International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
image, Figure 3. As mentioned earlier, the end points of the two
segments need not be conjugate. The similarity measure should
mathematically describe the fact that the line segment (1-2)
should coincide with the corresponding line segment (AB) after
applying the transformation function relating the reference and
input images. Such a measure can be derived by forcing the
normal distances between the end points of a line segment in
the reference image, after applying the transformation function,
and the corresponding line segment in the input image to be
zero (ie. nim n, =0°, Figure 3).
Equation 1 mathematically describes such a constraint for one
of the end points of the line segment in the reference image.
x; *cosQ 4 y; -sinO—p=0 (1)
where
(p, 0) :are the polar coordinates representing the line
segment AB in the input image
(x{, y; ) ‘are the transformed coordinates of point 1 in
the reference image after applying the registration
g pp!yıng g
transformation function.
The mathematical relationship between the coordinates of a
point in the reference image (x;, y;) and the coordinates of the
conjugate point in the input image (x; y;") can be described
either by Equations 2 or 3 depending on whether we choose
affine or 2-D similarity registration transformation function,
respectively.
T a
nl lal ta. ly
r= + (2)
Y b, b bl»
One pair of conjugate line segments would yield two
constraints of the form in Equation 1. Using a given set of
corresponding line segments, one can incorporate them in a
least squares adjustment procedure to solve for the parameters
of the registration transformation function.
5. MATCHING STRATEGY
To automate the solution of the registration problem, a
controlling framework that utilizes the primitives, similarity
measure, and transformation function must be established. This
framework is usually referred to as the matching strategy. In
this research, the Modified Iterated Hough Transform (MIHT)
is used as the matching strategy. Such a methodology is
attractive since it allows for simultaneous matching and
parameter estimation. Moreover, it does not require complete
correspondence between the primitives in the reference and
input images. MIHT has been successfully implemented in
several photogrammetric operations such as automatic single
photo resection and relative orientation (Habib et al., 2001,
Habib and Kelley 2001a, 2001b).
MIHT assumes the availability of two datasets where the
attributes of conjugate primitives are related to each other
through a mathematical function (similarity measure
incorporating the appropriate transformation function). The
approach starts by making all possible matching hypotheses
between the primitives in the datasets under consideration. For
each hypothesis, the similarity measure constraints are
formulated and solved for one of the parameters in the
registration transformation function. The parameter solutions
from all possible matching hypotheses are stored in an
accumulator array, which is a discrete tessellation of the
expected range of parameter under consideration. Within the
considered matches, correct matching hypotheses would
produce the same parameter solution, which will manifest itself
as a distinct peak in the accumulator array. Moreover, matching
hypotheses that contributed to the peak can be tracked to
establish the correspondence between conjugate primitives in
the involved datasets. Detailed explanation of the MIHT can be
found in Habib et al., 2001. The basic steps for implementing
the MIHT for solving the registration problem are as follows:
e Approximations are assumed for the parameters which are
not yet to be determined. The cell size of the accumulator
array depends on the quality of the initial approximations;
poor approximations will require larger cell sizes.
e All possible matches between individual registration
primitives within the reference and input images are
evaluated, incrementing the accumulator array at the location
of the resulting solution, pertaining to the sought-after
parameter, from each matching hypothesis.
e After all possible matches have been considered; the peak in
the accumulator array will indicate the most probable
solution of the parameter in question. Only one peak is
expected for a given accumulator array.
e After each parameter is determined (in a sequential manner),
the approximations are updated. For the next iteration, the
accumulator array cell size is decreased to reflect the
improvement in the quality of the parameters. Then, the
above two steps are repeated until convergence is achieved
(for example, the estimated parameters do not significantly
change from one iteration to the next).
e By tracking the hypothesized matches that contributed
towards the peak in the last iteration, one can determine the
correspondence between conjugate primitives. These
matches are then used in a simultaneous least squares
adjustment to derive a stochastic estimate of the involved
parameters in the registration transformation function.
6. EXPERIMENTAL RESULTS
To illustrate the feasibility and the robustness of the suggested
registration process, experiments have been conducted using
real data from different imaging systems, Table 1. These scenes
were captured at different times (multi-temporal) and exhibit
significantly varying geometric and radiometric properties.
Table 1. Multi-temporal images for the city of Calgary with
various geometric and radiometric resolutions
Source Date Size Ground
Rows xColumns Resolution
Aerial 1956 1274 x 1374 5.0 (m)
Aerial 1972 1274 x 1374 3.5 (m)
Ortho-photo 1999 2000 x 2000 5.0 (m)
Landsat 7 | 2000 500 x 500 15 (m)
Landsat 7 2001 300 x 300 30 (m)
930
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