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A microscopic information system (MIS) for petrographic analysis


内容提示: A microscopic information system (MIS) for petrographic analysisSimone Tarquinin , Massimiliano FavalliIstituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa, Pisa, 56126, Via della Faggiola 32, 56126 Pisa, Italya r t i c l e i n f oArticle history:Received 18 May 2009Received in revised form3 September 2009Accepted 4 September 2009Keywords:Granitoid rocksGeographic Information System (GIS)Image processingPetrographya b s t r a c tThe database and visualization facilities of Geographic Information...

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A microscopic information system (MIS) for petrographic analysisSimone Tarquinin , Massimiliano FavalliIstituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa, Pisa, 56126, Via della Faggiola 32, 56126 Pisa, Italya r t i c l e i n f oArticle history:Received 18 May 2009Received in revised form3 September 2009Accepted 4 September 2009Keywords:Granitoid rocksGeographic Information System (GIS)Image processingPetrographya b s t r a c tThe database and visualization facilities of Geographic Information System (GIS) software are employedto support the analysis of rock texture from thin section by image processing. A MicroscopicInformation System (MIS) is hence obtained. The method is applied to transmitted light images of 137samples obtained from 8 granitoid rocks. A slide scanner and a mount for crossed polarization are usedto acquire the input images. For each thin section 5 collimated RGB images are scanned: 4 underdifferent directions of crossed polarization and 1 without polarization. A grain segmentation procedure,based on two region growing functions is applied. The output is converted to vector format and refinedusing editing tools in the MIS environment, which enables a straightforward match between the inputimagery and the final vectorized texture. GIS software provides optimal management of the MISdatabase, allowing the cumulative measurement of more than 87,000 grains.& 2010 Elsevier Ltd. All rights reserved.1. IntroductionA great variety of images types are employed in the Earth andplanetary sciences, ranging from microscopic scale images of rocksamples to continental scale satellite surveys. The instrumentsdeveloped for different scales of examination are based on varioustechnologies, but in general the common basis is a sensor thatrecords a signal from the target surface to produce an image.Different types of software have been developed to deal withsuch signals, ranging from remote sensing to image processingunits, but Geographic Information System (GIS) software isparticularly flexible, allowing the combined handling and visua-lization of data in different formats over a wide resolution range(Burrough, 1989; Pareschi et al., 2000). This software has beenrecently introduced to the study of rock textures at microscopicscale, using transmitted light microscope images. Li et al. (2008)use GIS software for the segmentation and analysis of grainboundaries, presenting a procedure tested on a few samples.Barraud (2006) applies GIS software to refine and analyze thevectorized texture obtained after segmenting transmitted lightmicroscopy images with third party software (ITK, for ImageToolkit, http://www.itk.org). Fernandez et al. (2005) use GISsoftware to compute shape-fabric parameters and strain factorsfrom grain boundary maps. In this paper, we present a systemwhich uses GIS software to manage the analysis of a largecollection of thin sections, applying a custom image processingprocedure based on region growing algorithms. This systemrepresents a stand-alone, inexpensive tool that can substitute forthe microscope itself in performing a preliminary petrographicsurvey. It also allows for statistical examination of coarse grainedrocks which is difficult with regular microscopes. Any geographicreference is absent, hence we prefer to call the obtainedInformation System ‘‘Microscopic’’ instead of geographic (MIS).Petrographic analysis of thin sections by transmitted lightmicroscopy is one of the principal methods for rock characteriza-tion and classification. Digital image analysis is the process ofidentifying and quantifying features in a digital image startingfrom pixel values (Russ, 2002). When applied to transmitted lightmicroscopy images, the aim of image analysis is to quantify therock composition and texture by measuring parameters such asmodal fractions, crystal/grain size distributions and crystal/grainshapes. These features result from petrogenetic processes, andtheir accurate determination is central in the fields of petrology,volcanology or tectonics (e.g. Jerram et al., 2003; Boorman et al.,2004; Higgins, 2006; Trullenque et al., 2006; Williams et al., 2006;Keulen et al., 2007; Fornaciai et al., 2008; Piochi et al., 2008).Several authors have applied digital image analysis to auto-mate and speed up the quantification of rock texture fromtransmitted light microscopy images of thin sections (e.g.Armienti et al., 1994; Launeau et al., 1994; Lumbreras