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Application of image-based granulometry to siliceous
and calcareous estuarine and marine sediments
Stanislav Franc ˇ is ˇkovic ´ -Bilinskia,*, Halka Bilinskia, Neda Vdovic ´ b,Yoganand Balagurunathanc, Edward R. Doughertyc
aDepartment of Physical Chemistry, Institute ‘RuC er Bos kovic ’, P.O. Box 180, 10002 Zagreb, CroatiabCenter for Marine and Environmental Research, Institute ‘RuC er Bos kovic ’, P.O. Box 180, 10002 Zagreb, Croatia
cDepartment of Electrical Engineering, Texas A&M University, College Station, TX 77843, USA
Received 8 October 2002; accepted 3 March 2003
Abstract
Grain-size analysis has long been used as a descriptor of transport and depositional processes. This paper presents the possibility
of using image-based granulometries, not yet widely used in the earth sciences, to characterize granulometric composition of
unconsolidated estuarine and marine sediments. To test the method, conventional sediment analysis of siliceous and calcareous
sediments are compared to image-based analysis of sediments obtained along the O ¨ re estuary (Northern Sweden) and the Adriatic
Sea (Croatia and Italy). These grains have different textural characteristics, composition, roundness and specific surface area.
Granulometric parameters are calculated using both a graphical method and the mathematical method of moments. Grains have
been imaged using a microscope and mathematical granulometries have been applied to the digital data. Image-based granulometric
moment descriptors are compared with sieve+Coulter counter-derived moments. Although it is not claimed that digital-imaging
should be the only method used in sedimentology, the results show the potential of applying digital electronic imaging to
granulometric analysis of sediments. In this way, sampling for granulometric analysis and sieving processes combined with Coulter
counter analysis of fraction <32lm could be eliminated and a large area of sediment surface could be covered in a short time.
2003 Elsevier Ltd. All rights reserved.
Keywords: siliceous sediments; calcareous sediments; grain size characteristics; digital image processing; granulometries
1. Introduction
Pioneered by Plumley (1948), sediment grain size has
often been used to determine sediment transport patterns.
McLaren and Bowles (1985) refined the previous work
and presented a model that demonstrates the relationship
between the grain-size distribution of sedimentary depos-
its and the direction of transport. Gao and Collins (1991,
1992) proposed a modification based upon the general
principles of spatial changes in grain-size parameters
resulting from sediment transport. Since the method
compared small numbers of samples (two stations), Le
Roux (1994a) showed the limitation of the method in
identifying the true transport direction. Le Roux (1994b)
later proposed an alternative approach that significantly
increased the accuracy of the trend vectors defined by
grain-size parameters. The sediment-size distribution also
reflectsthe nature of the source rocks and the resistance of
particles to weathering and erosion (De Lange, Healy, &
Darlan, 1997). According to Guyot, Jonanneau, and
Wasson (1999), granulometric characterization of river-
bed and suspended sediments allows the main geo-
morphological valley types to be distinguished. There
are various reviews of conventional techniques used in
modern geological particle size analysis (Barbanti &
Bothner, 1993; Beuselinck, Govers, Poesen, Degraer, &
Froyen, 1998; Molinaroli, De Falco, Rabitti, & Portaro,
2000; Syvitski, Le Blanc, & Asprey, 1991).
Most conventional experimental procedures are time
consuming and introduce operational bias to textural
distributions. Laser diffraction methods used in the US* Corresponding author.
E-mail address: francis@rudjer.irb.hr (S. Franc ˇ is ˇkovic ´ -Bilinski).
Estuarine, Coastal and Shelf Science 58 (2003) 227–239
0272-7714/03/$ - see front matter 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0272-7714(03)00074-X
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Geological Service can determine a full range of particle
sizes from very fine clay to small pebbles; however, time
is required for sediment pre-treatment prior to laser
analysis. A rapid electronic method, without pre-treat-
ment of sediments would be advantageous. Develop-
ment in this regard has been slow due to the complex
nature of natural sediment shapes and complicated bythe difficulty in comparing the results to mass-based
sieving. Moreover, marine sediments also contain
broken shell debris, branched lithothamnids and bryo-
zoa. Initial work akin to a sieving size distribution has
been reported by Francus (1998), who used basic image
processing methods to segment soft clastic sediments
images into different grain size class intervals. He pre-
sented grain size with respect to a circular shape, just
short of the actual computation of a size distribution.
