In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009
63
a b
Figure 4. Applying morphological opening operator with
structuring element of size 5*5 to last pulse range images, a) the
first dataset, b) the second dataset
3.2 Evaluation of the Clustering Results
The results of k-means and boost k-means clustering algorithms
applied to features of our two datasets are shown in figure 5 and
figure 6. In our experiments the cluster number is considered
fixed and equal to 3 because our objects of interest in urban
areas are bare earth (blue), vegetation (green) and buildings
(red). For the creation of confusion (error) matrix, first, the
ground truth (also known as reference clustering results) should
be defined. For this, 3D vectors of these areas consist of
vegetation and building areas are used. The areas of polygons in
pixel unit (number of pixels in the vector polygons of objects)
are used as the values of reference clusters in error matrices.
The user values are computed by counting the number of truly
clustered patterns inside the polygons.
a b
Figure 5. Overlay of reference vectors on clustering results of
first dataset, a) result of k-means algorithm, b) result of boost k-
means algorithm.
a b
Figure 6. Overlay of reference vectors on clustering results of
second dataset, a) result of k-means algorithm, b) result of boost
k-means algorithm.
On the first view, both clustering algorithms provide reasonable
classes of vegetation, buildings and ground but an accurate and
numerical comparison will be carried out comparing the true
object elements in the areas of interest.
In Tables 1, 2, the confusion matrices contain the number of
pixels assigned to each cluster in the results of k-means
clustering is provided. The confusion matrices and NMI factor
of the results of boost k-means algorithm are also given in
Tables 3, 4.
Table 1. Error matrix and quality factors of k-means clustering
applied to first dataset.
Error Matrix
Reference Map
Building
Tree
Ground
C/3
Building
34077
41
975
3
C/3
Tree
205
6844
1178
C4
Ground
7946
2197
65607
Producer Accuracy
80.7%
75.4%
96.8%
Producer Accuracy
97.1%
83.2%
86.6%
Overal Accuracy
89.5%
K-factor
0.801
Table 2. Error matrix and quality factors of k-means clustering
applied to second dataset.
Error Matrix
Reference Map
Building Tree Ground
Results
Building
Tree
Ground
58393 120 1858
261 9808 1810
10025 3809 68570
Producer Accuracy
85.0% 71.4% 94.9%
Producer Accuracy
96.7% 82.6% 83.2%
Overal Accuracy
88.4%
K-factor
0.798
It should be noted that the confusion matrix is should be
diagonal in the ideal case. According to the above confusion
matrices and NMI factors and also visual interpretation,
improvement in results of clustering using boosting method is
obvious for our classes of interest in theses datasets.
Table 3. Error matrix and quality factors of boost k-means
clustering applied to first dataset.
Error Matrix
Reference Map
Building Tree Ground
Results
Building
Tree
Ground
39378 77 1895
303 7757 1997
2547 1248 63868
Producer Accuracy
93.2% 85.4% 94.2%
Producer Accuracy
95.2% 77.1% 94.4%
Overal Accuracy
93.2%
K-factor
0.876