and Serrat,1996; Goodchild and Fueten, 1998; Launeau and Cruden, 1998;Heilbronner, 2000). However, the application of this method tomany rocks is hampered by the complexity of related transmittedlight microscopy images.Here we address the problem of digital image analysis of thinsections by applying four approaches: (i) the use of a slide scannerto acquire input imagery in transmitted light from thin sections,leaving aside the petrographic microscope (De Keyser, 1999;ARTICLE IN PRESSContents lists available at ScienceDirectjournal homepage: www.elsevier.com/locate/cageoComputers & Geosciences0098-3004/$-see front matter & 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.cageo.2009.09.017n Corresponding author: Tel.: +39 050 8311932; fax: +39 050 8311942.E-mail address: tarquini@pi.ingv.it (S. Tarquini).Computers & Geosciences 36 (2010) 665–674 ARTICLE IN PRESSArmienti and Tarquini, 2002; Boorman et al., 2004); (ii) thestorage of the resulting images in a GIS-like database structurethat is extremely useful to retrieve, browse and analyze a largearchive of thin sections; (iii) the application of a custom imageanalysis procedure based on region growing concepts; and (iv) therefinement of the regions after raster to vector conversion usingGIS software.2. From geographic to Microscopic Information System (MIS)2.1. Thin sections and GISThin section images are often unintentionally handled using aGIS-like concept. When researchers perform localized microana-lysis on their samples (e.g. scanning electron microprobe), theyoften mark the analyzed spots on these images to organize themeasurements (Di Vincenzo et al., 2001, 2007). A series oflocalized information arranged on an image in a reference frame,such as a Cartesian X–Y coordinate system, is a type of graphicinformation system. If we neglect the effect of geographicprojections, the difference between this system and a GIS is thatthe former is referenced to a local coordinate system, while thelatter is referenced to a global Earth surface reference system.Once we are aware of this difference, GIS software can be used inan unconventional way to handle a MIS.2.2. Image analysis and thin sectionsOne of the basic concepts of image analysis is that there is adirect relationship between pixel values (the color) and specificclasses of features. In the case of transmitted light microscopy thisrelationship is not straightforward. The main reasons are listedbelow:(i) In non-isotropic minerals the orientation of the indicatrixwith respect to the direction of polarization of light affectsthe birefringence value and in some case the absorptioncolor.(ii) The optical properties of many minerals are modified byincidental factors such as uneven alteration or ion substitu-tion.(iii) Intra-crystalline structures of many minerals often result incomplicated patterns (e.g. twinning, cleavage, zoning), lead-ing to an uneven response to light transmission and possiblyadding noise to the images.(iv) Slight differences in thin section preparation can substan-tially influence the transmitted light behavior of minerals.(v) Without using special devices (e.g.Thompson et al., 2001), thepetrographic microscope is well suited to human vision but itis not, per se, an accurate system for the quantification oflight (Pirard, 2004).These factors have hampered the determination of reliablespectral signatures for specific minerals in transmitted lightmicroscopy, and automatic image analysis solutions have beendevised only for constrained cases: monomineralic rocks or rocksshowing easily distinguishable mineral phases (e.g. Heilbronner,2000; Armienti and Tarquini, 2002; Perring et al., 2004; Fornaciaiet al., 2008; Li et al., 2008). This paper provides a contribution toovercome this limitation for granitoid rocks. In addition, thepresented methodology is ideal to deal with coarse grainedsamples which are difficult to deal with by using a regularmicroscope or even a macroscope, owing to the complexity toobtain fields of view greater than 1–2 cm.2.3. The samplesIn this study, we analyze 137 thin sections obtained from 49samples of eight different granitoid rocks that are commonly usedin the decorative stone industry (Table 1). The most commonminerals in the samples are plagioclase, quartz and K-feldsparwith minor mafic minerals (mostly biotite and amphiboles).3. The image database3.1. Image acquisitionFollowing the idea of De Keyser (1999), we used a slidescanner (Nikon Coolscan II) for image acquisition, along with anin-house mount for scanning under crossed polarized light(Armienti and Tarquini, 2002) (Fig. 1). The scanner allows aresolution up to 9.4 m m/pixel. This value is optimal for our rocksamples, where the smallest crystals are usually larger than100 m m in equivalent diameter. This resolution is also very closeto that recently attained by using a digital camera coupled with amicroscope (Perring et al., 2004; Barraud, 2006; Obara andKozusnikova, 2007; Smith and Beermann, 2007). The mount is arectangular frame with three internal slots holding a thin sectionand two polarizing filters: one below and one above the