3.1 Image processing
Original images by default present an excessive amount of
information where sometimes, like now, this image
representation is not desirable. In order to transform this
information to a useful one, an edge detector (Pratt, 1991;
Gonzalez and Woods, 1992), for example the gradient operator,
is used. If the edge is defined as a change in image intensity, a
gradient operator is the choice (Mikhail et al., 2001). Roberts,
Prewitt and Sobel edge detector kernels are commonly included
in the gradient operators.
Another edge detector, which is very popular in image
processing, is the Canny operator (Canny, 1986). Susan
operator (Smith and Brady, 1995) is another powerful edge
detector. Both they can be used to produce edge images. The
fate is to get an edge image presenting the edges in an enhance
mode, which is an effective way to detect edges and moreover
to find the breaklines.
Figure 3. Edge image
Additionally, image processing is applied in one more stage of
the framework; in the original images in order to perform a
radiometric balance between images that are used in image
matching. Images’ photometric characteristics are a vital
condition to have the optimum balance so as image matching
has good chances to succeed. Differences in contrast and
brightness between images define bad conditions for image
matching.
3.2 2D image model reconstruction
In close range problems, especially in architectural and
industrial applications, lines are considered to be almost
horizontal or almost vertical. This definition was assumed in the
current approach.
In order to proceed to the reconstruction of 3D model, first is
requisite to calculate the 2D model in image space. Hough
Transform (HT) was selected as the tool for the 2D image
model reconstruction. HT is used to extract geometric shapes
from an image and still remains powerful tool for detecting
predefined shapes like lines and ellipses or circles. HT has been
used for more than three decades in the research field of image
processing, pattern recognition and computer vision (Duda and
Hart, 1972; Ballard, 1981; Ballard and Brown, 1982;
Illingworth and Kittler, 1988). However, in digital close range
Photogrammetry HT has only rarely been used (Adamos and
Faig, 1992; Stylianidis and Patias, 2000).
In the current approach, HT is a line-searching tool for specific
values of lines' direction. Actually, HT is working in the range
of angle values near to 0° and near to 90°, i.e. is searching for
almost horizontal or vertical lines. In real conditions, HT is
searching every black pixel in the edge image that satisfies
angle restrictions. Additional constrains, like line-length can be
set up as well, in order to avoid small line segment tracking
where commonly are not used in 3D reconstruction.
The result is like the one presented in Figure 4. In Figure 4a it is
shown how hough lines are extracted in the image space. The
2D image model is constructed by the intersection of lines,
which is clearly presented in Figure 4b.
À | | l
(b)
Figure 4. (a) Hough lines in image space (b) 2D image model
3.3 3D approximate model
Using inverse collinearity equations, XYZ ground coordinates
are calculated for each corner point of the created 2D image
model. Therefore, an approximate 3D object model can be
generated. Besides, using the direct collinearity equations, the
produced approximate 3D model can be projected to any other
image.
In Figure 5 it is shown with the line-frame (4 points) how and
where the 3D approximate model is located after its projection
in other image. The projected model in any other image is not
adjusted in the correct position due to the fact that the Z
coordinate taken into account is not the real, but an approximate
one. Moreover, in the same figure, the 4 individual points
present the correct position of the corresponding approximate
model points.
The Z value (depth), which is the only unknown parameter in
collinearity equations, is assumed to be in the range of a
minimum (Z,) and a maximum (Z;) value in the object space.
This condition defines the two extreme pairs of (x,y) values,
(Xmin:Ymin) 4nd (Xmax-Ymax), i.e. indicates the searching area for
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