application of image-based granulometry to siliceous and

Estuarine, Coastal and Shelf Science 58 (2003) 227–239

Application of image-based granulometry to siliceousand calcareous estuarine and marine sediments

Stanislav Franciskovic-Bilinskia,*, Halka Bilinskia, Neda Vdovicb,Yoganand Balagurunathanc, Edward R. Doughertyc

aDepartment of Physical Chemistry, Institute ‘RuCer Boskovic’, P.O. Box 180, 10002 Zagreb, CroatiabCenter for Marine and Environmental Research, Institute ‘RuCer Boskovic’, 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 possibilityof 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 calcareoussediments are compared to image-based analysis of sediments obtained along the Ore estuary (Northern Sweden) and the AdriaticSea (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 havebeen imaged using a microscope and mathematical granulometries have been applied to the digital data. Image-based granulometricmoment descriptors are compared with sieve+Coulter counter-derived moments. Although it is not claimed that digital-imagingshould 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 Coultercounter 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 hasoften been used to determine sediment transport patterns.McLaren and Bowles (1985) refined the previous workand presented amodel that demonstrates the relationshipbetween the grain-size distribution of sedimentary depos-its and the direction of transport. Gao and Collins (1991,1992) proposed a modification based upon the generalprinciples of spatial changes in grain-size parametersresulting from sediment transport. Since the methodcompared small numbers of samples (two stations), LeRoux (1994a) showed the limitation of the method inidentifying the true transport direction. Le Roux (1994b)

* Corresponding author.

E-mail address: [email protected] (S. Franciskovic-Bilinski).

0272-7714/03/$ - see front matter � 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0272-7714(03)00074-X

later proposed an alternative approach that significantlyincreased the accuracy of the trend vectors defined bygrain-size parameters. The sediment-size distribution alsoreflects the nature of the source rocks and the resistance ofparticles to weathering and erosion (De Lange, Healy, &Darlan, 1997). According to Guyot, Jonanneau, andWasson (1999), granulometric characterization of river-bed and suspended sediments allows the main geo-morphological valley types to be distinguished. Thereare various reviews of conventional techniques used inmodern 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 timeconsuming and introduce operational bias to texturaldistributions. Laser diffraction methods used in the US

mailto:[email protected]

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

Geological Service can determine a full range of particlesizes from very fine clay to small pebbles; however, timeis required for sediment pre-treatment prior to laseranalysis. A rapid electronic method, without pre-treat-ment of sediments would be advantageous. Develop-ment in this regard has been slow due to the complexnature of natural sediment shapes and complicated bythe difficulty in comparing the results to mass-basedsieving. Moreover, marine sediments also containbroken shell debris, branched lithothamnids and bryo-zoa. Initial work akin to a sieving size distribution hasbeen reported by Francus (1998), who used basic imageprocessing methods to segment soft clastic sedimentsimages into different grain size class intervals. He pre-sented grain size with respect to a circular shape, justshort of the actual computation of a size distribution.Heilbronner (2000) introduced a new segmentationmethod, called ‘lazy grain boundary’, for analyzingpolarization micrographs of quartzite images. Imagedgrain sizes were segmented and a grain-size distributioncomputed for three- (3D) and two-dimensional (2D)profiles (gray scale and binary images). These imagingtechniques do not obtain the size distribution of thewhole sample as conventionally required by geologists.

