the 
eir 
ich 
nd 
2 
x=mg1/M99 
y=m10/m00 
r-Mx'/My' 
Mx'-(M29*M9g2)2 *sqri[ (M29-Mg2)?/4*M, 4? ] 
My'=(M20+M02)/2 -sqri[(M29-Mg2)?/4*M,1?] 
(8) 
where mp => X iP-j4-gij and Mpg 7 2X(-x)P-G-y)gij. 
[p-0.1.—. q70.1.—] are the (p--q) order moment about the 
origin and moment about the central. If r is smaller than 
threshold rq, the target is round, otherwise the target is 
not round. 
Trinder (trinder 1989) found that the result is subject to 
variations in window size, position and threshold value, 
and the location error may be up to 0.5 pixel. So he used 
the gray level value wij as a weight factor for each pixel : 
X=1/M «EX | gij wi] 
Y=1/M 23 igij wij 
M=2 2 gij wij (9) 
under ideal circumstances, the precision of point with 
Trinder method can approach 0.02 pixel, but there are 
few such points in digital image. 
1.3 Mikhail method (Mikhail. 1984) 
Let f(s,t) represent the output of a perfect imaging system. 
Considering a linear, spatially-invariant imaging system 
with a normalized point-spread function p(s,) assumed 
known. The sampling value g(s.t) is 
g(s.)#(s.) « p(s.) (10) 
where » denote the convolution operation. 
Suppose the distinct target can be characterized with a set 
of parameters X, then equation 10 may be rewritten as: 
l(s,t)-f(s,t; X) * p(s.t). (11) 
‘Thus least squares method can be used to calculate the set 
of parameters X. 
For one-dimensional edge, if p(x) is Gaussian function, 
equation 11 may be expressed as: 
g(x)=f(x; g1,g2,x0) * p(x) (12) 
Using least squares method, gl, g2 and xO can be 
calculated. So the position and shape of edge can be 
determined. For a cross target, it may be characterized 
with seven parameters. In ideal condition, the accuracies 
have reached within 0.03-0.05 pixel. But the point-spread 
function must be known in the method. 
1.4 Hough Transformation (Ballard 1982) 
Hough Transformation transforms image space into 
parameter space. It can detect not only straight line, but 
also other curves, such as circle, ellipse and parabola. But 
with the increase of the number of parameters, much 
79 
computation time and more memory are spent. So Hough 
Transformation is mainly suitable to detect straight line. A 
straight line can be represented using two parameters: (1) 
the angle between the X-axis and the normal of the line 
(0), (2) the distance (p) from origin to the line , i.e. 
p=x cos 0 + y sin 0. (13) 
Because of the limitation of quantization classes of p and 
0, as well as the error of gradient direction and noise, the 
error of Hough Transformation is large. 
1.5 Fórstner method (Fórstner 1986) 
Fórstner method is a famous in Photogrammetry. There 
are the advantages of fast speed and good accuracy in the 
method. Corner location consists of selecting optimal 
window and weighting centering. For cach image 
window, the roundness q and weight w can be 
caclulated: 
4DetN 
qe 
(TN)? 
1 Det N 
WE Em em em cm cen 
TrQ TrN 
gu! gugv| ! 
Q-N-1- (14) 
Suv 8v 
where gu-gi«1,j1 - &ij 
£v-8i-1,j £j. 
If q and w are larger than their thresholds and if it is 
extreme maximum, the window is an optimal window. 
Forstoer method is a least squares method. It regards the 
distance from the origin to the straight line as observed 
value, and weight of observed value is the square of 
gradient. There are many advantages with the method. 
However, its location accuracy is not very good. When 
window size is 5*5 pixel, The accuracy of corner location 
is about 0.6 pixel in ideal condition. 
Dr. Wu Xiaoliang in Wuhan Technical University of 
Surveying and Mapping proposed a method which 
regards the direction of edge as observated value. It 
seems (o be more reasonable in thought, but none of 
gradient operators can compute accurately the direction of 
edge. 
Most of above methods can be used to location of 
corners or lines, but the high accuracy can be acquired 
with only few of them, and it is necesssary in some 
aspects of Phologrammetry, such as interior orientation 
and relative orientation. So a high accurate method for 
the location of point and line has to be developed. 
2 HIGH ACCURATE METHOD FOR 
THE LOCATION OF POINT AND LINE 
2.1 The error of gradient operators 
If an ideal edge line whose gradient is k passes through