thinsection (Fig. 1). One short side of the mount is open, allowing theinsertion and removal of the thin section and of the filters. From asheet of polarizing plastic we cut 4 pairs of filters with mutuallyorthogonal directions of polarization with an angular spacing of22.51 (Fig. 1d). By substituting these pairs in the slots, images ofthe thin section are acquired under 4 directions of crossedpolarization together with an image without polarization (Fig. 2).The acquisition of multiple images leads to a bettercharacterization of the sample (Terribile and FitzPatrick, 1992;Heilbronner and Pauli, 1993; Launeau et al., 1994; Lumbreras andSerrat, 1996; Fueten, 1997; Goodchild and Fueten, 1998;Heilbronner, 2000; Fueten and Goodchild, 2001; Barraud, 2006;Li et al., 2008).Images have been acquired using the software bundled withthe scanner. The acquisition takes typically 20 min per thinsection for matrices of about 2300?3400 pixels. An advantage ofthis acquisition method is that, unlike standard microscope-basedtechniques, the entire surface area of the section is scanned atonce (about 2.2?3.2 cm 2 ); moreover, a slide scanner is inexpen-sive compared to a microscope. The 5 perfectly collimated RGBimages can be viewed as a single 15 channel image (Fig. 2)analogous to a multi-spectral satellite image (Terribile andFitzPatrick, 1995). In a satellite image the channels recordTable 1Input samples. All these rocks are called granite in decorative stone jargon.CommercialnameCountry Region/StatePetrographicclassificationhandsamplesthinsectionsDesert cream India TamilNaduMonzo-granite 5 5Grigio sardo Italy Sardegna Monzo-granite 3 9YellowtopazioBrasil EspiritoSantoGneiss 5 15Golden moon Brasil – Gneiss 1 3Silver cloud USA Georgia Monzo-granite 5 15Barre gray USA Vermont Granodiorite 10 30Lanhelin France Bretagne Monzo-granite 10 30Tolga White Norway Hedmark Tonalite 10 30Totalnumber49 137S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 666 ARTICLE IN PRESSdifferent wavelengths of radiation captured by the sensor. Herethe difference is due to different polarizing filter combinations.This perspective of viewing the imagery is the key that inspiresthe image analysis procedure described by Launeau et al. (1994)and Terribile and FitzPatrick (1995).3.2. The image repository in GIS environmentFor the handling of our petrographic database we use theArcView GIS 3.2 package. A significant advantage of GIS softwarecompared to image processing units is that the former is designedto handle data in different formats (e.g. raster or vector), whilemost image processing units work only with images. To store andefficiently retrieve our data we borrow the repository andbrowsing concept from a GIS database (Tarquini et al., 2007).GIS software is designed to handle large datasets, and toefficiently address subsets belonging to portions of the area, theinformation layers are usually arranged in small subsets accord-ing to a geographic grid (the ‘‘reference’’ grid). For our purpose webuild up a reference grid where each feature is linked to a thinsection. In this way, all the files belonging to a particular thinsection are retrieved and displayed by clicking on the correspond-ing feature of the reference grid: a useful tip when dealing withlarge datasets.The 5 images acquired for each section have a standardizedsuffix unequivocally identifying the original filter combination.Using this structure, all input items are directly accessible fromthe reference grid for visualization and/or analysis.When loaded by GIS software an image is required to havegeoreferencing information. For the purpose of our MIS the onlynecessary condition is that all the images scanned from thesame thin section have a coherent reference frame, so theinitial coregistration is maintained. We simplify the system bysetting the lower left corner of all the images to the origin(coordinates 0, 0), and by setting the pixel size to 1 in the X and Ydirections. The actual pixel resolution is considered later, whenthe measurements are carried out. The mount warrants a perfectmechanical stability, hence acquired images are usually coregi-strated. To correct occasional misalignments, three tie points areidentified on each image by the user, then affine transformationsre-align images in the same way GIS software aligns geographicimages using geo-referenced points.After image acquisition and storage, our MIS providescomputer assisted visual analysis that can substitute the use ofthe microscope by performing a preliminary thin section survey.This facility in many cases enables instant mineral determinationand possibly rock classification. Moreover, the reference gridpermits a rapid visual research over a large archive of thinsections, optimizing data handling.Fig. 2. An example of 5 input images. In a corner, RGB channels are shownseparately. Global input imagery consists of 15 perfectly coregistrated bands, 8 biteach. These images refer to monzo-granite Grigio sardo (see Tables 1 and 2).Fig. 1. Mount used for scanning thin sections under different polarization conditions: (a) insertion of thin section, (b) insertion of