Mathematical granulometries, originally proposed byMatheron (1975) to characterize sieving processes inrandom sets, are used for grain and texture classificationbecause they provide a comprehensive statistical anal-ysis of grain sizes (Chen & Dougherty, 1994; Chen,Dougherty, Totterman, & Hornak, 1993; Dougherty,1992; Dougherty, Newell, & Pelz, 1992). Granulometriesyield a size distribution, called the pattern spectrum,with respect to a reference shape called the structuringelement. The shape-based size distributions are similarto geological sizing derived by physical sieving, but theypossess 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 isbased on mass ratios, whereas morphological-granulo-metric sizing is based on shape area (binary image) orvolume (gray scale image). These are highly correlatedrandom variables. Owing to a wide range of grain sizes,granulometric computation needs to be adapted toimitate the sediment sieving processes. Balagurunathan,Dougherty, Franciskovic-Bilinski, Bilinski, and Vdovic(2001) have done this and have applied the adaptationto simulated sediments to show the applicability. Thedistributional type and parameters of the simulatedgrain model were chosen to describe siliceous sedimentscharacterized by Franciskovic-Bilinski, Bilinski, Tibljas,and Hanzel (2003). Imaging results were later comparedto real sediment sieving. The present study investigatesthe possibility of applying granulometric digital imageprocessing to real (not simulated) images of sedimentgrains, as an alternative to conventional sieving

methods. Experimental data from two shelf areas inEurope with siliceous and calcareous sediments of dif-ferent textural characteristics, composition and specificsurface area (SSA) are used to test the new method.

2. Study areas

Siliceous sediments were studied in the Ore estuary inNorth Sweden. Fig. 1 shows the location of the estuaryalong with the sample stations. These types of sedimentsare characteristic for many other estuaries of borealregion and are mostly sandy silts or silts. The chosenestuary is a semi-closed water-body, partly isolated fromthe outer sea by a dense archipelago. The salinity variesbetween 1 and 7, which depends on the discharge in theOre river. The mean annual salinity is 5:0� 1:2 andthe mean annual pH is 7:7� 0:2. The total area of theestuary is 50 km2, with water volume of about 109m3

and a mean depth of 15m. The maximum depth reaches35m. The Ore rivers catchment has an area of 2940 km2,

Fig. 1. Map shows the locations of four siliceous sediment stations

along the Ore estuary. The sample stations locations and water depths

are: 1 (63�309893N, 19�449189E, 2m), 2 (63�309624N, 19�449257E,6m), 3 (63�309672N, 19�459931E, 19m), 4 (63�309218N, 19�469168E,21m).

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

with Precambrian granites and gneisses being the mainmineral (rock) type. Approximately 65% of the super-ficial Quaternary deposits in the drainage basin consistof glacial till. A permanent snow cover occurs fromNovember to March. Rapid snow melt in April and Maycauses a pronounced high flow in a single event. Thesummer season brings both low and high flow, a singleevent being caused by a rainstorm.More details about theregion can be found in the studies by Forsgren andJansson (1992, 1993), Forsgren, Jansson, and Nilsson(1996), Franciskovic-Bilinski et al. (2003) and Kwokal,Franciskovic-Bilinski, Bilinski, and Branica (2002).

Carbonate sediments, mostly sands or silts, werestudied by taking samples at seven different locationsalong the northern and middle Adriatic Sea (Croatiaand Italy). The relative contribution to the sediments ofancient carbonate rocks and modern marine organismswas not determined. Fig. 2 shows the region of studywith sample station locations. The Adriatic Sea is aninland sea, and is part of the Mediterranean Sea. It isabout 783 km long, with an average width of 248 kmcovering an area of 138,597 km2 with average depth of173m. The mean annual salinity is 38.3. Samples 3k, 4kand 5k were taken from the North Adriatic, which istypically a shelf area. Sample 2k was taken from theNorth Adriatic island area, which is typically an under-water karst. Samples 1k, 6k and 7k were taken from thecentral region of the Adriatic island area. All thesamples from this region have significant amounts ofMesozoic carbonates with some igneous rocks. Moredetails about the region are in the studies by Brambati,Bregant, Lenardon, and Stolfa (1973), Giorgetti andMosetti (1969), Sondi, Juracic, and Pravdic (1995),Vdovic, Biscan, and Juracic (1991) and Vdovic andJuracic (1993).

