CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation
of parameters for roundabouts are derived. Second, the central
island is extracted using a level set approach making use of
prior information obtained from the previous step. Finally, the
roundabout is reconstructed using a snake-based method. The
proposed approach has the aerial image, a topographic database
and the road arms as input, and the roundabout border
connected to the existing road arms as output. The reader is
referred to Ravanbakhsh et al. (2008) or Ravanbakhsh (2008)
for a description of how the road arms are extracted.
3.1 Pre-analysis of topographic database
Roundabouts are usually represented in topographic databases
in one of two ways, either as an area object when the diameter
of the inscribed circle is larger than the threshold (Fig. la), or as
a point object when the diameter of the inscribed circle is small
(Fig. lb). The actual representation threshold varies in different
topographic databases. This vector data is used to focus the
extraction process to the image regions where roundabouts are
located. Furthermore, the approximate diameter of the central
island and width of the circular roadway can be initially
determined (Fig. 3).
It is noteworthy that the width of the circular roadway depends
mainly upon the number of entry lanes. The width of entry
lanes is also derived from vector data. According to
construction standards, the roadway must be at least as wide as
the maximum entry width and generally should not exceed 1.2
times this width (U.S. Federal Highway Administration, 2000).
In case that a roundabout appears as a point object, attributive
information must be included in the topographic database
implying that the node represents a small roundabout. This
means that the diameter of the inscribed circle is below the
threshold that has been defined in the topographic database.
3.2 Central island extraction
With roundabouts, a correct extraction of the central island
helps facilitate the extraction of the outline. The reason for this
is that the central island, when enlarged, influences the shape of
the roundabout outline. The initial detection of the central
island can then provide a good idea of how the outline appears
in the image. The proposed method to detect central islands is
based on level sets.
Geometric active contours were introduced by Caselles et al.
(1993) and Malladi et al. (1995). These models are based on
curve evolution theory and the level set method. The basic idea
is both to represent contours as the zero level set of an implicit
function in a higher dimension, usually referred to as the level
set function <f>, and to evolve the level set function according to
a partial differential equation (PDE). It is well known that a
signed distance function, a function which introduces the
minimum distance from every point in a defined domain to the
zero isocontour of a level set function, must satisfy the
desirable property of |V^ |=1 (Osher and Fedkiw, 2002). The
following formula has been proposed to provide the internal
energy of a snake which penalizes the deviation of (f) via a
signed distance function (Li et al., 2005):
m= f Liv<ii-ifdxdy (i)
2
is a metric to characterize how close the function (f> is to a
signed distance function in a specified computational domain
Qc R 2 . The external energy is defined by
E m ((/>) = AL g {(f)) + v A g {(f>)
(2)
where /i>0 and v is a constant and the length termL^
area term A g (<j)) are defined by
(^) and
L g ((/)) = gS(<f>) | V (f> | dxdv
(3)
A g (</>) = J Q gH (-(f)dxdy
(4)
with the edge indicator function g being given by
1
g= ,
(5)
1+|VG CT */1 2
Here, H is the Heaviside function, 8 the univariate Dirac
function, G,j the Gaussian kernel with standard deviation cr ,
and / image intensity.
INPUT DATA
PROPOSED APPROACH
RESULT
Roundabout area
Road arms
Roundabout
Roundabout border | Central area
Central island
(a)
Figure 2. (a) Roundabout model and (b) workflow of roundabout extraction.
20
