orthophoto. Having a redundance of „spectral and 
radiometric control points“ the transformation elements 
are determined by the method of a least squares 
adjustment. Afterwards the PTC-orthoimages can be 
determined from all the ClR-orthoimages using the 
transformation elements computed in equation (3): 
Rerc = a10+ A1 - Ror+ A12- Gorr + A13 - Ber 
Gerc= an+ an - Roir+ A2 -Goir+ A23- Boir (4) 
Berc= a30 + as - Rer+ as - Goir + A33 - Ber 
3.3.3 Classwise determination of transformation ele- 
ments: As described in Chapter 2 there is a object spe- 
cific reflectance of radiation. A second approach is the 
classwise determination of transformation elements: 
Rrc,a — d104- a11- Reim, ct 4- A12- Goir, + A13- Ber, a 
Grc,« — d209- d21- Rar, a+ az- Ger, a+ az- Ber a (5) 
Brc, «1 = A30 + A3 - Rom, 4 + as- Ger, a+ ass- Ber, o 
For the described project ten object classes were defined 
(water, needle forest, deciduous forest, traffic lines, roofs 
light, roofs dark, field with vegetation, meadow, fallow 
land, field with sparse vegetation). An experienced inter- 
preter visually classified the different classes on the 
reference orthoimages by delimiting areas of same 
objects. Within each of the ten classes transformation 
parameters were determined using class specific 
,Spectral and radiometric control points“ and the method 
of least squares adjustment. 
3.3.4 Land use classification: In order to calculate 
PTC-orthoimages, the object information for each pixel is 
necessary. For this purpose a maximum-likelihood clas- 
sification has been done for all ClR-orthoimages. As 
training sets for this computer assisted image classifica- 
tion the visual interpreted object areas were used. After- 
wards the pixel values of the CIR-colour space were 
transformed to the PTC colour space for each object 
class separately: 
Rerc, d = à10+ A11 - Roir, a + A12- Gerr, 4 + A13- Boir, ct 
Grrc, ed = A20+ A21 - Reir, a + a22- Gem, 1 + A23- Beir, 1 (6) 
Berc, a = A30 + A31 - Roir, a + az2- Gem, a + A33- Boir, el 
3.3.5 Calculation of transformation elements by 
means of class centers: The method described in 
Chapter 3.3.1 prefers classes with a higher frequency in 
the reference orthoimage. This disadvantage can be 
avoided by computing the center values of each class in 
both colour spaces. Afterwards all the center values are 
used as ,spectral and radiometric control points", and the 
influence of each class by computing the transformation 
elements is weighted equally. Besides this method also 
allows an individual ponderation of each class. The 
transformation of the CIR values to the PTC values will 
be done class independent using equation (4). 
3.3.6 Calculation of transformation elements by 
means of class centers with subsequent improve- 
ment of some classes: The calculation of transforma- 
tion elements by means of class centers enables on the 
whole good results. Only the colours of few classes are 
not transformed correctly into the PTC-colour space T, 
overcome this lack by a subsequent improvement 0 
single classes can be done. In a first step the transforms. 
tion parameters between CIR-colour space and TC-co. 
lour space are determined using class centers an 
equation (3), and a PTC-image will be calculated, |n 4 
second step the quality of the PTC-image will be 
controlled and for object classes with insufficient coloy 
values the transformation parameters will be calculated 
individually using equation (5), and the class specific 
pixels are transformed to the PTC-image with equation 
(6). The class information of the pixels will be obtained as 
described in Chapter 3.3.4. 
3.3.7 Simplified methods: Theoretically the transforma- 
tion parameters between CIR-colour space and TC-co- 
lour space must be calculated for all three bands to get a 
PTC-image. Due to the high correlation of the green band 
of the CIR-image with the red band of the TC-image 
(both corresponding with. the red part of the natural 
electromagnetic spectrum) and the high correlation of the 
blue band of the CIR-image with the green band of the 
TC-image (both corresponding with the green part of the 
natural electromagnetic spectrum) the transformation 
between the two colour spaces can be simplified: 
Brc= ao+ ar- Rer+ az- Ger + as - Ber (7) 
and the simulation of the PTC-image can be done by 
Rere = Ger 
G»rc — Bom (8) 
B»rrc — ao-4- ai- Rom d2- Gom 4- a3: Bon 
If there was no yellow filter in use to cut off the blue part 
of the electromagnetic spectrum during the photo flight 
for getting the CIR-photographs, the transformation para 
meters can be calculated using the equation below: 
Grc — d1o4- d11- Rom + A12 - Gorr + A13 - Ber (9) 
Bre = az + a2ı- Rear + a22- Ger + A2 - Bcir 
The respective transformation equations read: 
Rerc = Ger 
Gere = avo + an - Rer+ az - Ger + as - Ber 
(10) 
Brrc = a2 + az - Rar + A22 - Ger + az3- Ber 
Also within this simplified method there is the possibilty 
to variate the computation algorithms for the transforme 
tion elements such as 
* classwise transformation, 
* means of class centers and 
+ means of class centers with subsequent improvement 
of some classes. 
3.3.8 Implementation of the algorithms: All described 
algorithms in Chapter 3.3.1 to Chapter 3.3.7 were imple 
mented on a UNIX computer. For a test image all trans 
formations were calulated and investigated. Some of the 
472 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996 
CC m" rr 
cm 
zm