3. Methods

3.1. Sampling and sample preparation

Samples from the Ore estuary were taken at fourstations with geographic coordinates given by GPS (Fig.1), using a boat and a GEMENI (OY KART AB,Finland) coring device, which is 790mm long and 80mmin diameter. At each station, two depth-incrementsamples were collected. Surface layer samples (0–5 cm)are indicated by the suffix ‘a’, while the deeper layersamples (30–35 cm) are given a suffix ‘b’. The physicalterrain prevented a deep sediment sample from beingcollected at sample station 2. Adriatic Sea samples weretaken at seven different locations (Fig. 2). Samples 1k, 2k,3k, 6k and 7k were obtained by scuba diving, whilesamples 4k and 5k were obtained using a modifiedHaamer vibrocorer (details are given by Vdovic et al.,1991).

3.2. Laboratory analysis

Sediment samples were granulometrically analyzedby wet sieving, using ASTM standard sieves for grainsizes >32 lm and a Coulter Counter (Model TA II,Coulter Electronics Ltd, England) for the grain sizes<32 lm. Wet sieving was used as it has been shown to bebetter for aggregates of clay minerals. Besides, Coultercounter analysis uses suspension, obtained by wetsieving. The sediments were classified according to theirsand–silt–clay ratio as described by Shepard (1954).Statistical descriptors were computed using both thegraphical method (Folk & Ward, 1957) and the methodof moments (Boggs, 1987). To evaluate the grain shapeof natural sediments, digital imaging method usingmathematical granulometry was used. The fractionswere photographed using a digital microscope (ZeissAxiovert 35 with a Sony digital camera). Differentmagnifications were chosen for each grain fraction dueto the large size range. The fractions were categorizedinto sand (>63 lm), coarse silt (32–63 lm) and mediumto fine silt+clay fraction (<32 lm). Lens magnificationsfor the respective fractions were set at 2.5� (resolution3.67 lm), 10� (resolution 0.92 lm) and 40� (resolution0.37 lm), respectively. The siliceous sand fraction wasimaged using 5� lens (resolution 2.3 lm). Figs. 3 and 4show images of all three fractions of real siliceous andcalcareous sediments.

The SSA (m2 g�1) was determined using a Flow SorbII 2300 (Micrometrics, USA), ‘single point procedure’and a mixture of gases (30% N and 70% He).Adsorption of nitrogen was measured at 77K, 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 calcareoussamples.

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 measuresmay be associated with an object to quantify the degreeto which the object fits one of the generic aspects, suchas the measure of circularity. In image processing, themorphological approach to shape involves quantifyingthe manner in which a structuring element (probe) fitsinside the object. The most commonly employedmorphological shape descriptors are based on granulo-metries. These have been developed to model sievingprocesses (Matheron, 1975). The essential idea is tooperate on an image in such a way that fine structure isprogressively eliminated. The area of the remainingimage is continuously diminished, and this decreasingarea is considered as a size class interval.


Fig. 2. Map shows the locations of seven calcareous sediment stations along the Adriatic Sea.

To define a binary granulometry, consider a fixedconvex set B. For any positive real number r and t, theopening of a set S by the structuring element tB isdenoted by ctB(S) and defined as the union of alltranslates of the structuring element that are subsets ofS. As t increases, ctB(S) diminishes, which means thatfor t> r, ctB(S)� crB(S). The s-parameterized mappingctB is called a granulometry and B is called its generator.For each set S, a size distribution is defined by lettingX(t) be the area of ctB(S). X(0) is the area of S. Thepattern spectrum U of S is defined by normalizing thesize distribution, so that it ranges from 0 to 1, namely

UðtÞ ¼ 1� XðtÞXð0Þ ð1Þ

The pattern spectrum is a probability distributionfunction, for which derivative of U is often used. Themoments of U, called granulometric moments, arepowerful 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 ordinarygranulometry, which diminishes each grain progressively


Fig. 3. Various fractions of real siliceous sediment grains, taken by a light microscope with 40�, 10�, 5� lens. The fractions are: (a) clay (1–5lmfor all three figures); (b) total silt (5–63lm for the first two figures), coarse silt (32–63lm for the third figure); (c) sand fractions (63–125, 125–250,

