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The correspondence of the line segments is described by a 
mathematical constraint, which ensures the coincidence of 
conjugate line segments after applying the proper 
transformation function relating the involved images or 
surfaces. 
To illustrate the concept of the registration procedure using line 
segments, let us consider Figure 3, where a line segment a, 
defined by the end points / and 2, in the first dataset is known 
to be conjugate to the line segment ^, defined by the end points 
j and 4, in the second dataset. Let us assume that the line 
segment a, defined by the end points / "and 2’, is the same line 
segment a after applying the transformation function relating 
the two datasets in question. In this case, we need to introduce a 
mathematical constraint, which guarantees that the end points /° 
and 2’ lie along line 5 but not necessarily coincide with points 3 
and 4. In other words, the mathematical model should minimize 
the normal distances between the transformed end points in the 
first data set, points / "and 2°, and the corresponding line in the 
second dataset, line b. The implemented transformation function 
depends on the nature of involved datasets. For example, either 
2-D similarity or affine transformations can be used for image- 
to-image registration. On the other hand, 3-D similarity 
transformation can be used for surface-to-surface registration 
applications. 
Transtormation function 
d TUM 
Figure 3. Correspondence of conjugate line segments in two 
datasets 
4. APPLICATIONS 
This section briefly outlines the implementation of linear 
features in various photogrammetric and medical applications 
such as automatic space resection, photogrammetric 
triangulation, camera calibration, image matching, surface 
reconstruction, image-to-image registration, and absolute 
orientation. We are mainly illustrating the value and the benefits 
of using linear features. However, detailed analysis of such 
applications can be found in the provided references. 
4.1 Single Photo Resection (SPR) 
In single photo resection, the EOP of an image are estimated 
using control information. Traditionally, the SPR problem has 
been solved using distinct control points. However, the SPR can 
be established using control linear features, which can be 
derived from MMS, existing GIS databases, and/or old maps. 
Conjugate object and image space straight-line segments can be 
incorporated in a least squares procedure, utilizing the 
constraints in Equation 1, to solve for the EOP. A minimum of 
three non-parallel line segments is needed to solve for the six 
elements of the EOP. This approach can be expanded to handle 
free-form linear features, which can be represented by a set of 
connected straight-line segments, Figure 4. Habib et al. (2003b, 
C) introduced the Modified Iterated Hough Transform (MIHT) 
to simultaneously establish the correspondence between object 
and image space line segments as well as estimate the EOP of 
an image captured by a frame camera. The MIHT successfully 
61: 
estimated the EOP while finding the instances of five object 
space linear features within twenty-one image space features, 
Figure 4. 
  
(a) (b) 
Figure 4. SPR using control linear features (a) while 
establishing the correspondence with image space 
features (b) 
4.2 Photogrammetric Triangulation 
In this application, straight lines can be implemented as tie 
features, control features, or a combination of both. Habib et al. 
(1999, 2001a) showed the feasibility of utilizing straight lines in 
photogrammetric triangulation using straight-line segments in 
imagery captured by frame cameras and linear array scanners, 
respectively. It has been proven that the photogrammetric 
triangulation of scenes captured by linear array scanners 
incorporating straight-line segments leads to a better recovery of 
the EOP when compared to those derived using distinct points. 
4.3 Digital Camera Calibration 
Camera calibration aims at determining the internal 
characteristics of the involved camera(s). Traditionally, the 
calibration starts by establishing a test field containing many 
precisely surveyed point targets, which requires a 
photogrammetrist or surveyor. On the other hand, the 
calibration test field incorporating linear features is very easy to 
establish compared to that containing point targets. In addition, 
the linear features can be automatically extracted allowing non- 
photogrammetric users of digital cameras to produce high 
quality positioning information from imagery. Straight lines 
could be beneficial for estimating the internal characteristics of 
frame cameras. Deviations from straightness in the image space 
are attributed to various distortions (e.g., radial and de-centring 
lens distortions). Habib and Morgan (2002, 2003) and Habib et 
al. (2001a; 2002) used object space straight-lines in a calibration 
test field as tie features for digital camera calibration. 
Figure 5-a shows an image of the test field comprised of straight 
lines, where distortion parameters led to deviations from 
straightness in the image space. Figure 5-b illustrates the 
recovery of the straightness property using the estimated IOP 
from the calibration procedure. Moreover, the calibration results 
turned out to be almost equivalent to those derived from 
traditional point-based calibration procedures. 
  
  
  
  
   
(a) 
Figure 5. Straight line before calibration (a) and after calibration 
(b). Straight dotted lines were added to show the 
recovery of the straightness property