International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
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Figure 1: Left: geometry of a Zwickel: p; is the intersection point of the lines /; and l5 which are extended by a factor
(extension are shown dashed) to ensure intersection. Right: For the rectification the lines l4 and l5 with the enclosed angle
v are mapped to an orthogonal frame using the affine transform matrix A. The transform maps the intersection point p;
to origin and the lines to the axes of the coordinate system.
those segments are extended by a predefined factor to en-
sure that lines, that are close enough, will intersect. All
reported intersections are then handed over to the Zwickel
formation procedure. For the line detection we use a hi-
erarchical approach, that finds straight lines in a coarse-
to-fine pyramid search. In every pyramid layer we extract
Canny edges (Canny, 1986) with sub-pixel accuracy and fit
straight line segments to sets of collinear edges. In order
to compute intersections we extend the resulting line seg-
ments to ensure a sufficient number of line intersections.
The detection of Zwickels is affine invariant. The lines of
the detected Zwickels are ordered clockwise to ensure the
correct correspondence between the lines of two match-
ing Zwickels. As already mentioned we extend the origi-
nally extracted lines, therefore the intersection points may
lie in a homogeneous region. This is one of the additional
advantages over point-of-interest methods that rely on de-
tection of location of high gradient curvature such as the
Harris corner detector (Harris and Stephens, 1988). Fig-
ure 2 shows two examples of extracted Zwickels with low
gradient curvature at the intersection point.
2.2 Zwickel rectification
In order to compute an affine invariant representation of
a Zwickel, we map the image data inside the sector that
is bounded by the lines to an orthogonal frame (see Fig-
ure 1). An affine transform is computed from one cor-
responding point (the intersection point is mapped to the
origin) and the two line directions. The image region in
the sector is then rectified by applying the affine transform
that maps the sector to an orthogonal frame with the in-
tersection point as origin and the lines as axes of the co-
ordinate system. Equation | shows the general form of
an affine transform and its decomposition into a rotation,
scaling and shear transform. The rectification eliminates
the four of the six unknowns of the affine transform: the
translation [t,,¢,] through shifting the intersection point
to the origin and rotation q and skew s through mapping
the lines as orthogonal axis. The remaining unknowns are
the scale factors s, and s,. In order to determine the un-
known scale we use a similar approach as in (Lowe, 1999,
Mikolajezyk and Schmid, 2001). Both approaches use a
scale space search to find the correct scale of the support
region.
1120
(a)
(b)
Figure 2: Examples of extracted Zwickels where the inter-
section point (denoted by the circle) of the two extended
lines does not lie on a location of high gradient curvature
i.e. no Harris corners would be detected at the intersection
point.
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Figure 3 shows two examples of the rectification step.
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2.3 Descriptor
In order to achieve affine invariance we apply a scale in-
variant descriptor. The descriptor is inspired by Lowes (Lowe,
1999) SIFT-features.
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