points measured. A successful segmentation into cloud objects
would require to take into consideration the spatial realtions
between the measured points. An existing method that attracted
attention was the modelling of potential 3D fields and the
display of iso-potential values, using implicit density functions.
Figure 4: Metaball of radius R (left), blending of metaballs in
2D (middle) and 3D (right)
These set of functions evaluate the value of the field using the
distance from specified ‘source points. A sphere around each
point defines the area of influence, out of which the density is 0
(Figure 4). This techique was first applied in modelling free
form surfaces, which are defined as the iso-potential surface of
a value V. The objects modelled in this manner are called
‘metaballs’, or ‘softballs’ or ‘blobs’ (Nishita, 1996). Their
Figure 5: Application of metaballs on GB measurements
with different metaball radii
application was extended into modelling clouds by (Dobashi,
2000), in combination with hardware accelerated rendering
with realistic results.
Our first effort in this direction was to construct the functions
that calculate the field density, based on the distance from the
‘source’ points. In our case the source points were the CBH
point measurements themselves and since the points were
organized on a regular grid, we used the resolution of this grid,
as the fall-out radius for the metaballs. The visualisation of the
isosurface at this stage has been implemented using polygons.
The extraction of the iso-surface into a polygonal model was
done using the well known ‘marching cubes’ algorithm. The
algorithm can be divided into three sub-routines. First the
object space 1s divided into cubes, at a resolution that we decide
and the user supplies the iso-value that desires to extract. Next
the algorithm for every cube evaluates the field on every cube
vertex and calculates the difference with the desired iso-value.
According to the sign of the difference on the cube-vertices,
the algorithm finds in a pre-calculated lookup table, in which
case falls the intersection of the iso-surface with the cube edges.
This speeds up the decision which cube-edges have to be
interpolated, in order to create the triangle that represents the
iso-surface.
The results depend on the resolution of the cube grid, and in our
case this plays a signifficant role in calculation and rendering
times. For example in GB measurements, depending on the
average bottom height the coverage varies from 1 to 4 Km in
each horizontal direction in a resolution of approximately 5m,
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
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depending again on the cloud average height. The coverage of
the scene from the point cloud is irrelevant, since this algorithm
covers the whole object space, disregarding holes in the object.
The time consuption is largely due to calculation of the
intersections and for a scene, with dimensions as described
above, 2-3 minutes are required to compute the triangular
surface.
We applied the forementioned 'metaballs' technique in order to
calculate the pixel values for a cloud scene. (Mayer, 2003),
(Nishita, 1996). Around each of the point measurements a
sphere of influence is placed, with the amount of influence
decreasing as the distance from the centre increases according
to a density function (Figure 4). This allows us to estimate a
density value on a regular grid, which comes from all
metaballs' that include the current grid vertex, weighted by
their influence. The result of applying this method on a set of
ground-based measurements is shown in Figure 5, where the
outer shell of the estimated cloud volume is shown in the form
of polygonal surface.
Due to the large computational times, for a whole scene taken
from EO measurements we started the implementation of
hierarchical grid structure, for increasing the storage and speed
performance. We noticed that this issue has been addressed in
the past by the computer graphics community and we chose a
software library used at the National Centre for Atmospheric
Research, at Boulder Colorado, for similar purposes as ours
(NCAR URL). It is based on the "shear-warp' algorithm for fast
volume rendering (Volpack URL) (Lacroute, 1994), and
facilitates a complete workflow from reading raw volumetric
data , storing colour, transparency and normal vector
information in compressed files, to rendering the volume data.
| Burtace Vistaleation + Pole:
Figure 6: The aLMo coverage
The compression schemes (r/e and octree) allow the storage of
the volume data values, together with the transfer functions
which determine the colour and opacity of the medium. The r/e
(Run Length Encoded) scheme is optimal for viewing the same
volume under different viewing transformations and shading
parameters, while the octree scheme performs better with
volumes with varying transfer function.
The pre-processed volumes have larger file size (up to four
times) in comparison with the raw binary data, and this happens
due to the material colour/transparency and normal vector
information that have to be stored within. Keeping all these
information together in one volume file, is though a more
important advantage since the processing time is significantly
reduced. The software is based on the Tcl scripting language
and can be combined with the existing C source easily. The
sequence of commands needed to be passed to the Tcl
interpreter are saved in script files, and can be called within any
C program. |
We continued by importing the alpine local model (aLMo)
(source: Meteo Swiss) into the volume rendering procedure.
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