Heilbronner (2000) introduced a new segmentation
method, called ‘lazy grain boundary’, for analyzing
polarization micrographs of quartzite images. Imaged
grain sizes were segmented and a grain-size distribution
computed for three- (3D) and two-dimensional (2D)
profiles (gray scale and binary images). These imaging
techniques do not obtain the size distribution of the
whole sample as conventionally required by geologists.
Mathematical granulometries, originally proposed by
Matheron (1975) to characterize sieving processes in
random sets, are used for grain and texture classification
because they provide a comprehensive statistical anal-
ysis of grain sizes (Chen & Dougherty, 1994; Chen,
Dougherty, Totterman, & Hornak, 1993; Dougherty,
1992; Dougherty, Newell, & Pelz, 1992). Granulometries
yield a size distribution, called the pattern spectrum,with respect to a reference shape called the structuring
element. The shape-based size distributions are similar
to geological sizing derived by physical sieving, but they
possess advantages, including speed of calculation,
precise sizing for very small probe size (sieve size) incre-
ments and the ability to use a variety of probe (sieve)
shapes. The basic difference is that conventional sizing is
based on mass ratios, whereas morphological-granulo-
metric sizing is based on shape area (binary image) or
volume (gray scale image). These are highly correlated
random variables. Owing to a wide range of grain sizes,
granulometric computation needs to be adapted to
imitate the sediment sieving processes. Balagurunathan,
Dougherty, Franc ˇ is ˇkovic ´ -Bilinski, Bilinski, and Vdovic ´
(2001) have done this and have applied the adaptation
to simulated sediments to show the applicability. The
distributional type and parameters of the simulated
grain model were chosen to describe siliceous sediments
characterized by Franc ˇ is ˇkovic ´ -Bilinski, Bilinski, Tibljas ˇ,
and Hanzel (2003). Imaging results were later compared
to real sediment sieving. The present study investigates
the possibility of applying granulometric digital image
processing to real (not simulated) images of sediment
grains, as an alternative to conventional sieving
methods. Experimental data from two shelf areas in
Europe with siliceous and calcareous sediments of dif-
ferent textural characteristics, composition and specific
surface area (SSA) are used to test the new method.
2. Study areas
Siliceous sediments were studied in the O ¨ re estuary in
North Sweden. Fig. 1 shows the location of the estuary
along with the sample stations. These types of sediments
are characteristic for many other estuaries of boreal
region and are mostly sandy silts or silts. The chosen
estuary is a semi-closed water-body, partly isolated from
the outer sea by a dense archipelago. The salinity varies
between 1 and 7, which depends on the discharge in the
O ¨ re river. The mean annual salinity is 5:0 1:2 and
the mean annual pH is 7:7 0:2. The total area of the
estuary is 50 km2, with water volume of about 109 m3
and a mean depth of 15 m. The maximum depth reaches35 m. The O ¨ re rivers catchment has an area of 2940 km2,
Fig. 1. Map shows the locations of four siliceous sediment stations
along the O ¨ re estuary. The sample stations locations and water depths
are: 1 (63309893N, 19449189E, 2 m), 2 (63309624N, 19449257E,
6m), 3 (63309672N, 19459931E, 19m), 4 (63309218N, 19469168E,
21m).
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with Precambrian granites and gneisses being the main
mineral (rock) type. Approximately 65% of the super-
ficial Quaternary deposits in the drainage basin consist
of glacial till. A permanent snow cover occurs from
November to March. Rapid snow melt in April and May
causes a pronounced high flow in a single event. The
summer season brings both low and high flow, a singleevent being caused by a rainstorm. More details about the
region can be found in the studies by Forsgren and
Jansson (1992, 1993), Forsgren, Jansson, and Nilsson
(1996), Franc ˇ is ˇkovic ´ -Bilinski et al. (2003) and Kwokal,
Franc ˇ is ˇkovic ´ -Bilinski, Bilinski, and Branica (2002).
