In. Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
Figure 3. Schematic illustration of the relationship between 
roundabout geometric parameters. Vector data is in green. 
The resulting total energy function can now be defined: 
E(</>) = M P(<f>) + E m (<t>) (6) 
where /¿>0 controls the balance between the first and second 
term. The evolution equation of the level set function is then 
obtained via calculus of variation (Courant & Hilbert, 1953) 
and application of the steepest descent process for minimization 
of the energy functional equation (Li et al., 2005) as 
-77 = P[&<t> ~ div( 7777)] + ^(^)div(g -^77) + vg5(<f>) 
ot | V <p | | V ^ | 
(7) 
For all examples of central island detection, the same set of 
control parameters, 2=4, //=0.13, v=2 and the time step dt=2, 
were tuned for the evolution equation (Eq. 7). 
Since either evolution type alone, shrinking and expansion, has 
its own limitations, a hybrid evolution strategy is employed. For 
instance, in case of only shrinking curve evolution, vehicles on 
the circulating roadway, and in case of only expansion curve 
evolution, structures inside the central island, can block the 
motion of the curve toward the central island’s border. Using a 
hybrid evolution strategy overcomes various kinds of 
disturbances often present inside and outside the central island. 
Often before the curve evolution begins, a pre-processing step 
is necessary to remove some fine features that might hinder the 
curve motion. First, a morphological closing operator is applied 
in order to remove dark spots and subsequently the opening 
with the same structuring element (disk structuring element; 
size=2) is performed to eliminate small bright features followed 
by Gaussian smoothing (Fig. 4c). 
(a) (b) (c) 
Figure 4. Pre-processing sequence: (a) Original image, (b) cut 
out marked by the red box in (a), and (c) pre-processed result. 
Shown in Fig. 5 is the first sequence for island extraction, when 
shrinkage curve evolution is applied. After the vertices of the 
polygonal area identified as a roundabout object in the 
topographic database are located, the polygon is enlarged so 
that its increased area is one-tenth more than its initial area (Fig. 
5a), thereby making sure that the new polygon is located 
outside the central island. Subsequently, shrinkage evolution 
begins through use of level sets. Among the obtained closed 
curves in Fig. 5b, the one with the largest area is selected as the 
initial guess for the island (Fig. 5c). This island candidate is 
subject to further processing. 
Next, the initial polygon obtained from vector data is made 
smaller so that its area is reduced by half (Fig. 5a). 
Subsequently, expansion curve evolution occurs (Fig. 6a). The 
largest resulting closed curve is most likely the desired solution 
due to the fact that the island is the largest object within the 
computational domain. This closed curve, however, can often 
not be regarded as the island because many disturbing features 
such as trees and various structures exist inside the island. This 
can block the motion of the evolving curve towards the island 
boundary. Leakages are therefore created at some points along 
the boundary of disturbing features where zero level curves 
have stopped in order to pass over them. 
(a) (b) (c) 
Figure 5. First sequence for island extraction: (a) Polygonal 
vector data (green) and its enlarged and reduced forms(red), (b) 
shrinking curve evolution result after 1335 iterations, and (c) 
the eventual result of shrinking evolution. 
With the assumption that disturbing objects inside the island do 
not contain smooth boundaries, cubic spline approximation is 
carried out to provide leakages (Fig. 6b). Subsequently, 
expansion evolution and spline approximation are repeatedly 
carried out (Fig. 6c) until no change in the position of the curve 
is reported. Again, the largest closed curve is regard as the 
island (Fig. 6d). Now that the results of island detection from 
the iterative expansion and shrinkage curve evolution have been 
obtained, the image positions of the resulting curves are 
compared and those points which are close to each other are 
selected, thereby eliminating curve positions that are not 
located on the island boundaries. The selection of points is 
based on their closeness in such a way that points having a 
distance below a certain threshold are selected. The final result 
is obtained when an ellipse is fitted to the selected points. 
When a roundabout appears as a point object in the topographic 
database (Fig. lb), the same hybrid evolution strategy is used 
but with a different initialization because the diameter of the 
inscribed circle is known to be below a given threshold, but 
how small it is is unknown. This brings some limitations for the 
shrinkage curve evolution. In order to apply the shrinkage 
evolution, the initial zero level curve must be placed outside the 
island. Since the approximate diameter of the inscribed circle is 
unknown, three successive circles are defined (Fig. 7a), on each 
of which the shrinkage curve evolution is carried out separately. 
The diameter of the circle interior to the central island is 10m 
and the diameters of exterior circles have an interval of 3 m. 
The results of shrinkage evolution on each initial curve from the 
largest to the smallest circle are depicted in Figs. 7b, c and d. In 
the next step, the iterative expansion evolution is carried out