/ Part B3. Istanbul 2004 
> image flow measures 
flight altitude and the 
scene plane is levelled). 
giving accelerations and 
ns, speed sensors giving 
ute height and magnetic 
n. Special care has to be 
of the camera and lens, 
the non-focal-plane-array 
- misunderstood by the 
desirable to calibrate a 
system to ground-truth. 
, 1999. Real Time Motion 
'VIU, Vol.78, pp. 32-52. 
08. Projective Geometry. 
al Computer Vision. MIT 
1981. Random sample 
tting with applications to 
tography. Comm. Assoc. 
c for Low Level Feature 
Computer. Vision - ECCV 
fultiple View Geometry in 
idge University Press, 
7. Robust regression using 
v. Comm. Statist. Theor. 
ıl Time Robust Template 
) 
nation of vehicle movement 
video sequences. 2nd 
Remote Sensing and data 
, IEEE, pp 105-109. 
Good sample consensus 
vehicle movment detection 
leipke C, Mayer H, Pakzad 
alysis PIA'03. [International 
smote Sensing. Vol. 34, Part 
03. IIMSAC: Synthesis of 
sample consensus. 1EEE — 
ing motion and structure 
] image warping. ICPR 94, 
. 1, pp. 403-407. 
al analysis of aerial images. 
y and remote sensing, Vol. 
Linear Feature Based Aerial Triangulation 
A. Akav, G. H. Zalmanson and Y. Doytsher 
Department of Transportation and Geo-Information Engineering 
Faculty of Civil and Environmental Engineering 
Technion - Israel institute of technology 
Technion City, Haifa 32000, Israel 
(akav, garry, doytsher)@tx.technion.ac.il 
KEY WORDS: feature based photogrammetry, orientation parameter estimation, registration, homography, fundamental 
matrix 
ABSTRACT: 
For the past fifteen years line photogrammetry has been an extremely active area of research in the photogrammetry and computer 
vision communities. It differs from traditional analytical photogrammetry in the nature of the primitives employed in a variety of its 
fundamental tasks. While in traditional photogrammetry zero-dimensional entities, i.e., points are exclusively used as a driving power 
in its various orientation and exploitation procedures — in line photogrammetry as the name suggests linear, that is one-dimensional 
features often corresponding to elongated man-made features in the object space are employed. Of course, that means that no prior 
correspondence between distinct point in object space and its projection in the image is required and the entire linear feature (with 
arbitrary geometry) is accommodated in the appropriate mathematical model. However, despite a great effort in that field, only the 
resection problem, i.e. the solution of the exterior orientation from linear features’ correspondences has been thoroughly investigated 
so far. Two additional fundamental photogrammetric problems - space intersection and relative orientation, completing a triple of the 
most basic photogrammetic procedures needed to support feature-based triangulation have not been adequately addressed in the 
literature. This paper provides that missing link by presenting a procedure for relative orientation parameters estimation from linear 
features. We restrict our attention in this paper to planer curves only. We start with the simple idea of optimization procedure using 
ICP algorithm and proceed to the recovery of the homography matrix induced by the plane of the curve in space. 
I. INTRODUCTION 
Line Photogrammetry (LP) has been a tremendously active field 
of research for almost two decades. Over these years many 
researchers have argued in favor of accommodating linear 
features instead of points for different photogrammetric tasks. 
Some of their central arguments are set forth as follows: 
I. In many typical scenarios, linear features can be detected 
more reliably than point features (Mikhail, 1993). 2. Images of 
urban and man made environment are rich of linear features 
(Habib, 2001). 3. Close range applications employed in 
industrial metrology often lack an adequate amount of natural 
point features, thus requiring a costly use of artificial marks for 
automating the involved mensuration tasks. (Kubik, 1989) 4. 
Matching linear features is easier and more reliable than 
matching point features (Zalmanson, 2000). 
This paper presents possible solutions for the classic problem of 
determining the relative orientation parameters. The procedures 
proposed here are based on using free form 3-D planar curves 
instead of conjugate points. 
In the resent years we are witnessing the entrance of more and 
more digital photogrammetry workstations. Developing 
automatic processes for photogrammetric applications has 
attracted a large body of research in the photogrammetry and 
computer vision communities. The natural step towards 
automatic aerial triangulation would be to adopt higher level 
entities for determining orientation parameters. Autonomous 
solutions for relative orientation with linear features employing 
Hough search techniques have been proposed by Habib (2003, 
2001). Solutions for relative orientation using a subclass of 
linear features, namely, planar curves and conic sections have 
3rd 
been introduced by Shashua (2000) who dealt with 3* degree 
algebraic planar curves, Ma (1993) who used planar conics and 
Petsa (2000) who worked with straight coplanar lines. 
2. USING PLANAR FREE FORM CURVES 
We represent free form curves in image space by a sequence of 
2-D points. Trying to represent such curves in polynomial or 
parametric form would yield a more simplified mathematical 
modeling but at the same time would result in some loss of 
information. due to inherent generalization process being 
involved. 
The procedures shown here are valid for planar curves. We start 
with the simple idea of recovering the relative orientation 
parameters from free form planar curves. Every planar curve 
adds 3 parameters to the overall solution. The redundancy and 
the minimum number of planar curves needed for recovering 
the R.O.P will be discussed later. 
2.1 Simplest idea 
First we have to determine initial parameters. Since we try to 
recover the relative orientation, we can refer to the model space 
as the object space in exterior orientation. Initial parameters for 
the relative orientation can be determined in the classical way, 
assuming aerial photos, most likely near-vertical and highly 
correlated. Dependent relative orientation. model had been 
chosen, which defines the model coordinate system parallel to 
the first (left) image's coordinate system. As for the plane in the 
model space, horizontal plane can be used to determine initial 
parameters. 
After determining all initial parameters needed, one can project 
the curve from both images to the plane in the object/model 
space and get the intersections of the surfaces created by the