Carbonate sediments, mostly sands or silts, were
studied by taking samples at seven different locations
along the northern and middle Adriatic Sea (Croatia
and Italy). The relative contribution to the sediments of
ancient carbonate rocks and modern marine organisms
was not determined. Fig. 2 shows the region of study
with sample station locations. The Adriatic Sea is an
inland sea, and is part of the Mediterranean Sea. It is
about 783 km long, with an average width of 248 km
covering an area of 138,597 km2 with average depth of
173 m. The mean annual salinity is 38.3. Samples 3k, 4k
and 5k were taken from the North Adriatic, which is
typically a shelf area. Sample 2k was taken from the
North Adriatic island area, which is typically an under-
water karst. Samples 1k, 6k and 7k were taken from the
central region of the Adriatic island area. All the
samples from this region have significant amounts of
Mesozoic carbonates with some igneous rocks. More
details about the region are in the studies by Brambati,
Bregant, Lenardon, and Stolfa (1973), Giorgetti andMosetti (1969), Sondi, Jurac ˇ ic ´ , and Pravdic ´ (1995),
Vdovic ´ , Bis ˇc ´ an, and Jurac ˇ ic ´ (1991) and Vdovic ´ and
Jurac ˇ ic ´ (1993).
3. Methods
3.1. Sampling and sample preparation
Samples from the O ¨ re estuary were taken at four
stations with geographic coordinates given by GPS (Fig.
1), using a boat and a GEMENI (OY KART AB,
Finland) coring device, which is 790 mm long and 80 mm
in diameter. At each station, two depth-increment
samples were collected. Surface layer samples (0–5 cm)
are indicated by the suffix ‘a’, while the deeper layer
samples (30–35cm) are given a suffix ‘b’. The physical
terrain prevented a deep sediment sample from being
collected at sample station 2. Adriatic Sea samples were
taken at seven different locations (Fig. 2). Samples 1k, 2k,
3k, 6k and 7k were obtained by scuba diving, while
samples 4k and 5k were obtained using a modified
Haamer vibrocorer (details are given by Vdovic ´ et al.,
1991).
3.2. Laboratory analysis
Sediment samples were granulometrically analyzed
by wet sieving, using ASTM standard sieves for grain
sizes >32 lm and a Coulter Counter (Model TA II,
Coulter Electronics Ltd, England) for the grain sizes
<32lm. Wet sieving was used as it has been shown to bebetter for aggregates of clay minerals. Besides, Coulter
counter analysis uses suspension, obtained by wet
sieving. The sediments were classified according to their
sand–silt–clay ratio as described by Shepard (1954).
Statistical descriptors were computed using both the
graphical method (Folk & Ward, 1957) and the method
of moments (Boggs, 1987). To evaluate the grain shape
of natural sediments, digital imaging method using
mathematical granulometry was used. The fractions
were photographed using a digital microscope (Zeiss
Axiovert 35 with a Sony digital camera). Different
magnifications were chosen for each grain fraction due
to the large size range. The fractions were categorized
into sand (>63lm), coarse silt (32–63 lm) and medium
to fine silt+clay fraction (<32lm). Lens magnifications
for the respective fractions were set at 2.5 (resolution
3.67lm), 10 (resolution 0.92 lm) and 40 (resolution
0.37lm), respectively. The siliceous sand fraction was
imaged using 5 lens (resolution 2.3 lm). Figs. 3 and 4
show images of all three fractions of real siliceous and
calcareous sediments.
The SSA (m2 g1) was determined using a Flow Sorb
II 2300 (Micrometrics, USA), ‘single point procedure’
and a mixture of gases (30% N and 70% He).
Adsorption of nitrogen was measured at 77 K, withaccuracy of 5%. Obtained values were: 3.99 (1a), 0.96
(1b), 4.76 (2), 9.65 (3a), 11.50 (3b), 13.30 (4a), 12.58
(4b) for siliceous samples and 1.6 (1k), 2.8 (2k), 7.4 (3k),
2.5 (4k), 4.5 (5k), 3.9 (6k), 59.2 (7k) for calcareous
samples.
3.3. Description of image-based granulometries
The word shape is typically used in a generic manner,
referring to various geometric aspects of an object—
circularity, elongation, convexity, etc. Various measures
may be associated with an object to quantify the degree
to which the object fits one of the generic aspects, such
as the measure of circularity. In image processing, the
morphological approach to shape involves quantifying
the manner in which a structuring element (probe) fits
inside the object. The most commonly employed
morphological shape descriptors are based on granulo-
metries. These have been developed to model sieving
processes (Matheron, 1975). The essential idea is to
operate on an image in such a way that fine structure is
progressively eliminated. The area of the remaining
image is continuously diminished, and this decreasing
area is considered as a size class interval.
