International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
Il 
Na >. N (utin 
i=e-lj=r-l 
Ys = > S un Eu. 
izc-hjzr-l 
Sg. = > SC =i XZ eg) 
izc-Mer-l 
— 4DetN 
gr = e M (7) 
en Ei; y 
Where, DetN represents the determinant of the matrix N; trN 
represents the sum of the elements along the diagonal of the 
matrix N. 
3.2 Homologous Point Generation by Pyramid-Layered 
Template Matching 
After the feature points have been extracted from the image to 
be registered (or the reference image) by the Fórstner operator, 
the homologous points of the feature points in the reference 
image (or the image to be registered) can be obtained by 
calculating the normalized standard correlation coefficient, 
which is described in the following equation. In order to speed 
the process, the pyramid-layered image searching mechanism is 
adopted in this period. 
M-IN-1, 
  
s Y ten) = nuc +e,n+r)- 8) 
efe M +i S = MN (8) 
iS > (fer) — Jj) > > (e(m tcntr)- gy 
ex rzü c0 rzü 
Where, fíc,r) is the grey value of the pixel (c,r) in the template 
image; g(m+e,n+r) is the grey value in the matching image, 
where (m,n) is the centre of the searching area, (c,r) is the 
searching extent; /,z is the mean value of the pixels in each 
window. Take the feature points extracted from the image to be 
registered as an example. 
(1) Generate the pyramid image series of the image to be 
registered fand the reference image g respectively, which 
are f; and g;. (i=1,2,...N, for example, N=3). Map the 
feature points onto the image series fy. 
(2) Begin with i=N, in image gy, calculate the value a(f;g), 
which is corresponding to the feature points in image fy 
The homologous points are the points corresponding to the 
maximum value of a(f,g). Map these homologous points 
onto the layer i-1, i.e. g-1, and let /=i-1. 
(3) In the layer i, within the rectangular extent of WxH in 
image g; calculate the homologous points corresponding 
to the feature points according to the algorithm in step (2), 
until 1. 
(4) All the feature points and the corresponding homologous 
points construct the control point pairs. 
3.3 Gross Error Elimination 
Because the entire original image has been roughly registered, 
the horizontal and vertical deviation value A and A, of the 
control point pairs should be less than the threshold T, and T;. 
Thus, the following method is adopted to eliminate the 
mismatched control point pairs. 
Assuming that the number of control point pairs is n, each 
control point pair is constituted by /(i,/) and g(k,/), then we have 
the following expressions describing the mean square errors of 
the horizontal and vertical deviation: 
1 2 1 ” 
V (Ar, it nm. >. , GC, ER EH (Ay, SE m, X (9) 
n-1 = n-1 
3 ^ 
: 1 1 
Where, m, = => Ax, [t 
n i=] n m=l 
Ax, -k-i Ay -1—j Gf; kb, lim -M2,A ,n) (10) 
Let 7, 23o, and T, -3o,, 
  
OO; = 
m, = 
while it meets Ae aT and Ap, 7 T. ithe control point pair 
Ri,j) and g(&./) can be considered as the mismatched points. 
858 
4. HIGH PRECISE REGISTRATION TRIANGLE BY 
TRIANGLE 
After the control point pairs have been automatically collected, 
the reference image and the image to be registered can be 
divided into several triangular regions by TIN, which is 
constructed by the control points. The affine transformation 
model can be applied in each triangular region to fulfill the 
precise registration. 
4.1 TIN Construction 
Among the different methods constructing TIN, Delaunay TIN, 
which is constructed by Thiessen Polygon method is close to 
optimum. Because the control points are obtained after the 
image has been divided into several rectangular regions which 
have the same given size, the situation that four points are 
concyclic may occur, and this cannot meet the condition to 
construct Delaunay TIN. The Minimum-Distance method is 
simple and has better executive efficiency, it is adopted to 
construct TIN in this paper. 
(1) Determination of the Initial Triangle 
Find the closest two points in the control point set, then find 
another point that is closest to the connection line of the two 
points but is not collinear with the two points. The initial 
triangle can be determined by the three points. 
(2) TIN Generation by Triangle Expansion 
Triangle Expansion starts from the first edge of the first triangle. 
Assuming that the vertexes of the triangle are pi, p» and p;, and 
the first edge is p, p; (See figure 3), it is obviously that the 
expanded point q(x',y') should not be the point located at the 
same side of the line p, p» just like the point p; and also not the 
point on the line p; p», The straight line equation is: 
F(x,y)9y-Ax- B (11) 
If F(x’,y’)>0, (x’,y’) is located at the positive zone of the line; if 
F(x’,y’)=0, (x’,y’) is located at the line; if F(x’,y”)<0, (x’,y”) is 
located at the negative zone of the line. So, when 
Fx3,y3)F(x’,y")<0 (12) 
q(x',y") is the point that possibly to be expanded. 
After the points that are possibly expanded have been obtained 
by equation (12), using the law of cosines, equation (13), we 
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