ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
194 
3D RECONSTRUCTION OF A BUILDING FROM SINGLE IMAGE 
Yawen LIU 
Department of Information Engineering 
Wuhan Technology University of Surveying and Mapping 
39 Luoyu Road, Wuhan, P. R. China(430079) 
e-mai!:lywlucky@263.net 
Zuxun ZHANG 
Department of Information Engineering 
Wuhan Technology University of Surveying and Mapping 
Jianqing ZHANG 
Department of Information Engineering 
Wuhan Technology University of Surveying and Mapping 
Keywords: orientation parameters the distance ratios 3D reconstruction 
Abstract 
In architectural photogrammetry, the buildings are designed with a few basic shapes with parallel lines. So, in this paper a new approach 
to 3D-reconstruction of building from single images is presented. The method requires three sets of parallel lines. In the first step, three 
couples of parallel straight lines are used to determine the rotation parameters, interior orientation parameters and translate parameters. 
In the second step, the ratios of the distance from the projection center to the corner points of the parallelogram are computed using 
only parallelity information. With the result of two steps, 3D coordinates of building can be computed. The method was based on 
stronger theory of mathematics. So it's robust, accurate. 
1 Introduction 
The 3D reconstruction of buildings has been an active research 
topic in computer vision as well as in digital photogrammetry in 
recent years. Three dimensional building models are 
increasingly necessary for urban planning, tourism. Manual 3D 
processing of images is very time consuming. Therefore, 
speeding up this process by automatic or semiautomatic 
procedures has become a necessity. 
There are a lot of systems that work solely with monocular 
images. These systems exploit shadows either to infer the third 
dimension or to verify the generated hypothesis. Other systems 
use widely stereo images, the determination of the third 
dimension by epipolar matching of different features extracted 
from both images. 
The approach presented in this paper, works solely with 
monocular images. The buildings are assumed to be rectangular 
or rectilinear flat roofs. The procedure consists of two steps. In 
the first step, the interior and exterior orientation parameters can 
be determined with parallel lines information and two object 
control points. In the second step, the ratios of distance from the 
projection center to the corner points of the parallelogram are 
computed using only parallelity information. The method makes 
full use of linear features and constrains(coplanar, parallel, 
vertical).It is robust and stable due to its strong geometric and 
mathematical relations. 
2 Determination of interior and exterior orientation 
parameters From figure 2-1,we can see that the perspective 
center, straight line in 3-D object space and its projection on 
image plane can form a plane. The coplanar constrain is the 
foundation of this new algorithm. 
In order to have a good understanding of this, we take the 
following symbols 
L: straight line in the object space 
I: projection of L on the images plane 
S: perspective center of image 
n: the normal vector of plane defined by S and I 
p: any point of I on the image plane 
c: the center of the image plane 
c-xy: image plane coordinate system 
o: the principle point of the image 
S-xyz: image space coordinate system 
O-XYZ: object space coordinate system 
Notion: vectors are printed in bold. 
Suppose (x 0 ,yo) is the coordinate of the principle point in image 
plane coordinate system c-xy, (xi.yi.-f) is the coordinate of point p 
in the image space coordinate system S-xyz. the direction vector 
of I in S-xyz as 
/ = 
(1) 
where v x ,v y and 0 are three coordinates of I on the x-,y-,and z- 
axes respectively. 
The direction vector of Sp as 
Sp = 
Xi - xo 
(2) 
y>~y o 
-/ 
We can obtain the normal vector of plane defined by S and I in 
S-xyz through the cross-product of I and Sp 
-Vyf 
Vx-f 
di - V* • yo + Vy • xo 
(3) 
where di = Vx • y> — Vy ■ Xi 
Suppose vX,vY and vZ are three coordinates of L on the x-,y- 
and z- axes in the image space coordinate system S-xyz 
respectively. 
L = 
Figure 2-1 interpretation plane and normal vectors 
VX 
vY 
vZ 
(4)