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To define a binary granulometry, consider a fixed
convex set B. For any positive real number r and t, the
opening of a set S by the structuring element tB is
denoted by ctB (S ) and defined as the union of all
translates of the structuring element that are subsets of
S . As t increases, ctB (S ) diminishes, which means that
for t> r, ctB (S ) crB (S ). The s-parameterized mapping
ctB is called a granulometry and B is called its generator.
For each set S , a size distribution is defined by letting
X(t) be the area of ctB (S ). X(0) is the area of S . The
pattern spectrum U of S is defined by normalizing the
size distribution, so that it ranges from 0 to 1, namely
UðtÞ ¼ 1 XðtÞ
Xð0Þ ð1Þ
The pattern spectrum is a probability distribution
function, for which derivative of U is often used. The
moments of U, called granulometric moments, are
powerful shape and texture descriptors (Batman &
Dougherty, 1997; Dougherty et al., 1992; Dougherty &
Pelz, 1991; Sand & Dougherty, 1998; Theera-Umpon
& Gader, 2000). An alternative to use an ordinary
granulometry, which diminishes each grain progressively
Fig. 2. Map shows the locations of seven calcareous sediment stations along the Adriatic Sea.
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until its elimination, is to apply a reconstructive
granulometry, which is defined by passing in full any
grain not completely eliminated. A reconstructive
granulometry represents a true sieve: for each grain
a value t0 exists such that the grain is unchanged for
t t0
and is eliminated for t > t0
. The cut-off value t0is the granulometric size of the grain. A grain is passed
by a reconstructive granulometry if and only if its
granulometric size exceeds the parametric multiple of
the generator. The pattern spectrum is defined in the
same manner as for an ordinary granulometry. Re-
constructive granulometries are used for both pattern
classification and image filtering (Dougherty & Chen,
1999). Details and applications are discussed by
Dougherty and Astola (1999). Fig. 5 shows binarized
sand-sized grains, subdivided into three classes and
Fig. 6 illustrates the granulometric (conventional)
opening and reconstructive opening operations using
a flat structuring element in each of the parts,
respectively. It can be seen that the grains are sieved
(removed) as the size of the structuring element
increases. In a reconstructive opening the shape is
maintained till they are sieved. Fig. 7 shows the digital
granulometric size distribution using flat structuring
elements for the grains in Fig. 5a–c; Table 1 shows the
grain-size moments of these fractional images using
a flat structuring probe. The first granulometric
moment shows the mean grain size in the image, while
higher order moments show the deviation and spread
in the grain sizes for the given grain (image) sample. It
is interesting to note that the analogous size descriptive
ability of granulometric moments depends both on the
size and shape of the structuring element used.
This paper applies granulometries generated by a
single structuring element, although granulometries can
be generated in more complicated ways. Experience
Fig. 3. Various fractions of real siliceous sediment grains, taken by a light microscope with 40, 10, 5 lens. The fractions are: (a) clay (1–5 lm
for all three figures); (b) total silt (5–63 lm for the first two figures), coarse silt (32–63 lm for the third figure); (c) sand fractions (63–125, 125–250,
250–500 lm).
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has shown that linear structuring elements are
generally successful for shape and texture classifica-
tion, and there are fast algorithms for implementing
granulometries generated by linear structuring ele-
ments. Since the purpose of this paper is to emulate
sedimentary procedure, it is restricted to use of the
flat structuring element, which resembles the conven-
tional sieve mesh.
3.4. Application of image-based granulometries
to natural sediment
Whether using the graphical approximation or the
direct statistical calculation, the particle-size frequencies
need to be physically calculated. Using electronic im-
aging technology, the entire process can be automated.
If a grain sample is reasonably well spread and elec-
tronically imaged, granulometric analysis using mathe-
maticalmorphologycanbeusedtoelectronicallycompute
the granulometric size distribution and the correspond-
ing moments. Individual grain separation may not be
possible at all instances. Some may overlap. These were
digitally separated in these experiments. Numerous
automatic morphological segmentation methods exist
(Meyer & Beucher, 1990; Vincent & Dougherty,
1994). An opening filter with a small digital disk-like
structuring element was used to reduce the overall
grain size by a few pixels, and then to separate them
from their neighbors to obtain an accurate size distribu-
tion. Though segmentation methods introduce some
discrepancy, segmentation to approximate ideal non-
overlapping grains yields acceptable granulometric
moments (Balagurunathan et al., 2001). Digital grain
Fig. 4. Various fractions of real calcareous sediment grains taken by a light microscope with 40, 10, 2.5 lens. The fractions are: (a) medium to
fine silt+clay (<32lm for all three figures); (b) coarse silt (32–63 lm for all three figures); (c) sand fractions (63–125, 125–250, 250–500 lm).
