INMENTS
Detection, Invariants
| of manhole covers as
les us to automatically
ching procedure which
a cadastral database.
spondences per image,
les) are available from
stem; and, as we will
d with high precision,
ites from the cadastral
0 major aspects in this
arks of the considered
0 match constellations
ole positions from the
> following the interior
to be known.
:CTION AND
ANDMARKS
based on a parametric
cation, size, shape, and
picted manhole covers.
or between the model
model parameters and,
Imark's position in the
This can be shown for
i. À short description of
| be given below. More
Rohr, 1995).
lar Landmarks
rers varies from country
ific type which consists
rk concentric ring (see
normally are recorded
plane, images of these
ge intensities of a cross-
he considered type form
| also take into account
ise of the band-limiting
ed shape as sketched in
roximately be described
, and Tmin, Where hmaz
na 1996
h max
C mu h 0
h min
mmm mmm mmm mgm mm mmm
----R-------4
Figure 1: Ideal appearance of a manhole cover (left) and blurred cross-section intensities (right).
and Amin are the relative values of the function's maximum
and minimum with respect to the background-level ho; Tmin
denotes the distance of the minimum from the center. As
suggested by Figure 1, we approximate the ideal intensity
profile using an analytic model whose general shape corre-
sponds to the second derivative of the 2D Gaussian. However,
the shape of this function is controlled by only two param-
eters (amplitude and variance), while three parameters are
needed for adequately describing the intensity profile of the
landmark. Therefore, we represent the model by a modified
function, which, on the one hand, well approximates the sec-
ond derivative of a Gaussian, and, on the other hand, has
three parameters describing its shape, namely ai, a2, and o:
2
M(z,y) = ao + (as + a2 - 1”) - exp (zx) ©
with r? = (x —x0)? + (y — vo)” and (xo, yo) being the image
coordinates of the landmark center.
Given our model function M and the image intensities of an
instance of a manhole cover, we minimize the error E between
the image and the model. In our approach, E is defined by
the sum of the squared differences between the image intensi-
ties I and the model M (which is a function of ao, a1, a5, c,
zo, and yo) at some data points taken from a square window
centered around the initial location estimate of the landmark.
Since we are dealing with a non-linear model, we apply the
iterative Levenberg-Marquardt method for minimizing the er-
ror function. This method requires to analytically calculate
the first partial derivatives of M with respect to each of the
parameters to be optimized. An example for a model fitting
result is given in Figure 2.
2.2. The Landmark Extraction Scheme
In our landmark extraction scheme, we obtain an initial set
of potential landmark positions by exploiting the normalized
cross-correlation for all local intensity maxima in the image,
using a landmark prototype template. The potential land-
marks detected this way are submitted to the parameter op-
timization procedure described above which adapts the ana-
lytic model function to the intensities of the given landmark.
The results of the model fitting are twofold: the set of opti-
mally adapted parameters and the final approximation error.
Both are checked in a subsequent verification step in order to
decide whether the adapted model describes a valid landmark
instance. In this way, we are able to suppress a large fraction
of false detections and obtain a high-precision localization of
the actual landmarks.
The initial parameter values required to set up the parame-
ter optimization process are obtained from a small number
of representative examples which have to be selected by the
operator in a preceding training phase. The training results
are also used to derive the thresholds applied in the verifi-
cation step and to generate the prototype template used for
landmark detection.
2.3. Localization Precision Obtained by Model Fitting
We investigated the localization precision obtained by model
fitting for simulated landmark images which have been gen-
erated with known parameters. The physical landmark size
was assumed to be 80 cm; the acquisition parameters and
the pixel size were set to typical values (see below), giving
a pixel resolution of 15 cm on the ground, i.e. a landmark
is typically represented by 6 by 6 pixels (unblurred). Using
our simulation technique we are able to statistically evaluate
the localization precision with respect to variations in image
blur, sampling effects, noise, perspective projection, regular
shape distortions, and interaction effects with background
structures (e.g. road markings). In a large number of random
experiments we found that the localization error is well be-
low a hundredth of a pixel (less than 1 mm on the ground)
for noise-free images and less than a tenth of a pixel (about
1 cm on the ground) for images having a realistic amount of
noise. Even in the presence of serious background distortions
the localization precision is still in the lower sub-pixel range
for most kinds of distortions.
2.4. Extraction Performance on Real Image Data
Experiments on real image data have been done on a number
of data sets. We used color infrared photographs, which have
been acquired with a Zeiss RMK A-30/23 camera from an
altitude of 1500 m, giving an image scale of 1:5000. The
photographs have been scanned at a resolution of 30 um,
resulting in a pixel size of 15 cm on the ground and an image
size of about 7700 by 7700 pixels (covering a ground area of
about 1.3 km?).
A number of 400 to 500 manhole covers is visible in each
of the images, including a significant fraction of landmarks
which are seriously distorted by background structures, have
very low contrast, or do not agree with the ideal landmark
model at all. According to these effects, the extraction
process typically yields a number of 100 to 200 detections.
The percentage of false detections is in the range of 1076
to 20% of the total number of detections, which is very
low considering the high complexity of the analyzed scenes.
147
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
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