250–500lm).

until its elimination, is to apply a reconstructivegranulometry, which is defined by passing in full anygrain not completely eliminated. A reconstructivegranulometry represents a true sieve: for each graina value t0 exists such that the grain is unchanged fort � t0 and is eliminated for t > t0. The cut-off value t0is the granulometric size of the grain. A grain is passedby a reconstructive granulometry if and only if itsgranulometric size exceeds the parametric multiple ofthe generator. The pattern spectrum is defined in thesame manner as for an ordinary granulometry. Re-constructive granulometries are used for both patternclassification and image filtering (Dougherty & Chen,1999). Details and applications are discussed byDougherty and Astola (1999). Fig. 5 shows binarizedsand-sized grains, subdivided into three classes andFig. 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 elementincreases. In a reconstructive opening the shape ismaintained till they are sieved. Fig. 7 shows the digitalgranulometric size distribution using flat structuringelements for the grains in Fig. 5a–c; Table 1 shows thegrain-size moments of these fractional images usinga flat structuring probe. The first granulometricmoment shows the mean grain size in the image, whilehigher order moments show the deviation and spreadin the grain sizes for the given grain (image) sample. Itis interesting to note that the analogous size descriptiveability of granulometric moments depends both on thesize and shape of the structuring element used.

This paper applies granulometries generated by asingle structuring element, although granulometries canbe generated in more complicated ways. Experience


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 (<32 lm for all three figures); (b) coarse silt (32–63lm for all three figures); (c) sand fractions (63–125, 125–250, 250–500lm).

has shown that linear structuring elements aregenerally successful for shape and texture classifica-tion, and there are fast algorithms for implementinggranulometries generated by linear structuring ele-ments. Since the purpose of this paper is to emulatesedimentary procedure, it is restricted to use of theflat structuring element, which resembles the conven-tional sieve mesh.

3.4. Application of image-based granulometriesto natural sediment

Whether using the graphical approximation or thedirect statistical calculation, the particle-size frequenciesneed 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-maticalmorphology canbeused toelectronically computethe granulometric size distribution and the correspond-ing moments. Individual grain separation may not bepossible at all instances. Some may overlap. These weredigitally separated in these experiments. Numerousautomatic morphological segmentation methods exist(Meyer & Beucher, 1990; Vincent & Dougherty,1994). An opening filter with a small digital disk-likestructuring element was used to reduce the overallgrain size by a few pixels, and then to separate themfrom their neighbors to obtain an accurate size distribu-tion. Though segmentation methods introduce somediscrepancy, segmentation to approximate ideal non-overlapping grains yields acceptable granulometricmoments (Balagurunathan et al., 2001). Digital grain


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) 250–500lm.

sizing gives a rapid and very precise measurement ofeach grain. Image-based granulometric momentshave been used for about a decade to distinguishimage textures and to characterize granular processes(Chen & Dougherty, 1994; Chen et al., 1993; Dougherty,1992).

The granulometric analysis of the sediments wastested on previously separated three fractions—mediumto fine silt+clay (<32 lm), coarse silt (32–63 lm) andsand (>63 lm). A small sample from each fraction wasrandomly picked and imaged. Digital granulometry wasthen applied on these sample fractions, and adaptedgranulometric sizing distribution was used to obtain theimage-based grain sizing and later moments werecomputed. Due to equipment limitation, it was not easyto separate grain sizes less than 32 lm for imagingmedium to fine silt+clay fractions. A size-basedgranulometric digital filter was therefore used to removegrain sizes to obtain this fraction. Size-based digitalfilters could remove grains of sizes above a certainrange, 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 practicallyimpossible to use a single magnification for imaging. Inthese experiments grains were divided into three majorfractions (sand, silt, clay) and these were imaged using2.5� (5� for siliceous type), 10� and 40� lenses,respectively for each size range. Since magnificationwould make the image lattice grow by the sameproportion, digital adjustments were made to thegranulometric sizing equations to compensate.

