3.- Transformation to Plain Coordinates: finally, 
according to the Gauss-Kruger Plain Conform 
projection, a new conversion was made, using the 
Militar Geographic Institute (M.G.I.) formulas: 
X = 5 + (/cos<j>) 2 A7/2 
+ (/ cos <f) ) 4 A 7 / / 24(5 — / 2 9rj 2 +h 4 ) 
+ (/cos<|>) 2 7W/720 
* (61 - 58/ 2 +1* + 270n 2 - 330^ 2 ) 
Y = n 1.000.000 + 500.000 + / cos<j)N 
+ (/cos<j>) 3 yV/6(/-i 2 +r| 2 ) 
+ (/cos<|>) 5 A7120 
* (5 — 18/ 2 +r 4 14r| 2 -330/ 2 r| 2 ) 
in the GPS campaings, due to the fact that they made a 
previous location of the pixels in the hardcopy image 
that they had during their work. Any located point has 
an image coordinate given for the pixel row and column 
in which it is located. To every one of them a calculated 
coordinate is assigned in the Gauss-Kruger system. 
Based in these data, the software calculates the 
transformation matrix and provide the errors per point 
and the total root mean square(RMS) error. The 
software supplies this information in pixels units. 
Values less than "¡4 pixel were considered as an 
acceptable error. 
With the coordinates of the points located in the images 
to rectificate expressed in pixels, the software carried 
out, in our case, a linear rectification. The rectificated 
images pixels coordinates are obtained with the 
expresions: 
where: 
*0 = ^+ n 2 x i + a.y i 
S is the meridians are whose valué for the 
internacional ellipsoid is: 
y 0 = b l + b 2 x¡ +b 3 y, 
5= 111136.5367(90+<t> 0 ) -16107.0345 8sen 2<J> 
+16.97619693sen 4<j> - 0.022262484sen 6<j> 
+ 0.0000310999sen 84. 
t = í> 
r| = 0.082268890cos<j) 
where: 
Xj, yj are row and column coordinates, of the image to 
be rectificated pixels; 
x 0 , y 0 are rectifcated coordinates. 
The last equations can be expresed in matricial format, 
as it follows: 
The values obtained in the step 3 are the input 
coordinates for the images rectification and 
georeferentiation software. 
a, a 2 a 3 
* 
V 
x, 
_6, b 2 63 _ 
y, m 
The rectification is the data transformation process 
from a grid system to another, using for this purpose a 
n-order polynomial. Because the pixels of the new grid 
could not be aligned with original grid pixels, a 
“resample” process is needed that is the pixel digital 
level (colour) extrapolation process in the new grid, 
based on the original digital levels of the pixels. 
The georeferentiation is the procedure of map 
coordinates assignment to the image data. Rectification 
per definition include the georeferentiation, because all 
the projection systems are associated with any map 
coordinate system.(Erdas 1995) 
S: is the origin coordinate matrix. In this 3x1 vector, 
the first element is “1”, so the first coeficient is used 
as a constant in the equation 
C: is the 2x3 transformation matrix. 
R: is the rectificated coordinates matix. 
Now an example is presented with the points utilized 
with its respective coordinates and the results of 
transformation matrix, for a given image: (see Tables 
1,2,3) 
For this process, measured grown control points were 
located in the computer screen. In this step was very 
useful the colaboration of the persons who participate