International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
window in order to use them in roof facet segmentation and
reconstruction.
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Moving windows over irregular LIDAR points
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Figure 1: Moving windows for plane fitting over the irregular
LIDAR points.
2.2 Key factors in designing moving surfaces algorithm
The grid spacing and fitting window size are two critical factors
in this procedure. In case the data density is high, the grid
spacing is based on the desired detail level and accuracy of the
extracted roof facets. The reason is that grid spacing “cell size”
defines the minimum precision that could be reached in
breaklines between roof segments. However small cell size does
not always yield fine details, especially if the data density is
low. In addition to that, the smaller the cell size the higher the
cost of computation. So in general, the data density sets the
effective minimum limit for the cell size while the desired level
of detail and accuracy defines the maximum limit. In this work
and according to the available data with a density of
approximately one spot height per square meter, the grid
spacing "cell size" was one meter in both x and y directions.
This spacing seems to be effective even though it is somewhat
large. However, the main goal of this work is to test the
suitability of LIDAR data for roof details reconstruction rather
than their positional accuracy.
The other key factor is the moving window size used in plane
fitting. The main factor that influences the window size is the
data density since it controls the number of points inside each
window. The window should be large enough to contain enough
point observations to reliably estimate a unique set of plane
parameters through the reweighted least squares adjustment.
The number of points should exceed the minimum requirement
in order to have redundancy in the adjustment. The redundancy
helps to accommedate the inconsistency between data points
and strengthen the soundness of the estimated parameters. In
general the denser the data the smaller is window that can be
used since there will be enough data to estimate the plane
parameters.
During the plane fitting procedure, the estimated plane
parameters are recorded at the center of the moving window.
However, when gaps occur in data which consequently means
not enough points fall within that window, the fitting procedure
will not be applied and zeros for the parameters (slope in x,
slope in y, and height intercept) will be assigned to that window
center. In addition to that, a high RMSE will be assigned since
the parameters are not valid. This high value is utilized in the
best fitting search by giving an indication of bad fitting on that
cell. After completing the plane fitting procedure and recording
results, a best fitting algorithm is applied. In general, this
algorithm minimizes the fitting error in each cell by assigning it
to the plane which has the minimum RMSE among all planes
containing this point (Alharthy and Bethel, 2002). Results of
this procedure are used in the segmentation as discussed below.
3. SEGMENTATION OF PLANAR ROOF FACETS
BASED ON THE ESTIMATED GEOMETRIC
SURFACE PARAMETERS
In this research, the roof planar segments were extracted
utilizing the estimated geometrical plane parameters resulting
from the previous step. Starting from a small set of “seed” cells,
region growing by a cell (pixel) aggregation technique was used
to construct large roof facets. Steps of this procedure are
discussed below.
3.1 Region growing segmentation by cell aggregation
Region growing is an approach for image segmentation, in
which neighboring pixels are examined and added to a region if
they have common characteristics. Those characteristics or
parameters form the membership criteria (descriptors), based on
which the decision will be made to include or exclude the cell.
The region growing technique starts from defined seeds, which
are known to be the center of the class (roof segment) and
consists of a group of cells or “pixels” which are strongly
homogenous. Those cells carry almost the same parameter
values and the cost function between them is small. The key
factor in this algorithm is the design of the membership criteria
“cost function” and its computation. The way this technique is
used in this work is similar to typical clustering or classification
techniques, in which pixels are given the same label in a
parameter space based on some similarity measures. However
connectivity is required between pixels here unlike in general
clustering algorithms. In this work starting seeds were defined
based on the resulting RMSE from the plane fitting procedure.
Low RMSE means excellent fitting and consequently good
consistency among cells. The membership criteria and cost
function used in aggregation are discussed below. However
prior to that some preprocessing steps were performed on the
estimated parameters that form the parameter space to fit the
needs of the application.
3.1.1 Preprocessing steps to form the segmentation search
space
There were three basic independent parameters (slope in x,
slope in y, and height intercept) assigned at each cell inside
each processed building polygon. Based on roof shape and
direction complexity, one, two, or the three parameters could be
used to form the parameter space and define the membership
criteria for the region growing technique. As a preprocessing
step, parameter magnitude range consistency was imposed over
those parameters in order to make the parameter space uniform.
Based on the knowledge of building roof facets, typical slope in
both directions (x, y) does not exceed the value of one.
Accordingly, the slope values were set to be with a range of +1.
Values out of this range are discarded since they are not
realistic. The slope might have a high response during the
fitting procedure due to the fact that the processed window may
contain data points that lie in between two planar surfaces and
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