IEEE Geoscience and Remote Sensing Magazine - December 2015 - 24

f(x)
700
600
500
400
300
200
100
0

dex once the regional roofs
are detected. Thereafter,
the optimal matching pair
is evaluated based on the
Euler number matrix and
histogram. The similarity
metrics are computed following the description of
"a small value corresponds
to high similarity."

Figure 3. Distribution diagram of pending edge gradient in a rectangular elastic template.

complete the non-enclosed rectangular structures; the
template identifies the edge by gradient. 6) Post-processing helps to reduce the complexity of an urban scene,
including merging the rectangles belonging to the same
building and eliminating false structures.
B. GeneratinG internal structure
Heterogeneous blocks appear as distinctive spectral features as compared with the smooth roof. K-means is a
classical unsupervised classification algorithm that
only needs the input of the
By using the
initial number of distinct
constructed similarity
categories. A classification
measurements Fully
map can then be obtained
descriBing the regional
for automatic and rapid image processing. In our study,
Features, a FavoraBle
a binary classified map is
image matching result
directly obtained using kthat overcomes complex
means clustering by setting
urBan scenes is
the number of categories to
oBtained rapidly.
two. However, the irregular
margin is too complex to
calculate quantitatively. A
morphology open operation is performed to obtain regular patches with a smooth boundary. Hence, the areas of
interests are not only surrounded by an outer contour line
but are also separated with inner heterogeneous patches.
2.2 Feature description and similarity metrics
Compact and stable descriptors are necessary to measure
the feature similarities between a reference image and
a target image. We obtained the area index, gray histogram, and topological aspects of the Euler number matrix to describe the contour feature, original spectrum
characteristics, and internal heterogeneous structure,
respectively. The regional features between the reference
image and target image are compared one by one. Instead of a complex constraint and strategy, the simplest
traversal pattern can accomplish fast and accurate image matching, which benefits from the small number of
high-level object features.
Given a reference image and a target image, the candidate matches are firstly chosen based on the area in24

a. area index
The area of contour measures the distribution range,
which is the simplest descriptor to represent the contour
for fast matching judgment. Perspective distortion and
grouping deviation make the same roof different in the
matched images. However, the difference would be a
relatively small value unless the perceptual organization
leads to wrong or inexact results. Although the area index cannot ascertain a match, the similarity can serve as
an optimal technological procedure to eliminate absolute
mismatches and exclude the conspicuously different extracted results of the same roof. The similarity (S A) is estimated as follows:
ai - b j
s A = min (a , b ) i = 1, g, m; j = 1, g, n;
i
j

(1)

Here, a i and b j represents the area of building roof in
candidate images.
B. topoloGical matrix
A topological relationship has the invariance of translation, rotation, and scaling, and the effects are obtained
from image matching. Building contours topologically
contain internal heterogeneous blocks. Such a relationship descriptor can be constructed to examine similarities.
Conventional topological descriptors (e.g., adjacent graph
and Euler number) may be problematic and indistinctive
in the presence of holes.
We proposed an Euler number matrix. The rectangular
roof is first divided into four quadrants, and the Euler number in each subdomain is calculated. A 2 # 2 matrix is then
constructed. The Euler number matrix describes an internal
spatial structure to provide more evidence of distinctiveness
than the Euler number, and the low computational complexity is suitable for fast image matching. The similarity distance
a 1, a 2
b 1, b 2
1 and (
2, is
between the constructed matrixes, '
a 3, a 4
b 3, b 4
calculated as follows:
sT =

/ 4i = 1 (a i - b i) 2
/ 4i = 1 a i - b i

(2)

Here, a i and b i represents Euler number in each
quadrant.
ieee Geoscience and remote sensing magazine

december 2015

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2015