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sizing gives a rapid and very precise measurement of
each grain. Image-based granulometric moments
have been used for about a decade to distinguish
image textures and to characterize granular processes
(Chen & Dougherty, 1994; Chen et al., 1993; Dougherty,
1992).
The granulometric analysis of the sediments was
tested on previously separated three fractions—medium
to fine silt+clay (<32lm), coarse silt (32–63 lm) and
sand (>63lm). A small sample from each fraction was
randomly picked and imaged. Digital granulometry was
then applied on these sample fractions, and adapted
granulometric sizing distribution was used to obtain the
image-based grain sizing and later moments were
computed. Due to equipment limitation, it was not easy
to separate grain sizes less than 32lm for imaging
medium to fine silt+clay fractions. A size-basedgranulometric digital filter was therefore used to remove
grain sizes to obtain this fraction. Size-based digital
filters could remove grains of sizes above a certain
range, which allows correct size distribution computa-
tion. This filtering in removing grain sizes ð f < 32 lmÞcontributes in the deviation of higher order moments.
Wide size range of the grains makes it practically
impossible to use a single magnification for imaging. In
these experiments grains were divided into three major
fractions (sand, silt, clay) and these were imaged using
2.5 (5 for siliceous type), 10 and 40 lenses,
respectively for each size range. Since magnification
would make the image lattice grow by the same
proportion, digital adjustments were made to the
granulometric sizing equations to compensate.
Granulometric size distributions for disjointed shapes
do not depend on grain positions. To obtain the
granulometric size distribution analogous to real sedi-
ments for the entire sample, the area coverage of each
fraction is linked to the mass ratio of the real fractions.
In general, two adjustments have to be made to the size
distribution. The first is area compensation due to the
lens magnification. The second is that the imaged samplehas to be normalized to the original fractional propor-
tion. This means that the formula for the size dis-
tribution X(t) must be adapted by multiplying by a
factor (ak) in each fractional class. In addition, only
a sample of each full class is available. If the grains for
the fractional class compose the fraction pk of the total
Fig. 6. Digital granulometric sieving of original image from Fig. 5a, by square shaped structuring elements of size 5 5, 21 21, 29 29, 37 37,
4545, respectively from left to right. Row (a) shows opening granulometric sieving and row (b) shows reconstructive opening. The grain sizes were
randomly picked from 63 to 125lm, imaged using 5 microscopic lens (resolution of 2.3 lm). Analogous digital sieve sizes for the above example are
11.5, 48.3, 66.7, 85.1, 103.5 lm, respectively. The original image is shown Fig. 5a.
Fig. 5. Sand-sized sediment grains imaged using 5 lens and binarized. Random grains were selected for imaging, grain sizes are: (a) 63–125, (b) 125–
250 and (c) 250–500 lm.
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area of all grains (not just those provided for gran-
ulometric analysis), then for it to be relative to the total
sediment population, the size distribution must be nor-
malized by a factor of pk for the kth class. The size dis-
tribution, or pattern spectrum, as it is commonly called,
takes the form:
UðtÞ ¼ 1
Pn
k¼1 pka1k M 2
k XkðM ktÞP
nk¼1 pka1k M 2k Xkð0Þ ð2Þ
Mathematical formulation (2) was originally presented
by Balagurunathan et al. (2001). The process of
image-based sizing is schematically illustrated in Fig.
8. The binary version of the formulation used to
adapt granulometries to replace standard sieving
methods on real grains has been provided. Granulo-
metric sizing moments were obtained statistically from
the grain sizing distribution U. In this analysis, lower
order moments show closer resemblance than do
higher order ones. This is attributed to the small
sample size and other imaging limitations (size re-striction, binarization).