Granulometric size distributions for disjointed shapesdo not depend on grain positions. To obtain thegranulometric size distribution analogous to real sedi-ments for the entire sample, the area coverage of eachfraction is linked to the mass ratio of the real fractions.In general, two adjustments have to be made to the sizedistribution. The first is area compensation due to thelens 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 afactor (ak) in each fractional class. In addition, onlya sample of each full class is available. If the grains forthe 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,

45�45, 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 2.3lm). Analogous digital sieve sizes for the above example are

11.5, 48.3, 66.7, 85.1, 103.5lm, respectively. The original image is shown Fig. 5a.


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.

area of all grains (not just those provided for gran-ulometric analysis), then for it to be relative to the totalsediment 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 pka�1k M�2

k XkðMktÞPnk¼1 pka

�1k M�2

k Xkð0Þð2Þ

Mathematical formulation (2) was originally presentedby Balagurunathan et al. (2001). The process ofimage-based sizing is schematically illustrated in Fig.8. The binary version of the formulation used toadapt granulometries to replace standard sievingmethods on real grains has been provided. Granulo-metric sizing moments were obtained statistically fromthe grain sizing distribution U. In this analysis, lowerorder moments show closer resemblance than dohigher order ones. This is attributed to the smallsample size and other imaging limitations (size re-striction, binarization).

4. Results

4.1. Conventional sieving of sedimentsand surface area determination

The results of conventional grain-size measurementsare presented as cumulative grain-size curves (cum. mass% vs. grain size in U units), which are plotted in Figs. 9and 10 for siliceous and calcareous sediments, respec-tively, following the conversion table (mm to U units) ofMuller (1967). Graphic moment parameters werecomputed according to formulations by Folk and Ward(1957). The advantage of the log based graphicalmethod is that shapes of cumulative curves can becompared visually. Although, graphic moments ob-tained convey much geological information, they are notstatistically accurate for certain skewed size distribu-tions, as recognized already by Folk and Ward. Toobtain the true sizing moments in contrast with grap-hical methods, the statistical moments were computed asby 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 0.25–0.5mm, respectively.


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.

2(a) and (b), whereas Table 3(a) and (b) shows themeasures for calcareous sediments. Figs. 9 and 10 showthe profile of siliceous and calcareous samples. FromSSA presented in Section 3 the empirical equations havebeen obtained, which relate SSA and Mz for siliceousand 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 thegraphicmoment features. Sediments from the Ore estuaryare composed of fine sand, silt and clay. The mean grainsize (Mz) was coarsest for the sample in station 1 andfinest 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 thesamples in station 1. A positive skewness was observedfor the sample in station 2 and a nearly symmetricaldistribution for samples in stations 3 and 4. The kurtosis(Kg)measures relative sorting of the center and tails of thegrain-size distribution. A mesokurtic type distributionwas observed for all the samples except for sample 1b,which is leptokurtic.

Sediments from the Adriatic Sea show differenttextural characteristics. The coarsest sand was observedfor samples 1k, 6k and 2k, collected in the northern tocentral regions of the Adriatic island area. The resultsagree with the reported study for the Croatian coast

(Vdovic & Juracic, 1993). Sample 7k was sandy silt witha high silt content. Samples 3k, 4k and 5k, obtainedfrom the northern Adriatic, contained fine sand and silt.The Mz was coarsest for station 1k and finest for station7k. Sample 3k was very poorly sorted. Distributionswere very positively skewed for samples 1k, 2k, 4k and5k, positively skewed for samples 3k and 6k, and nearlysymmetrical for sample 7k. The kurtosis for samples 3kand 7k was mesokurtic, leptokurtic for samples 5k and6k, and very leptokurtic for samples 1k, 2k and 4k.

