OL POINTS 
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ecture photogrammetry, 
and photogrammetry, 
hortage of the theory 
1 calibration based on 
ts in multi images is 
g precision of interior 
10DEL UTILIZING 
NGLE IMAGE 
, which are parallel in 
image plane, this point 
urface image of objects 
line information (such as 
of the building surface), 
fully utilizing vanishing 
1ing points 
arc based on vanishing 
was engaged in the study 
re he calibrated camera 
inly calibrated interior 
ilizing the image with 
photogrametry was used 
reconstruction. Roberto 
ised strict geometrically 
m and orthogonality) to 
tation parameters of the 
Is of the scene from only 
positions [6]. 
ss of vanishing points for 
tive is to steer a mobile 
of parallel lines in its 
xagon as the calibration 
he ground plane from its 
arameters include the 
length of a camera [9]. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
Prof. Nevatia in University of Southem California calibrated the 
camera by utilizing the vanishing line in level plane and the 
vanishing point in perpendicular in order to analyze people's 
motion [8]; from the viewpoints of photogrammetry, [4] 
proposed an adjustment model of vanishing point that views line 
information in images as observation, thereby realized modeling 
only with single image. Its geometric model is shown as Fig. 1: 
Yo 
Xoo 
  
  
  
Figure 1. The relationship between vanishing points 
and orientation parameters 
Suppose vanishing points in three orthogonal directions in one 
image respectively are Xoo, Yoo, Zoo i|! ie. three-point 
perspective, and S denotes the perspective center. According to 
Fig.l, The principal point lies at the orthocentre of the triangle 
formed by the vanishing points.. The focal length f is: 
  
/ = x e. Y Xv d Fx : Ye ( 1) 
Three exterior angle parameters are: 
m im 2 2 2 2 
f zr X Ze d Ya, f + X xo + var 
f/ 
tank zr. v. 
  
tan 9 
Il 
  
tan e 
2.2 Adjustment model 
Vanishing point is the key factor of calibrating because the 
parameters being calibrated are all the functions of vanishing 
points. Many methods can obtain vanishing points: in 1983 
Barnard first proposed the expression of vanishing point based on 
Gaussian sphere representation [11], on the basis of this method, 
E. Lutton obtained vanishing point through Hough Transform 
[12]; Canadian John C.H.Leung discriminated the true vanishing 
points from points which naturally arise as the mutual 
intersection of many lines in the image utilizing the invariable 
property of vanishing points in two images [13]. In this paper an 
adjustment model between image lines and vanishing points is 
formulated to calibrate camera (detailed in [4]). 
Supposing that onc group of parallel lines in one-image crosses 
in vanishing point V, ij is one of those lines (Fig.2). Then three 
points 7, J, V needs the condition of collinearity, if the 
coordinates of vanishing points (x, » Vy ) is unknown, thus we 
can build indirect observation adjustment model with unknown 
(formula 3): 
  
  
Figure 2. The definition of vanishing 
points 
(yy = X; Me (x; c )v,; rwy, )vy 
+x, x aly, =p Yh lx, ax yy, +L, =0 
Li = —(x, = X, M, = y.) + (y, mU. Xx, = X) 
(3) 
When the angle between straight line and the 
horizontal Ó « 45? , formula 3 can be approximated by: 
(x; m v, toy -—*x, Wert (y, — yj), 
(4) 
+(x, =), + Ly = 0 
When the angle between straight line and the 
. &o . 
horizontal @ > 45° | formula 3 can be approximated by: 
(Vy — Y: )us TY, — yy y T (V; - y,)dx,. 
wh 
Ser’ 
+(x, x, dy, +L, =0 
Although many existing methods have the common feature that 
is based on single view. In next section we will, according to 
simulation, analyze errors of interior parameters calibrated by 
vanishing points of single view. 
3. ERROR ANALYSIS 
Single-view calibration using vanishing points is feasible 
theoretically. However, practical application indicates that this 
method only can do week calibration. Because generally the 
focus length is evaluated accurately but the principal point is not 
so precise [10]. Thus, a feasible assumption is that the principal 
point lies at the center of the image, which is a simple 
approximation [6]. 
From cube images of multi angle views simulated by computer 
(shown as Fig. 3), we can analyze the error trend of interior 
parameters calibrated by single-view method with vanishing 
points. The length of the cube is 50m, there are 11 straight lines 
in each direction. Given that the focal length of camera is