4. Results
4.1. Conventional sieving of sediments
and surface area determination
The results of conventional grain-size measurements
are presented as cumulative grain-size curves (cum. mass
% vs. grain size in U units), which are plotted in Figs. 9
and 10 for siliceous and calcareous sediments, respec-tively, following the conversion table (mm to U units) of
Mu ¨ ller (1967). Graphic moment parameters were
computed according to formulations by Folk and Ward
(1957). The advantage of the log based graphical
method is that shapes of cumulative curves can be
compared visually. Although, graphic moments ob-
tained convey much geological information, they are not
statistically accurate for certain skewed size distribu-
tions, as recognized already by Folk and Ward. To
obtain the true sizing moments in contrast with grap-
hical methods, the statistical moments were computed as
by Boggs (1987). Graphic and statistical moments forthe siliceous estuarine sediments are presented in Table
Table 1
Granulometric moments computed using flat structuring element for three different sizes of sand grain samples, shown in Fig. 5a–c
Reconstructive granulometry Opening granulometry
Moments Image (a) Image (b) Image (c) Image (a) Image (b) Image (c)
Mean 0.1151 0.2350 0.3661 0.0974 0.1876 0.3080
Standard deviation 0.0308 0.0469 0.0500 0.0378 0.0714 0.0960
Skewness 0.3788 0.7125 2.0405 0.0574 0.7033 1.0811
Kurtosis 4.2215 2.5820 12.2575 3.3803 2.8261 3.7027
The grain sizes in the sample (a)–(c) were in the ranges of 0.063–0.125, 0.125–0.25 and 0.25–0.5 mm, respectively.
Fig. 7. Granulometric sizing distribution using flat structuring element, analogous to the sieve shape. The plots (a)–(c) correspond to grain fractions
in Fig. 5a–c.
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2(a) and (b), whereas Table 3(a) and (b) shows the
measures for calcareous sediments. Figs. 9 and 10 show
the profile of siliceous and calcareous samples. From
SSA presented in Section 3 the empirical equations have
been obtained, which relate SSA and Mz for siliceous
and calcareous sediments, respectively
log½SSA ðcm2=gÞ ¼ 6:06 1:1 log Mz ðlmÞ ð3Þ
log½SSA ðcm2=gÞ ¼ 6:48 0:87 log Mz ðlmÞ ð4Þ
The textural characteristics can be described from the
graphic moment features. Sediments from the O ¨ re estuary
are composed of fine sand, silt and clay. The mean grain
size (Mz) was coarsest for the sample in station 1 and
finest for the sample in station 4. The sorting (So) is poor,
being the worst for the samples in station 1. The skewness
(Sk) shows the distributional tendency of the grain sizes.
An extremely positive skewness was obtained for the
samples in station 1. A positive skewness was observed
for the sample in station 2 and a nearly symmetrical
distribution for samples in stations 3 and 4. The kurtosis
(Kg) measures relative sorting of the center andtails of the
grain-size distribution. A mesokurtic type distribution
was observed for all the samples except for sample 1b,
which is leptokurtic.
Sediments from the Adriatic Sea show different
textural characteristics. The coarsest sand was observed
for samples 1k, 6k and 2k, collected in the northern to
central regions of the Adriatic island area. The results
agree with the reported study for the Croatian coast
(Vdovic ´ & Jurac ˇ ic ´ , 1993). Sample 7k was sandy silt with
a high silt content. Samples 3k, 4k and 5k, obtained
from the northern Adriatic, contained fine sand and silt.
The Mz was coarsest for station 1k and finest for station
7k. Sample 3k was very poorly sorted. Distributions
were very positively skewed for samples 1k, 2k, 4k and5k, positively skewed for samples 3k and 6k, and nearly
symmetrical for sample 7k. The kurtosis for samples 3k
and 7k was mesokurtic, leptokurtic for samples 5k and
6k, and very leptokurtic for samples 1k, 2k and 4k.
4.2. Image-based sieving of sediments
Granulometric sizing was obtained using the adapted
pattern spectrum density relation of Eq. (2) and the
moments have been derived. Table 4 shows the
numerical values of granulometric sizing moments com-
pared to conventional sieving moments for calcareous
sediments. Table 5 shows similar results for two selected
siliceous sediments: 1a, with highest percent of sand and
3a, with highest percent of clay. Both opening and
reconstructive granulometries were used in this study.
