THE LINE BASED TRANSFORMATION MODEL (LBTM): A NEW APPROACH TO
THE RECTIFICATION OF HIGH-RESOLUTION SATELLITE IMAGERY
Ahmed Shaker
Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong
a.shaker@polyu.edu.hk
KEY WORDS: Remote Sensing, Geometry, Correction, Rectification, Georeferencing, Imagery, Model, High-resolution
ABSTRACT:
For various satellite imagery applications, geo-referencing through rectification is a common operation. Rigorous mathematical
models with the aid of satellite ephemeris data can present the relationship between the image space and object space. With
government funded satellites, access to calibration and ephemeris data allowed the development of these models. However, for
commercial high-resolution satellites, these data have been withheld from users, and therefore alternative empirical rectification
models have been developed. In general, most of these models are based on the use of control points. The lack of control points in
some remote areas such as deserts, forests and mountainous areas provides a catalyst for the development of algorithms based on
other image features. One of the alternatives is to use linear features obtained from scanning/digitizing hardcopy maps, from
terrestrial mobile mapping systems or from digital images.
In this work, a new model named the Line Based Transformation Model (LBTM) is established for satellite imagery rectification.
The model has the flexibility to either solely use linear features or use linear features and a number of control points to define the
image transformation parameters. As with other empirical models, the LBTM does not require any sensor calibration or satellite
ephemeris data. The underlying principle of the model is that the relationship between line segments of straight lines in the image
space and the object space can be expressed by affine or conformal relationships. Synthetic as well as real data have been used to
check the validity and fidelity of the model, and the results show that the LBTM performs to a level comparable with existing point
based transformation models.
1. INTRODUCTION center passing through a point on the image line must intersect
the object line. In their approach, the standard point-based
photogrammetric collinearity equations were replaced by line-
circle based ones. Instead of the regularly used two collinearity
equations, a single equation is established to ensure the
coplanarity of a unit vector defining the object space line, the
vector from the perspective center to a point on the object line,
and the vector from the perspective center to a point on the
image line. Furthermore, coordinate transformations are
implemented on the basis of linear features. In this case, feature
descriptors are related instead of point coordinates.
Point feature based transformation models have been, for
several decades, used extensively in photogrammetry and
remote sensing for image rectification and terrain modeling.
They are driven by linking points in the image space and the
corresponding points in the object space using rigorous
mathematical models. However, under many circumstances
accurately identifying discrete conjugate points may not be
possible. Unlike point features, which must be explicitly
defined, linear features have the advantage that they can be
implicitly defined by any segment along the line. In the era of
digital imagery, linear features can be easily identified in the
image by many automatic extraction tools and in object space,
they can be obtained from an existing GIS database, hardcopy
maps, and terrestrial mobile mapping systems (using for
instance kinematic GPS techniques). Therefore, using linear
features becomes an advantage, especially because they add
more information, increase redundancy, and improve the
geometric strength of adjustment (Habib et al, 2003). Some
effort has been made to use linear features in photogrammetric
applications for frame and linear array scanners. However,
some of these techniques use linear features as constraints and
are still based on rigorous mathematical models, which need all
sensor model information.
Further work has been done to accommodate linear features for
single photo resection and automatic relative orientation. Habib
et al (2002 and 2003) have suggested an algorithm to solve the
problems relating to the correspondence between image and
object space lines. This matching problem is solved through a
modified version of the generalized Hough transform. The work
introduced algorithms to incorporate straight lines into aerial
triangulation for frame and linear array scanner imagery. The
collinearity condition is used in single photo resection to
present the relationship between matching entities in image and
object space and the coplanarity condition is used in case of
automatic relative orientation. This work suggests that linear
features can be used to provide constraints in photogrammetric
applications.
Mulawa and Mikhail (1988) present the concept of linear
features in photogrammetric tasks in which linear features and In the absence of sensor calibration and satellite orbit
photogrammetric observations are combined in the formulation. information, there are several limitations in applying such
Kanok (1995) and Mikhail and Kanok (1997) have used an techniques to High Resolution Satellite Imagery (HRSI): a) all
independent set of linear feature descriptors to present the !hose presented are based on rigorous mathematical models
relationship between image space and object space. The method Which require sensor and system parameters that are withheld
is based on the observation that any ray from the perspective from the HRSI user community; b) when using linear features,
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