4.2. Image-based sieving of sediments

Granulometric sizing was obtained using the adaptedpattern spectrum density relation of Eq. (2) and themoments have been derived. Table 4 shows thenumerical values of granulometric sizing moments com-pared to conventional sieving moments for calcareoussediments. Table 5 shows similar results for two selectedsiliceous sediments: 1a, with highest percent of sand and3a, with highest percent of clay. Both opening andreconstructive granulometries were used in this study.The results show a quantitative comparison of the lowerorder moments. The deviations are due to the in-homogeneity of the sample obtained due to geologicalterrain and various other factors (image binarization,filtering, sampling size) mentioned earlier. All compar-isons are made in a direct millimeter scale. It is evidentthat mass information cannot be fully captured bybinarized digital images. Due to varied size range of


Fig. 9. Cumulative grain-size distribution of siliceous sediments from Ore 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.


Table 2

Conventional moments of sediments from the Ore 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

grains considered in the present study (0.01–1mm), nopresent technology could image such a wide range withconsistent shade (light intensity) and acceptable digitalsize. As the grain sizes occupied on a digital latticedecreases, imaging algorithms (granulometric measures)becomes variant (Dougherty, 1992). Binarization wasconsidered as a viable and conservative estimate to formthe grain-size distribution to gray scale imaged grains.In most studies, binary size distributions are closeestimates to its gray scale counterparts and good com-parison was expected in this study. The grain fractionalratio information is considered in the formulation usingthe factor (pk).

5. Discussion

Statistical support of the compatibility between image-based sieving and conventional sieving is supplied byconsidering the closeness between granulometric andconventional sieving moments for all seven calcareoussamples. Two sets of sub-samples were taken for eachfraction and granulometric results were averaged for eachsample. Results for carbonate samples were taken tocompare the consistency between the image-based sievingto conventional sieving. The first moment (Mz) showsa fairly high degree of correlation between the twomethods conventional to reconstructive and conventional

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 Sand

5k 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


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 0.2789

3k 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

sieving. Skewness was well correlated for both recon-structive and opening granulometries, but the standarddeviation and kurtosis were not well correlated. Sincekurtosis has usually not proven useful in previous work,its lack of correlation is not of concern, due to limitedimage size and randomgrains in the sample results inwidedeviation of higher order moments.

The grains of selected natural sediment samples ofdifferent composition and textures have been imaged,using a light microscope. Possible application ofimage-based granulometric sieving to sediments hasbeen tested. The results using granulometries arepromising for binarized sample images, although thelower order moments match better than the higherorder moments. This can be attributed to variousimaging limitations and the sample size. The firstmoment (mean ¼ Mz) can be used to predict surfacearea of sediments. Image-based granulometries appearto be a promising digital tool for future sediment

analysis, especially with high quality gray scalesediment images.

Acknowledgements

This research was supported by Ministry of Scienceand Technology of The Republic of Croatia, project0098041. Sampling in Ore estuary was performed bysupport of USGS, Croatia joint project (JF-169). Wethank Professor Staffan Sjoberg for organizing the fieldtrip in Ore estuary. The authors thankMr SreckoKarasicfor his help in performing SSA measurements. Specialthanks are due to Professor Nikola Ljubesic, who kindlylet us use the microscopic equipment. The authors like tothank Professor. J.P. Le Roux, for critical and extremelyhelpful pre-review on the methodology and comments onthe manuscript. This paper in its preliminary form waspresented as a lecture at the conference MATH/CHEM/COMP 2002 in Dubrovnik (Croatia).

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


References

Balagurunathan, Y., Dougherty, E. R., Franciskovic-Bilinski, S.,

Bilinski, H., & Vdovic, N. (2001). Morphological granulometric

analysis of sediment images. Image Analysis and Stereology 20,

87–99.

Barbanti, A., & Bothner, M. H. (1993). A procedure for partitioning

bulk sediments into distinct grain-size fractions for geochemical

analysis. Environmental Geology 21, 3–13.