The results show a quantitative comparison of the lower
order moments. The deviations are due to the in-
homogeneity of the sample obtained due to geological
terrain and various other factors (image binarization,
filtering, sampling size) mentioned earlier. All compar-
isons are made in a direct millimeter scale. It is evident
that mass information cannot be fully captured by
binarized digital images. Due to varied size range of
Fig. 8. Illustration of image-based granulometric sediment sieving. Each of the fractions were imaged using different lens magnification, in this case
2.5 (or 5 in some cases), 10, 40 were used for sand, silt, clay fractions, respectively.
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Fig. 9. Cumulative grain-size distribution of siliceous sediments from O ¨ re estuary consolidated into an ‘envelope curve’, obtained using conventional
wet-sieving and Coulter counter analysis.
Fig. 10. Cumulative grain-size distribution of calcareous sediments from the Adriatic Sea consolidated into an ‘envelope curve’, obtained using
conventional wet-sieving and Coulter counter analysis.
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grains considered in the present study (0.01–1 mm), no
present technology could image such a wide range with
consistent shade (light intensity) and acceptable digital
size. As the grain sizes occupied on a digital lattice
decreases, imaging algorithms (granulometric measures)
becomes variant (Dougherty, 1992). Binarization was
considered as a viable and conservative estimate to form
the grain-size distribution to gray scale imaged grains.
In most studies, binary size distributions are close
estimates to its gray scale counterparts and good com-parison was expected in this study. The grain fractional
ratio information is considered in the formulation using
the factor ( pk).
5. Discussion
Statistical support of the compatibility between image-
based sieving and conventional sieving is supplied by
considering the closeness between granulometric and
conventional sieving moments for all seven calcareous
samples. Two sets of sub-samples were taken for each
fraction and granulometric results were averaged for each
sample. Results for carbonate samples were taken to
compare the consistency between the image-based sievingto conventional sieving. The first moment (Mz) shows
a fairly high degree of correlation between the two
methods conventional to reconstructive and conventional
Table 2
Conventional moments of sediments from the O ¨ re estuary
(a) Graphic method with experimentally determined percentage of sand, clay and silt
Sample Mz (U) Mz (lm) Md (U) Md (lm) So Sk Kg Sand (%) Silt (%) Clay (%) Type of material
1a 4.88 34.0 4.30 50.8 2.07 0.40 0.94 42.46 47.83 9.70 Sandy silt
1b 4.83 35.2 4.50 44.2 1.47 0.40 1.27 33.28 60.90 5.82 Sandy silt
2 5.65 19.9 5.55 21.3 1.52 0.17 1.11 10.20 81.58 8.22 Silt
3a 7.10 7.3 7.00 7.8 1.58 0.01 1.07 3.28 72.13 24.59 Silt
3b 6.80 9.0 6.70 9.6 1.33 0.11 0.96 1.51 80.79 17.97 Silt
4a 7.10 7.3 7.10 7.3 1.20 0.01 1.01 0.99 78.72 20.30 Silt
4b 7.25 6.6 7.20 6.8 1.18 0.04 1.07 0.66 75.90 23.44 Silt
(b) Statistical method of moments
Sample Mean
Standard
deviation Skewness Kurtosis
1a 4.79 2.08 0.61 2.77
1b 4.77 1.58 1.17 4.17
2 5.67 1.56 0.52 3.23
3a 6.98 1.62 0.40 3.22
3b 6.75 1.36 0.08 3.09
4a 7.03 1.24 0.35 3.90
4b 7.15 1.25 0.23 3.67
Table 3
Conventional moments of sediments from the Adriatic Sea
(a) Graphic method with experimentally determined percentage of sand, clay and silt
Sample Mz (U) Mz (lm) Md (U) Md (lm) So Sk Kg Sand (%) Silt (%) Clay (%) Type of material
1k 1.27 415 1.20 435 1.64 0.32 2.27 90.5 8.7 0.8 Sand
2k 1.97 255 1.80 287 1.96 0.31 1.62 86.5 12.8 0.7 Sand
3k 4.10 58 3.60 83 2.41 0.26 1.10 63.8 34.1 2.1 Silty sand
4k 3.40 95 2.80 144 1.80 0.49 1.80 78.9 20.0 1.1 Sand5k 4.40 47 3.80 71 2.08 0.39 1.32 55.3 41.9 2.8 Sand–silt
6k 1.67 314 1.60 330 1.90 0.24 1.13 89.0 10.4 0.6 Sand
7k 5.13 29 5.20 27 1.90 0.09 1.04 26.8 71.7 1.5 Sandy silt
(b) Statistical method of moments
Sample Mean Standard deviation Skewness Kurtosis
1k 1.58 1.95 2.30 7.97
2k 2.33 2.06 1.47 4.80
3k 3.99 2.26 0.54 2.72
4k 3.28 1.82 1.33 4.78
5k 4.34 2.09 0.56 3.18
6k 1.99 1.93 1.42 5.20
7k 5.09 1.95 0.28 2.94
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sieving. Skewness was well correlated for both recon-
structive and opening granulometries, but the standard
deviation and kurtosis were not well correlated. Since
kurtosis has usually not proven useful in previous work,
its lack of correlation is not of concern, due to limited
image size and random grains in the sample results in wide
deviation of higher order moments.
