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for grid samples of between 300 and 400 grains (Rice and
Church, 1996), and for areal samples of between 100 and
400 times the area of the largest grain (Graham et al.,
2010), indicating that these are the minimum sample
sizes required to have confidence.
particle shape remain somewhat obscure. In this case,
we recommend that between sites or through time
comparisons are based on examining similar size classes
in space or time, respectively.
15.3.3 Analysisofobliqueground images
15.3.2 Analysisof vertical images forparticle
shape
For oblique ground images, rectification is required in
order to allow quantitative measurements and compar-
isons. The rectification process requires a set of ground
control points and the procedure is generally more com-
plex than for aerial imagery, where the vertical acquisition
means the three orientation angles are close to zero. As a
result, the ground control network has to be more accu-
rate and include a larger number of points. It is advisable
to exceed the minimum required number (four) by at
least a factor of 2 or 3 (see for example Chandler et al.,
2002). A further difference with aerial imagery is the pixel
size that is quasi-unique in the vertical case, but can vary
on a large range in oblique imagery. The spatial resolu-
tion of the rectified image depends on the largest pixel
footprint (i.e. most distant from the camera). To limit
this problem it is better to reduce the analysed area to the
minimum required. Rectification procedures are detailed
in Chapter 8.
Applications with ground-based oblique images may
involve one single camera station (usually for temporal
analysis) or stereo pair acquisition. In the latter case,
photogrammetric techniques are possible that may lead
to the construction of a digital elevation model. Further
post-processing techniques may involve the automatic
recognition of objects including channel edges, bar or
bank characteristics or wood accumulation. The main
problems with this type of analysis are related to variations
Following Wentworth (1919) and Wadell (1932), well-
known roundness indices have been proposed that utilise
the radius of curvature of a clast's 'corners'. The ratio
between the mean radius of curvature of the corners
and the radius of the largest inscribed circle defines a
roundness measure (Wadell, 1932). Making the relevant
measurements for a large number of particles is time
consuming, so visual charts were proposed by Krumbein
(1941) for improving the efficiency of field measure-
ments. More recently, ground photos have been used
and different imagery procedures were tested to measure
the roundness based on Fourier transforms (Diepen-
broek et al., 1992), mathematical morphology (Drevin
and Vincent, 2002) or discrete geometry (Roussillon
et al., 2009) 3D laser scanning technologies have also been
applied to this problem (Hayakawa and Oguchi, 2005).
Roussillon et al. (2009) successfully calculated Wadell
indices from images. They also provided a simple indi-
cator of roundness which is fairly robust in comparison
with the Krumbein chart: the ratio of the perimeter of
the particle to the perimeter of the ellipse best fitting the
particle (Figure 15.5).
When considering image analysis for particle mor-
phometry,
sampling
strategy
is
critical
because
the
relations
between
river
position,
particle
size
and
1
2
3
4
5
Mean
±
1 standard deviation
1.2
1.18
1.16
1.14
1.12
1.1
1.08
1.06
1.04
n = 81
123456789
Classes of Krumben, 1941
6
7
8
9
Figure 15.5
Conversion chart of Krumbein (1941) classes from 1 (very angular) to 9 (very rounded) (with in black the ellipse fitted
and in grey the particle), and the average rP index (ratio of Particle/Ellipse perimeters) for each of the Krumbein classes.
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