two polarizers, (c) mount holding a thinsection and polarizers and (d) four pairs of polarizers with mutually orthogonal directions of light polarization. Thin red arrows show direction of polarization. (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 667 ARTICLE IN PRESS4. Database elaborationConsidering the complexity of the input imagery outlined inSection 2.2, the global procedure for texture determination isorganized in two stages (detailed in Sections 4.1 and 4.2,respectively): in the first stage, automatic image processingsegments the input images into a map of regions providing apreliminary result (Fig. 3a–c); in the second stage, this result isconverted into vector format (Barraud, 2006; Li et al., 2008), thenis revised using the customized GIS environment and grains arefinally assigned to mineral phases (Fig. 3d–f).4.1. The automatic image processingThe 15 input bands were analyzed to reduce the correlation ofthe global signal (Launeau et al., 1994; Higgins, 2006). The threefelsic minerals, plagioclase, K-feldspar and quartz, represent, onaverage, more than 90% of the 137 thin sections. These mineralsare colorless in polarized light and display birefringence colorswith the same range of gray tones (see Figs. 2–4). Mafic mineralsusually display more saturated colors, but in the global evaluationthey carry little weight due to their low abundance. The threebands of the input RGB images are strongly correlated, because agray color means that they have always approximately the samevalues. Consequently, for the automatic image processing, weused only the 5 input red bands, without a relevant loss ofinformation.A novel object segmentation procedure was developed in C++language, based on region growing methods. These functions areembedded in the GIS environment using Avenue TM scripts thatrun the executable via a command line. The basic concept of theregion growing method is the detection of relatively homoge-neous areas. High frequency information is therefore counter-productive and the input images are cleaned applying a medianfilter followed by an opening–closing sequence (Russ, 2002) priorto the region growing algorithm. This process acts as both a noise-reduction and low-pass filter that attenuates micro-fractures andcleavages (Fig. 4, rows 1 and 2).The segmentation procedure was devised by considering thetwo most recurrent color patterns (p x ) observed in the intra-crystalline textures of the studied samples: p 1 is a gently varyingshading (e.g. the color pattern originated by undulose extinctionin quartz grains), and p 2 is a quasi-bimodal distributions of pixelsvalues (e.g. the color pattern originated by polysynthetic twinningin plagioclase grains, see Figs. 3–5). An unseeded region growingfunction f g works on the color gradient to deal with p 1 (details inAppendix A), and a seeded region growing function f d works onFig. 3. Sub-images (a)–(c) show three steps of automatic image analysis procedure: (a) one of the input crossed polarized images; (b) output after automatic imagesegmentation based on region growing algorithms; (c) same output as (b), after raster to vector conversion, overlaid on original image (a). Sub-images (d)–(f) showrefinement of automatic output to obtain final texture (d); red contours are removed by merging polygons (regions) keeping only green ones; (e) green contours, identifiedby user as actual grain boundaries. Most of final grain boundaries already exist, while a few ones have been introduced by user; (f) final texture, where most of theidentified grains have been attributed to a mineral phase (yellow=K-feldspar, magenta=plagioclase, orange=quartz and blue=femics, white=unclassified regions). Theseimages refer to monzo-granite Lanhelin (see Tables 1 and 2). Yellow bar is 2 mm. (For interpretation of the references to color in this figure legend, the reader is referred tothe web version of this article.)S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 668 ARTICLE IN PRESSFig. 4. Images are arranged in six rows and eight columns identified by numbers and letters, respectively. Each column, from top to bottom, displays six steps of texturedetermination. Rows represent: (1) an input crossed polarized image; (2) same image after preliminary filtering; (3) regions obtained by f g ; (4) regions obtained by f d ; (5)final result. Legend for mineral phases is as in Fig. 3f; (6) final result overlain to the original image (row 1). Yellow bar is 2 mm. Columns a and c refer to Yellow topazio;columns b, e and h refer to Grigio sardo; column d refers to Desert cream; columns f and g refer to Silver cloud (see Tables 1 and 2). (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 669 ARTICLE IN PRESScolor distance to account for p 2 (details in Appendix B). The globalprocedure starts with a loop that triggers f g at all the image pixels,giving the preliminary region maps of row 3 in Fig. 4. Theseregions are subsequently broadened using f d , resulting in themaps of row 4 (Fig. 4).The automatic segmentation does not attribute all the pixels toregions, but unclassified areas are enclosed by classified areas andthey are usually well defined by their property of beingunclassified; some grains are simply identified by a singleunclassified area (see Fig. 4). Fig. 4 shows 8 representative casesFig. 