The grains of selected natural sediment samples of
different composition and textures have been imaged,
using a light microscope. Possible application of
image-based granulometric sieving to sediments has
been tested. The results using granulometries are
promising for binarized sample images, although the
lower order moments match better than the higher
order moments. This can be attributed to various
imaging limitations and the sample size. The first
moment (mean ¼ Mz) can be used to predict surface
area of sediments. Image-based granulometries appear
to be a promising digital tool for future sediment
analysis, especially with high quality gray scale
sediment images.
Acknowledgements
This research was supported by Ministry of Science
and Technology of The Republic of Croatia, project
0098041. Sampling in O ¨ re estuary was performed by
support of USGS, Croatia joint project (JF-169). We
thank Professor Staffan Sjo ¨ berg for organizing the field
tripinO ¨ re estuary.The authors thank Mr Srec ´ ko Karas ˇic ´
for his help in performing SSA measurements. Special
thanks are due to Professor Nikola Ljubes ˇic ´ , who kindly
let us use the microscopic equipment. The authors like to
thank Professor. J.P. Le Roux, for critical and extremely
helpful pre-review on the methodology and comments on
the manuscript. This paper in its preliminary form was
presented as a lecture at the conference MATH/CHEM/
COMP 2002 in Dubrovnik (Croatia).
Table 4
Comparison of granulometric moments with conventional sieving based statistical moments in millimeter scale (direct method) for calcareous
sediments (full sample)
Sample
Sediment sieving Reconstructive granulometry Opening granulometry
Mean Standard deviation Mean Standard deviation Mean Standard deviation
1k 0.5341 0.3059 0.5179 0.2146 0.4580 0.2251
2k 0.3759 0.3055 0.3182 0.2932 0.3164 0.27893k 0.1655 0.2262 0.1806 0.2099 0.1951 0.2110
4k 0.1836 0.1856 0.2585 0.1610 0.2134 0.1493
5k 0.1216 0.1957 0.1439 0.1532 0.1243 0.1410
6k 0.4483 0.3487 0.2266 0.1329 0.1947 0.1259
7k 0.0831 0.1594 0.0871 0.1116 0.0732 0.0973
Sample
Sediment sieving Reconstructive granulometry Opening granulometry
Skewness Kurtosis Skewness Kurtosis Skewness Kurtosis
1k 0.0332 1.8821 0.8430 3.2366 0.3359 2.4599
2k 0.7899 2.4579 0.0865 1.6021 0.3159 1.8591
3k 2.3760 8.2641 0.7401 2.9384 0.8176 3.2677
4k 2.8732 12.3850 0.1364 2.1333 0.5023 2.4374
5k 3.5773 15.7730 1.4903 4.0213 1.5911 4.7260
6k 0.4534 1.7066 0.3808 1.9622 0.7163 2.5056
7k 3.4787 14.5520 2.2543 7.5301 2.2478 8.1223
Table 5
Comparison of granulometric moments with conventional sieving based statistical moments in millimeter scale (direct method) for two selected
siliceous sediments
Sample
Sediment sieving Reconstructive granulometry Opening granulometry
Mean Standard deviation Mean Standard deviation Mean Standard deviation
1a 0.0794 0.09346 0.0654 0.0994 0.0604 0.0924
3a 0.0175 0.0352 0.0369 0.0503 0.0290 0.0445
Sample
Sediment sieving Reconstructive granulometry Opening granulometry
Skewness Kurtosis Skewness Kurtosis Skewness Kurtosis
1a 2.5370 10.6280 2.5610 10.8270 2.3210 8.6030
3a 5.8785 47.0860 3.4270 18.9720 3.4690 22.0620
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