International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B4, 2012 
XXII ISPRS Congress, 25 August - 01 September 2012, Melbourne, Australia 
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a (X -X ) +a (Y -Y) + a (Z -Z ) 
x = x o -/— — — i — 
a n (X p -X ) + aJY p -Y) + a u (Z -Z ) ( 2 ) 
a v (X f -XJ + a v (Y p -YJ + a j2 (Z p -Z ) 
aJX p -X ) + aJY-Y) + aJZ p -Z ) 
Where, 
x, v: corresponding to image coordinates of ground surface 
x ,y .z ■ P point’s object space coordinates; 
x,y,f '■ elements of interior orientation, principal point of 
photograph coordinates and principal distance of camera after 
checking; 
X ,Y ,z '■ three line elements of exterior orientation elements; 
a a : element of spin matrix between image coordinate system 
and object space coordinate system. 
Substitute formula (1) into formula (2), formula (3) can be 
derived: 
a t (X t +1(Z -XyX) + u. i (Y < +1 (f -7)-Y) + fl„(Z + A (Z, -Z )-Z ) 
x = x -/——-—-— : — : — : — 1 —— 
' aJX'+A'(X -XJ-XJ + oJY+A(Y -Y)-Y) + aJZ A + A (Z -Z )-Z) 
a o (X A +X (X t -X a )-X p ) + a v (Y t +X (Y t -Y t )-YJ + a n (Z i +Z(Z -Z )-Z) 
y=y - f— — 
a il (X A +A(X t -X i )-X) + aJY A +A(r i -r i )-rj + aJZ A +A f (Z t -Z j )-ZJ 
(3) 
Where, 
A : is the proportion parameter of P shown by line AB. 
Assume that elements of interior orientation are known and 
camera does not have any system error, formula (2) is 
expanded according to linear Taylor formula and error 
equation is set up, then the formula (3) is: 
V =b)-x + yf VI + A VY + A VZ + 
x v 7 Wo 12 « 13 n 
A X0 + A Vco+A Vk + B V2 
,4 r 15 16 " (3) 
v =(v)- y + A VX + A VY + A VZ + 
y \S Z S 21 .> 22 o 23 o 
AV<j> + A .Vco + A^Vk + B VZ 
Thus, the mathematical model between image coordinates and 
point clouds space straight line. This model can be considered 
as traditional collinearity equation formed by straight line 
instead of point feature, in object space. It is suitable both for 
the registration of single and multiple images and LiDAR points 
data. As for single frame image, its normal equation is 
simplified as formula (4): 
Where, 
t: means elements of exterior orientation of the image; 
A: means the matrix formed by unknown parameters of “line” 
As for multiple images, its normal equation formula (5): 
a‘ 
L 
t' 
11 
B ... B ... B 
- 
A‘ 
UJ 
Y 
n 
A" 
1nil 1 IUI 1 1 1 1 1 1 INI 
c_ 
Where, 
a is coefficient matrix of the i image’s elements of exterior 
orientation. If there is c corresponding points in the i image, 
a is 2 x c x 6 matrix; 
b : means that the j LiDAR point clouds space line’s 
corresponding coefficient matrix; 
T = [dX\ dYl dz\ d<j> ded dK ... dX" 0 dY 0 " dZ" 0 df da" dic'J 
A = [A , A ,...,A ,..., A ] , corresponding to k linear features of 
LiDAR point clouds space. 
l : means the i image’s corresponding image point residual 
vector. If there are c image point coordinates, P is 2 x c x 2 
matrix, 
f = [*,' - (f ) i - (y,' ) - f - (f ) y\ - Oj ) - \ - (x c ) y e - (j/, )] : 
Here, (jf , y‘ p ) means the p image point of the i image. 
4. REGISTRATION SCALE ANALYSIS 
There is a group of best combinations between point clouds 
density and image resolution which makes registration accuracy 
optimal. If it is a rather low or high image resolution in relative 
to point clouds density, registration result will bring loss or 
damage of the two data information. The method difined in this 
paper to resolve this problem is called scale analysis. Firstly, the 
influence of image resolution should be removed, then 
registration point position pixel error C is introduced. The 
coordinate of P in LiDAR poins space,corresspoding to 
p(x, y) in image. With registration transformation model, P is 
inversed to image coordinate system, and its image coordinate 
is p' (V, y), so | p(x,y) — p (x, y) \ is p and p ’s pixel 
coordinates deviation existed in image coordinate system. C is 
the average value of pixel coordinates deviations above of all 
checkpoints. The ratio of LiDAR point clouds average point 
distance and image resolution is defined as scale factor S. 
Registration’s scale problem can be semi-quantitatively 
analyzed by checking the relation of scale factor S and C . 
feature replacing “point” feature; 
Yl \ means the combinations of registration primitives of point 
and line; 
L: constant variables; 
V: residual vector 
5. EXPERIMENTAL RESULTS AND ANALYSIS 
5.1 Data Explanation 
DMC aerial image of Henan Province in china is adopted, and 
the respective flying heights are 600m, 1000m and 2500m, 
corresponding to the aerial image resolutions of 0.056m, 
0.1 lm and 0.25m respectively; point clouds data is acquired by 
ALS-50II, and its density is 1.306 point/ m . In order to