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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
are (Remondino, 2006, Xie, etc., 2003, Zhang, etc., 2006, Shu, 
etc., 2004): 1) the operator is simple and suitable for 
automatically feature detection. 2) The detected points are 
well proportioned and valid. 3) The quantity of detected 
points could be determinate by the users according to their 
requirements. 4) The detected points are invariant to scale and 
rotation, and the operator is stable. The disadvantage is the 
detection accuracy can only reach one pixel. 
2.1.2 Fòrstner operator (Fòrstner and Gulch, 1986) 
It uses the auto-correlation function to classify the pixels into 
categories (interest points, edges or region). The detection and 
localization stages are separated, into the selection of windows, 
in which features are known to reside, and feature location 
within selected windows. Further statistics performed locally 
allow estimating automatically the thresholds for classification. 
Fòrstner operator is well used for photogrammetric applications 
(Zhang and Zhang, 2002, Zhang, etc., 2001, Remondino, 2006). 
This algorithm can be operated with weight in the optimal 
window center. The accuracy is much higher. The 
disadvantages of this algorithm are that it requires a complicate 
implementation, and is sensitive to the lightness and contrast of 
images. 
method can be used for sub-pixel orientation (Zhang, etc., 2001, 
Xie, etc., 2003, Wu, etc., 2004). The idea of surface fitting is 
to be centered by the optimal point of pixel precision and do 
surface fitting according to similitude measure, then to find out 
the accurate matching site by solving minimum (maximum) 
point. The function is as: 
z(x, y) = ax 2 + by 2 + cxy + dx + ey + f, 
where z(x, _y) is the comer response value at position (X, y ) , 
£2, b, C, d, e, f are the unknown coefficients. Figure 1 and 
figure 2 illustrate the comer response window and their respect 
position. Here point (x, y} is the feature point, f A is its 
comer response value. The overdetermined equations 
(equation 3) can be formed with the 9 points in a 3x3 window. 
The coefficients can be derived from the equation. Then the 
surface fitting function is known. The maximum value is the 
precise position of the comer feature point. 
2.1.3 Methodology 
Firstly, feature points are detected by the Harris operator. 
Each point is corresponding to one pixel in the image. Then 
the detected points by Harris operator is regard as the window 
center of Forstner operator. The surface fitting algorithm is 
used to calculate the more accurate position of the feature. 
With this method, the matching accuracy can reach sub-pixel. 
The detailed implementation steps are as follows. 
If the intensity of the image is I(x,y) at the point (x, y), 
the matrix of auto-correlation is, 
M = G(cr) ® 
K IJy 
IJy Iy 
Where Cr(cr) is the Gaussian filter for image smoothing, I x and 
/0 
A 
/; 
/, 
A 
A 
/, 
A 
A 
Figure 1:3x3 window 
Cvo»*b) = H. -1 ) 
0^*]) = (-i,o) 
(T 2 ,*2) = (-U) 
Cm) = (O’- 1 ) 
o' 
0" 
II 
£ 
N ' 
(y 5 ,x 5 ) = (0,l) 
(j"6^ 6 ) = O»“ 1 ) 
Cm) = 0,°) 
0's,*«) = (U) 
Fig.2: respect position of points in 3 x 3 window 
The overdetermined equation is written as: Ax = B , where 
I are gradients in x and y direction. 
Then the comer response function in position 
(x, y) can be 
x 2 
9 
y 0 2 
9 
*0^0 
x 0 
^0 
1 
b 
written as: 
A = 
Xi 
y\ 
Vt 
Xi 
y\ 
1 
, X = 
c 
d 
f(x,y) = Det(M) = ^ 
7>(M) 4+4 
(2) 
_4 
y\ 
Vs 
x 8 
7s 
1 
e 
j_ 
/0 
Where 4 , À 2 are the eigenvalues of M, 
7> (M) = M XJC + M = Ay + ¿2 is the trace of M, 
Det{ M) = M xx M yy -(M x f=A i A 2 is the determinate 
of M. The interest feature point is detected where the response 
function has the maximum value. 
For high accuracy matching, the interest points need to be 
oriented in sub-pixel. The 2ed order polynomial surface fitting 
(3) 
Solving the equation with pseudo-inverse matrix method, then