Laras Cahyani Putri 21100113120050.pdf

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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: [email protected] (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

mailto:[email protected]

mailto:[email protected]



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).

228 S. Franc is kovic -Bilinski et al. / Estuarine, Coastal and Shelf Science 58 (2003) 227–239



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.

229S. Franc is kovic -Bilinski et al. / Estuarine, Coastal and Shelf Science 58 (2003) 227–239



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.




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).




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).




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.




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.




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.




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




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


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


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


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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