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results (Frey et al., 2003). Since GSD is derived from the
ratios of volumes, if the dispersion around the mean value
of the shape coefficient ( α ) for each class of diameters
is small it is not necessary to know this value. On the
other hand, the sediment discharge cannot be computed
without assessing at least the mean shape coefficient. It
was thought initially that velocities of particles could be
highly dispersed across the light table. However, pre-
liminary tests showed that dispersion around the mean
velocity was low. Furthermore, velocity was not correlated
with diameter of particles. Using sediment with grainsizes
ranging from 2-12 mm, the velocity of one class of diam-
eters was found to deviate no more than 10% from
the mean velocity, which is then only required to com-
pute sediment discharge. Because calculating sediment
discharge requires both mean streamwise velocity and
at least a mean shape coefficient, estimates of sediment
discharge are less accurate than estimates of the GSD.
Numerous tests were carried out in order to compare
medium diameters and masses obtained by image analysis
with measured values (see Frey et al., 2003). Motionless
particles with known shape coefficients were tested in a
first series. Diameters and mass predictions were good,
with uncertainties on the order of 3% and 6% respec-
tively. In a second series, the light table was attached
to the outlet of an experimental flume. The flume was
15 cm wide and had the same width as the transparent
ramp. A sample of 400 particles were mixed into the
flow slightly upstream of the outlet in order to simu-
late real experimental conditions. Results were improved
when volume calculations considered differentiated shape
coefficients, although results were remarkably good even
when a uniform shape coefficient was used. Considering
the diameters commonly used to describe grainsize: d 30 ,
d 50 ,andd 90 , where d xx is the diameter for which xx%
by weight of the sample is finer, the errors were 4%, 3%
and 1% respectively. The minimum number of particles
needed to achieve a significant statistical measurement - a
proxy for the length of time over which measurements
should be collected - for both GSD and sediment dis-
charge was approximately 4,000 particles. With more
than 2,500 particles the computed value was within 3% of
the actual value and with more than 1,500 it was approx-
imately 7%. A much lower number of particles (
(a)
(b)
(c)
Figure 13.2 Sequence of image processing steps for segmenting
particles (a) original image (b) result after segmentation (c)
result after object separation.
by assessing the third dimension perpendicular to the
image plane. In the study presented here, a user-friendly
image processing software called WIMA, developed by
the Laboratoire Hubert Curien (formerly TSI) of the
University of St. Etienne, was used (Ducottet, 1994). Any
image processing software with standard functions and
which permits users to modify and add new functions
can be used. The main goal of the image processing algo-
rithms is to segment the particles in order to gain access
to their dimensions. The three main image-processing
steps required to achieve this goal are segmentation (i.e.,
detection), object separation, and object measurement
(Figure 13.2). Edge detection techniques based on the use
of Canny gradient operators and localisation of maximum
gradient modulus were used (Jernot et al., 1982; Canny,
1986). Once these steps are achieved, the final step in the
image analysis consists of extracting the boundaries of all
detected particles in the image series. It is then possible
to calculate areas as well as minimum and maximum
principal diameters.
Assessing the volume of each particle is rather difficult
for particles with variable shapes, and several assump-
tions have to be made in order to do this. First, it
must be assumed that the particles flow in their stable
state. Considering that particles are described by their
three principal dimensions, it is possible to measure
the medium ( d ) and maximum ( D ) dimensions (corre-
sponding to the minimum and maximum diameters in
the image respectively) as well as area ( A ) in the image
plane. An ellipsoid shape is assumed for the particles, and
thus grain thickness, which is perpendicular to the image
plane, is a fraction of the medium diameter and is calcu-
lated using a shape coefficient (
α
). The shape coefficient
1000)
were required for low discharges in which coarser par-
ticles were dominant and the GSD was more uniform.
Empirical testing is recommended in order to determine
the optimal number of particles needed to achieve a
good statistical fit. This method has been used success-
fully to investigate mechanisms responsible for bedload
(
) must be calibrated for the sediment being used. The
volume of each particle then goes as:
α
6 a · d 2 D =
2
3 a · d · A
V =
(13.3)
Preliminary tests showed that calculating the volume
using area rather than diameters yielded more accurate
 
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