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)
