Proceedings 18 th International Symposium CIPA 2001 
Potsdam (Germany), September 18 - 21, 2001 
PHOTOINTERPRETATION AND SMALL SCALE STEREOPLOTTING 
WITH DIGITALLY RECTIFIED PHOTOGRAPHS WITH GEOMETRICAL CONSTRAINTS 1 
Gabriele Fangi, Gianluca Gagliardini, Èva Savina Malinverni 
University of Ancona, via Brecce Bianche, 60131 Ancona, Italy 
Phone: ++39.071.2204742, E-mail: fangi@popcsi.unian.it malinverni@popcsi.unian.it www.ing.unian.it/strutture/fimet/fangi 
KEY WORDS: Architectural Photogrammetry, Self-Calibration, Rectification, Stereoscopy, Vanishing Points 
ABSTRACT 
In the photographic images of buildings we can very often distinguish three main directions, intersecting at right angle. The vertical 
and horizontal lines converge to the Vanishing Points. The VP geometry is a powerful tool. We present here three cases: one, two, 
three VP. In the first two cases it is possible to rectify the image, apart two unknown scale factors in the two principal directions, in 
the last case in addition it is possible to estimate the orientation parameters, and the ratio base/height in the rectified image is correct. 
It is well know already that it is possible to use the vanishing point geometry to assess the orientation parameters of the photographic 
image, but here the computations are particularly easy and simple. We propose a numerical or graphical procedure to estimate such 
parameters, assuming that in the imaged object are present plane surfaces, straight-line edges, and right angles. In addition, by means 
of the same estimated parameters, it is possible to project the image onto a selected plane, say to rectify the image. The advantages 
are that non-metric images, taken from archives or books also, provided a good geometry and quality, are suitable for small scale 
plotting and photo-interpretation. The convergent non-stereoscopic images rectified with digital photogrammetric techniques, are 
then made suitable for stereoscopy. Some examples are shown. 
1. INTRODUCTION 
The possibility to use non-metric images is normally depends on the control information availability in the imaged object, usually 
control points to be input in a bundle adjustment procedure or DLT. There is also the possibility to use a-priori knowledge of the 
geometry of the object, such as parallelism of lines and perpendicularity of planes (Williamston & Brill, 2, 1987,3, 1988, Ethrog, 
8,1984, Krauss, 5, 1997, Van Heuvel, 7, 1999). In this way the study and the safeguard of the monuments can be helped by the 
biggest existing archive available to the researcher, the books. We propose an approach that has the advantage to be particularly 
simple and to be performed also in a graphical way by people not particularly expert in complicated computations. It uses the 
vanishing points geometry. We assume the geometry of the ideal pinhole camera. So far, the distortion is neglected. With the same 
estimated parameters it is possible to rectify the image and produce a stereo-couple from convergent non-stereoscopic photographs. 
Many computers have already main-board and graphical card suitable for stereoscopy (stereo-ready). In addition, digital workstations 
do not have devices such as dove-prism to rotate the optical field and to improve stereoscopy; therefore a good stereo-capability is 
more important than before. 
2. THE VANISHING POINT GEOMETRY 
In an image the parallel object lines converge in points called Vanishing Points. There are many methods for the detection of the 
Vanishing Points in the images. A good review is given by (V.Heuvel, 6, 1998), together with a proposal for a new approach, based 
on strong statistical base. Here the detection of the vanishing points will not be discussed. 
2.1 Perspective transformation with one vanishing point 
The transformation matrix, composed by a concatenation of a perspective and a projection onto Z =0 plane, is written (Rogers, 
Adams 1, 1980): 
[T] 
'1 
0 
0 
P 
'1 
0 
0 
o' 
'1 
0 
0 
P 
0 
1 
0 
0 
0 
1 
0 
0 
0 
1 
0 
0 
0 
0 
1 
0 
0 
0 
0 
0 
0 
0 
0 
0 
/ 
m 
n 
1 
0 
0 
0 
1 
/ 
m 
0 
1 
(1) 
In the case that l = m = 0 ( or we are not interested in the translation /, m ), an arbitrary point P with homogeneous co-ordinates 
[x,y,z,l] is transformed or projected, in 
[x,y,z, 1]. 
1 0 0 p 
0 10 0 
0 0 0 0 
0 0 0 1 
= [x,y,0,(x.p+\)]= 
y 
x.p +1 x.p +1 
0 1 
=[X, Y,0,1 ] 
(2) 
1 The present work has been financed by Cofin2001, Italian Ministry for Scientific Research