the shadow of a wall is changeable, according to the bearings
of wall features o, and the solar azimuth a, thus, the second
weighting factor to be considered is given by
cos(n /2-j, —a, |), if 0xl, -a,|«n/2
cos, -a.,| - n /2), if n/2X|, -a,|«n
) if x <ja, -a,|<3x/2
cos(fot, -a,|- 31/2), if 3 sk, -a, «2n
cos(3n / 2 - lo, m
In order to carry out image-and-map registration, the vector
data of the cadastral parcels with walls have to be provided by
spatial information systems and then converted into image
space, according to the imaging geometry and/or the processed
level. If the header data of Quickbird images gives relatively
good approximate geographic location of each corner, say on
the order of 10m, it is possible to start image-and-map
registration with no human intervention at all. However,
selecting a reference point manually identifiable both on map
and in image could speed up registration. The U-shape model
of intensity profile of a shaded wall is certainly not secured to
find an unique location for image-and-map registration,
therefore, the geometric characteristics of all polygons, i.e., all
of the given parcels with walls, have to be taken into account.
Then, all of the searching results of polygons are compared
with each other to filter out any candidate locations whose
geometric structure is not conformal to the vector data. In other
words, most of the polygons should have the best match at the
candidate locations with the same magnitude of translation and
rotation.
2.3 Image-and-Map Registration Error Modelling
Automation of photogrammetric practices are mainly based
upon prior knowledge derived from the manual operations,
therefore, error modelling on image-and-map registration has
to start with the analysis of the errors resulted from manual
operations. In case of the registration of a vector map and a
geometrically rectified image, the errors of registration may
result from various aspects. Errors coming from a rectified
image include residuals of rectification o;, random errors in co-
ordinate measurements of features/points Om and
misplacements of the identified features oy, such as walls, with
respect to the expected boundary lines. On the other hand,
errors resulted from a vector map contain residuals of
surveying adjustment o, and the error of digitisation of
cadastral maps o4. Obviously, image-and-map registration is a
process of linear combination of two types of data, and the
resultant error G, is propagated and derived as
2
2 2 2 2
e. = Jo} £0 +0 tal +0, (2)
The magnitude of rectification error o; depends upon the
imaging geometry, algorithms of rectification, ground
control/DEMs, and the terrestrial flatness. Since the advanced
satellite optical sensor produces images of 0.6m GSD, it is not
always available to derive DEMs of excellent accuracies on the
order of deci-meter, and the production of ortho-rectified high-
resolution satellite imagery of good quality is not guaranteed.
However, the rectification of satellite images over flat areas
does not necessarily need DEMs, and the proposed algorithm
for image-and-map registration is primarily aimed at flat areas
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
at this stage. Ground control is also not essential, provided
that on-board satellite positioning systems gives good
approximation of geographic locations for images. Thus, the
imaging geometry of the satellite sensor and the algorithm
to be used in rectification has to be considered. Assuming
that the rotational angles in across-track direction (pitch)
and in vertical direction (yaw) are relatively small and
neglected, the first author proposes a simplified equation to
calculate the relief displacement d, resulted from undulated
terrain surface in oblique satellite images regarding to the
rotational angles in along-track direction (roll). It is given
as
(f —r tan (Xf tan’ +r)
H
Hf {1 + tan? 1 (3)
(00055) un
if t — 0, then. d, & A 5—— —— — zh-—
He lc
if H>>h, then d, «A
where H= flying height, /-difference of elevation, f= focal
length, r= tilt angle (roll), r=radial distance from center to
an arbitrary point in image space. It can be calculated that
an elevation difference of 10m over the entire imaging area
may result in difference of relief displacement less than 0.3
pixels, in the case of the Quickbird imagery. This modest
displacement is due to the imaging geometry of extremely
narrow angular filed of view and relatively flat terrain.
Since the cadastral parcels are located at relatively flat
areas, where terrain variations are under 10m, the
magnitude of rectification error o; is relatively insignificant.
The second factor of errors oy, is caused by random errors
in co-ordinate measurements of features/points and is
related with the image sampling and re-sampling
procedures. It is obvious that a line feature of ground
distance of 1 GSD in a basic (raw) image taken (sampled)
by a satellite sensor may be sampled by 2 pixels in a
standard image, i.e., the blurred edges of the line features
in a rectified and re-sampled (standard) image convey
deviations up to 2 pixels. The third factor of errors or is due
to intentional misplacements of the identified features, such
as walls, in respect to the expected boundary lines.
Regulations of local governments demand some extent of
retreat in setting up walls regarding to the exact boundary
lines of a cadastral parcel to give way to the surrounding
roads and sidewalks. The extent of the retreat of wall is up
to 3 m, or 5 pixels in Quickbird imagery, contributing the
major error to the results of image-and-map registration.
The forth factor of errors is the residuals of cadastral
surveying and adjustment c, conveyed in the vector data of
cadastral parcels. The residuals of cadastral surveying
practices and adjustment computations are on the order of
centimetres, which is certainly much better than one GSD
of any advanced satellite optical sensor available. That is
also the reason why cadastral maps are proposed to provide
ground control for image-and-map registration.
In case that digitization for existing cadastral maps, instead
of surveying by using total-station or electronic distance
measurement (EDM) instruments, are the sources of vector
data, the fifth factor of errors o4 is resulted from the
process of digitization. The scale of cadastral maps is 1/500
(urban areas) or 1/1,000 (rural areas) for the new version of
cadastral maps in Taiwan and is 1/600 (urban areas) or
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