Batman, S., & Dougherty, E. R. (1997). Size distributions for

multivariate morphological granulometries: texture classification

and statistical properties. Optical Engineering 36, 1518–1529.

Beuselinck, L., Govers, G., Poesen, J., Degraer, G., & Froyen, L.

(1998). Grain-size analysis by laser diffractometry: comparison

with the sieve-pipette method. Catena 32, 193–208.

Boggs, S. Jr. (1987). Principles of sedimentology and stratigraphy

(pp. 1–784). Columbus, OH: Merrill Publishing Co.

Brambati, A., Bregant, D., Lenardon, G., & Stolfa, D. (1973).

Transport and sedimentation in the Adriatic Sea (Pubblicazione N.

20, pp. 1–60). Udine: Museo Friulano di Storia Naturale.

Chen, Y., & Dougherty, E. R. (1994). Gray-scale morphological

texture classification. Optical Engineering 33, 2713–2722.

Chen, Y., Dougherty, E. R., Totterman, S., & Hornak, J. (1993).

Classification of trabecular structure in magnetic resonance images

based in morphological granulometries. Mangetic Resonance

Medicine 29, 358–370.

De Lange, W. P., Healy, T. R., & Darlan, Y. (1997). Reproducibility

of sieve and settling tube textural determinations for sand-sized

beach sediment. Journal of Coastal Research 13, 73–80.

Dougherty, E. R. (1992). An introduction to morphological image

processing (pp. 1–161). Bellingham, WA: SPIE Press.

Dougherty, E. R., & Astola, A. T. (1999). Nonlinear filters for image

processing (pp. 1–453). Bellingham, WA: SPIE/IEEE Press.

Dougherty, E. R., & Chen, Y. (1999). Granulometric filters. In

E. R. Dougherty, & J. T. Astola (Eds.), Nonlinear filters for image

and signal processing (pp. 1–453). Bellingham, WA: SPIE/IEEE

Press.

Dougherty, E. R., Newell, J. T., & Pelz, J. B. (1992). Morphological

texture-based maximum-likelihood pixel classification based on

local granulometric moments. Pattern Recognition 25, 1181–1198.

Dougherty, E. R., & Pelz, J. B. (1991). Morphological granulometric

analysis of electrophotographic images—size distribution statistics

for process control. Optical Engineering 2, 177–187.

Folk, R. L., & Ward, W. C. (1957). Brazos river bar: a study in the

significance of grain size parameters. Journal of Sedimentary

Petrology 27, 3–26.

Forsgren, G., & Jansson, M. (1992). The turnover of river-transported

iron, phosphorus and organic carbon in the Ore estuary, northern

Sweden. Hydrobiologia 235/236, 585–596.

Forsgren, G., & Jansson, M. (1993). Sedimentation of phosphorus in

limnetic and estuarine environments in the river Ore system,

northern Sweden. Hydrobiologia 253, 233–248.

Forsgren, G., Jansson, M., & Nilsson, P. (1996). Aggregation and

sedimentation of iron, phosphorus and organic carbon in

experimental mixture of fresh water and estuarine water. Estuarine,

Coastal and Shelf Science 43, 259–268.

Francus, P. (1998). An image-analysis technique to measure grain-size

variation in thin sections of soft clastic sediments. Sedimentary

Geology 121, 289–298.

Franciskovic-Bilinski, S., Bilinski, H., Tibljas, D., & Hanzel, D. (2003).

Estuarine sediments from boreal region—an indication of weath-

ering. Croatica Chemica Acta 76, 167–176.

Gao, Shu, & Collins, M. (1991). A critique of the ‘‘McLaren method’’

for defining sediment transport paths—discussion. Journal of

Sedimentary Petrology 61, 143–146.

Gao, Shu, & Collins, M. (1992). Net sediment transport patterns

inferred from grain-size trends, based upon definition of ‘‘transport

vectors’’. Sedimentary Geology 80, 47–60.

