of an isotropic object represents the timely averaged two
dimensional location (Z) 4,, thus:
Te = (y At ) (5)
where Z. is calculated from the sum of all n segmented pixels
of a streak:
25 vig(zi yi) 2, yig(i yi)
Omm $1
em ET a à n : (6)
2 g(vi yi) 2, 9(vi y)
id
i=1
|
Now the knowledge of the location of the same particle in
the previous frame (at the time t — 1) enables the first-order
approximation the velocity field ü(t):
ü(t) = Rn e (7)
Repeating the described algorithm will automatically track
all encountered seeding particles from one frame to the next.
The segmentation and tracking algorithms have been imple-
mented on an 1860 board to achieve maximum performance.
Typical evaluation time of one image including digitization,
segmentation and tracking is 10s. Long image sequences
(200-1000) images can therefore be processed. Individual
particles can be tracked up to a concentration of 1000 parti-
cles/image.
4 0 EEE ern UD TT TR ET TT TTT
2.0
re
pic u
0.0
EUN ri P 2
noua. gout a a LI
0.0 2.0 4.0 6.0 8.0 10.0
velocity [cm/s]
TE!
LLL.
2.0 13.0 24.0
Figure 7: Trajectories of tracer particles measured by the PTV-
algorithm. Only a small fraction (less than 1 %) of all trajectories
plotted. The velocities are encoded as intensity.
3 COLOR IMAGING SLOPE GAUGE
Measurements of the spatial variations of the water surface
slope at Heidelbergs wind/wave facility performed using a
Color Imaging Slope Gauge (CISG).
234
towards camera
Water surface
Fresnel lens
i Color Illumination
Figure 8: Rays refracted under the same angle (same surface
slope) are focused on one point of the screen, independent of the
position on the surface and the water height. The slope of the
waves is imaged.
Figure 8 shows the schematic setup of the imaging slope
gauge which was first proposed by [Jähne et al., 94] using
a black and white CCD camera. A CCD camera is observ-
ing the water surface from far above. Therefore all the rays
that enter the camera are nearly vertical i. e. perpendicular
to a flat water surface. A single light emitting point on the
screen at the bottom of the system is in the rear focal plane
of a Fresnel lens. Therefore all rays emitted are parallel in
the water. This spot can be seen on an image pixel, if the
refraction for the corresponding point at the surface leads to
a vertical beam in the air. So each pixel of the CCD sees
a certain point of the screen, depending on the slope of the
corresponding imaged surface element. With an intensity or
color pattern on the screen, the slope of the imaged water
surface is encoded in gray value or color information respec-
tively.
The relation between surface slope s = tan(a) at a certain
point and the color imaged in the related pixel is independent
of:
e the location at the surface and
e the height of the surface
Rays crossing different locations on the surface ( or at
different heights) with the same slope have the same angle
of refraction and are therefore focused on the same screen
point, imaging the same color (see fig. 8). Analyzing the
color information in the digitized image, for each pixel the
slope of the corresponding location on the water surface can
be computed. One of to major advantages using this color
technique instead of the black and white one previously used
is that both slope components (streamwise and spanwise)
are measured simultaneously.
3.1 Energy of Capillary Waves
Of especial importance for the process of air/sea interaction
is the determination of the mean energy of a wave. According
to [Phillips, 80] the energy E. of a capillary wave with slope
8 is given by:
ag -
E. — a le I, (8)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
S Transferfunktion
Transferfunktion
Figure 9: Im:
Hilbert filter (:
2H and 3H (s
sigma denoti
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images using
A Hilbert filte
does not char
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the 7/2 phas
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shows already
construction -
tions with odi
(see [Jáhne, €
igi ur
t
= N=
No |
The transfer 1
in Fig. 9. Si
ters are only
in a limited
all images w
mid [Burt ur
the Hilbert t
multi-grid ap
40 pixels can
energy extrac
