# Full text: CMRT09

```CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation
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The finding of the maxima in the correlation image with sub
pixel accuracy by approximating the discrete correlation
function by a continuous polynomial function is broadly
discussed in Kraus (1996) and will not be described here.
Figure 7 shows an example were one search image was matched
with multiple reference images.
Figure 7: Correlation example. The brighter the pixels, the
higher the correlation, i.e. the greater the similarity
between search image and reference image.
For the practical implementation, the reference images of
buildings are stored in a library. For each of these buildings also
vector information (describing the building outline in the
reference image coordinate system) is available. Thus the
library contains multiple building types to which one image
patch and one vector representation corresponds.
Once a location of high correlation is found in the search image,
the vector data of this building is transformed into the
coordinate system of the search image.
Figure 8: Example on image matching with two reference
images and multiple orientations (Quickbird-subset
of Phoenix area). Note that the computed correlation
image is a multi-dimensional image. The number of
dimension corresponds to the number of rotations
(here: 120 with a rotation step of 3 degrees).
It is often the case that buildings of the same (or similar) shape
have different colours (grey values) in the images (e.g. due to
different roof materials). Therefore it is advisable not to store
image patches of the investigated buildings in the library, but
instead, register their edges. In this case, also the search image
has to be edge-extracted before applying the matching
procedure. For gaining the edge information, classical operators
like the Canny edge detector, Sobel operator, Laplacian of
Gaussian etc. can be applied.
Figure 8 shows an example of the image matching procedure.
2.3 Texture Analysis
One of the simplest ways for describing texture is to use
statistical moments of grey level histograms of an image or a
region. Measures of texture computed using only histograms
suffer from the limitation that they carry no information
regarding the relative position of the pixels with respect to each
other. One way to bring this type of information into texture
analysis process is to consider not only the distribution of
intensities, but also the distribution of intensity variation
(Gonzalez and Woods, 2002).
For this kind of textural examination, firstly the so-called co
occurrence matrix has to be derived for the examined area. This
particular matrix holds e.g. information of pixel changes in
multiple directions (usually horizontally, vertically and
diagonally). The co-occurrence matrix’ extents are same in both
directions and equal to the number of grey levels that will be
considered. For example, for an 8 bit image (256 grey values)
the co-occurrence matrix' extents would be 256 by 256. Usually
a recoding is carried out to reduce the number of grey value
classes (also called bins). A recoding of the original image
down to 16 grey levels is for most of the cases satisfying (Gong
et al., 1992). Nevertheless, during this research (on texture
analysis), all images were recoded to 40 bins.
Figure 9: Image and corresponding co-occurrence matrices in
horizontal (left to right) and vertical (top to down)
directions.
At each position mc,r the co-occurrence matrix holds the
number of changes from class r (=row indices) to class c
(=column indices) (see Figure 9). This computation is carried
out for multiple directions, meaning that one co-occurrence
matrix is created for each direction. Figure 10 illustrates the
creation of such matrices; here, four grey values exist and the
co-occurrence matrices are derived for horizontal and vertical
directions.
The task now is to analyze a given co-occurrence matrix in
order to categorize the region for which it was computed.
Therefore descriptors are needed that characterize these
matrices. Some of the most commonly used descriptors are
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