Giorgetti, F., & Mosetti, F. (1969). General morphology of the

Adriatic sea. In C. Morelli et al. (Eds.), Regional geophysical study

of the Adriatic sea. Bolletino di Geofisica Teoretica et Applicata

11(41–42), 49–56.

Guyot, J. L., Jonanneau, J. M., & Wasson, J. G. (1999). Character-

ization of river bed and and suspended sediments in the Rio

Madeira drainage basin (Bolivian Amazonia). Journal of South

American Earth Sciences 12, 401–410.

Heilbronner, R. (2000). Automatic grain boundary detection and grain

size analysis using polarization micrographs or orientation images.

Journal of Structural Geology 22, 969–981.

Kwokal, Z., Franciskovic-Bilinski, S., Bilinski, H., & Branica, M.

(2002). A comparison of anthropogenic mercury pollution in

Kastela Bay (Croatia) with pristine estuaries in Ore (Sweden) and

Krka (Croatia). Marine Pollution Bulletin 44, 1152–1157.

Le Roux, J. P. (1994a). Net sediment transport patterns inferred from

grain-size trends, based upon definition of ‘‘transport vectors’’—

comment. Sedimentary Geology 90, 153–156.

Le Roux, J. P. (1994b). An alternative approach to the identification of

net sediment transport paths based on grain-size trends. Sedimen-

tary Geology 94, 97–107.

Matheron, G. (1975). Random sets and integral geometry (pp. 1–261).

New York, NY: Wiley.

McLaren, P., & Bowles, D. (1985). The effects of sediment transport

on grain-size distributions. Journal of Sedimentary Petrology 55,

457–470.

Meyer, F., & Beucher, S. (1990). Morphological segmentation. Journal

of Visual Communication and Image Representation 1, 21–45.

Molinaroli, E., De Falco, G., Rabitti, S., & Portaro, R. A. (2000).

Stream-scanning laser system, electric sensing counter and settling

grain size analysis: a comparison using reference materials and

marine sediments. Sedimentary Geology 130, 269–281.

Muller, G. (1967). Methods in sedimentary petrology (pp. 1–283). New

York, NY: Hafner Publishing Co.

Plumley, W. J. (1948). Black Hills terrace gravels: a study in sediment

transport. Journal of Geology 55, 526–577.

Sand, F., & Dougherty, E. R. (1998). Asymptotic granulometric

mixing theorem: morphological estimation of sizing parameters

and mixture proportions. Pattern Recognition 31, 53–61.

Shepard, F. P. (1954). Nomenclature based on sand–silt–clay ratios.

Journal of Sedimentary Petrology 24, 151–154.

Sondi, I., Juracic, M., & Pravdic, V. (1995). Sedimentation in

a disequilibrium river-dominated estuary—the Rasa river estuary

(Adriatic sea, Croatia). Sedimentology 42, 769–782.

Syvitski, J. P. M., Le Blanc, W., & Asprey, D. W. (1991).

Interlaboratory instrument calibration experiment. In J. P. M.

Syvitski (Ed.), Principles, methods, and application of particle size

analysis (pp. 174–193). New York: Cambridge University Press.

Theera-Umpon, N., & Gader, P. (2000). Counting white blood cells

using morphological granulometries. Journal of Electronic Imaging

9, 170–177.

Vdovic, N., Biscan, J., & Juracic, M. (1991). Relationship between

specific surface area and some chemical and physical properties of

particulates: study in the northern Adriatic. Marine Chemistry 36,

317–328.

Vdovic, N., & Juracic, M. (1993). Sedimentological and surface

characteristics of the Northern and Central Adriatic sediments.

Geologia Croatica 46, 157–163.

Vincent, L., & Dougherty, E. R. (1994). Morphological segmenta-

tion for textures and particles. In E. R. Dougherty (Ed.), Digital

image processing methods (pp. 1–472). New York, NY: Marcel

Dekker.

application of image-based granulometry to siliceous and

Documents