
additional systematic errors present in the 
resulting image position. Three forms of 
polynomial were considered, each representing a 
progressive increase in the order. The same form 
of polynomial was used in each direction to 
transform c,r to x and then c,r to y, the reverse 
transformation of a similar form were also output, 
X.y to c and x,y.to r. .The.simplest form, a first 
order polynomial, is given by: 
C= 89 5.84X Todo (1) 
rom oag* tag + 85 Y (2) 
For higher order polynomials the following 
algorithm can be used: 
m m-j oe 
hil > aix y (3) 
j=0 k=0 
where: m = order of polynomial 
a = polynomial coefficient 
À similar expression for r can be written 
The coordinates of the control points are used to 
determine least squares estimates of the polynomial 
coefficients. 
Once the transformation coefficients have been 
computed the corrected image can be produced. This 
involves the transfer of the brightness value from 
the original image to the corrected image. This 
resampling process is complicated by the fact that 
it is unlikely that. the pixel centres of the 
original image will fall at the pixel centres of 
the correct image. A further requirement might be 
that the image is resampled to a different 
resolution from the original, then the area covered 
by the pixels will be different and thus the