4. (Continued)S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 670 ARTICLE IN PRESSof minerals and textures of the investigated samples. Columnsa–d displays cases where f g is very effective in segmentingpatterns such as undulose extinction in quartz (columns a and b),shaded extinction in K-feldspar (column c) or a more straightfor-ward texture as in column d. Columns e–h show cases where f dhelps when f g fails to classify a relevant portion of the matrix.These are the examples of more complex intra-crystalline colorpatterns such as perthitic intergrowth (column e) or microclinetwinning (column f) in K-feldspar, polysynthetic twinning inplagioclase (column g), or strongly altered plagioclase (columnse–h) possibly combined with strong zoning (column h).4.2. Vector textureResults of the automated image processing procedure aretransformed from raster to vector format (Barraud, 2006; Li et al.,2008). The methods described in Section 3.2 provide an effectiveand user-friendly comparison between the vectorized texture andthe input images (see also Figs. 3 and 4). The user can thereforeeasily recognize where the automatic result produces an over-segmentation or an undersegmentation, and can identify theregions that must be merged or split to obtain the actual grains(Barraud, 2006). f d and f g were tuned to obtain oversegmentationrather than undersegmentation, because the correction of over-segmentation is easiest. ArcView editing tools were developed tosimplify and speed up manual editing of the vector texture. Thesetools allow merging/splitting of polygons and the attribution ofpolygons to specific mineral phases. An ideal result of the imageprocessing algorithm would be the exact reproduction of amanually traced texture. A perfect tuning of a few specific casesis possible, but it can likely hamper the application of the systemto different samples. A good compromise is the separation of tasksby assigning the most difficult one to the machine (i.e., therecognition of the majority of grain boundaries in the rasterdomain) and planning manual refinement of the result using anefficient working environment (i.e., the effective editing andvisualization tools of the MIS). Manual refinement ensuresaccurate results (Heilbronner, 2000).For each thin section, the user defines the extent of a region ofinterest (ROI) where editing is carried out. For statisticalsignificance, the ROI should include at least 400 grains and isautomatically centered in the middle of the thin section.It is noteworthy that, despite the typical oversegmentation, thereal grain boundary contours are almost completely present in theautomatic result; only a fraction of the real contours are missingand must be introduced manually by the user (Table 2). Thevector format is ideally suited for the storage of the informationon the area, perimeter and mineral phase of all features. Once theediting session is completed, the analysis is finalized by carryingout measurements of the determined grains inside the ROIs. Toassess the chosen ROI extent, the measured mode is plotted vs.the ROI size (Fig. 6), and when the mode becomes stable, the ROIextent is accepted. All the performed measurements are storedaccording to the same repository structure described for images,hence results can be retrieved and displayed using the describedreference grid (e.g. Fig. 7).For every rock the crystal size distribution is derived (Higgins,2000). Table 2 reports statistics of the modal analyses. 87,064grains were identified within the 137 analyzed thin sections (onaverage more than 600 per thin section). The average cumulativelength of grain boundaries automatically detected for each sectionis about 1.6 m while the hand traced grain boundaries are about7 mm per thin section. The columns Kf_r, Pl_r and Qz_r report theratios between the regions and the actual grains for felsicminerals.Fig. 5. Distributions of values of red bands (R v ) calculated for a polysynthetictwinned plagioclase (above) and for a microcline twinned K-feldspar (below).Distributions have been calculated in red box of Fig. 4g1 (plagioclase) and 4f1(K-feldspar).(For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)Table 2For each rock: total number of thin sections (N_sect), total number of determined crystals (Nc), total number of determined K-feldspar, plagioclase, quartz and femiccrystals (respectively, NKf, NPl, NQz, NFm); average number of regions that have been merged to obtain a single crystal of K-feldspar, plagioclase, quartz (respectively, Kf_r,Pl_r and Qz_r); Cb-auto. and Cb-hand. are cumulative length of the automatically and manually derived crystal boundary; %Undet is percent of undetermined area insideROI.Commercial name N_sect Nc NKf NPl NQz NFm Kf_r Pl_r Qz_r Cb-auto.(mm/sect)Cb-hand.(mm/sect)%UndetDesert cream 5 2901 866 669 1099 267 2.42 1.61 1.18 1647.1 4.1 3.2Grigio sardo 9 5695 312 1614 1144 2625 10.12 2.68 1.93 1738.0 11.0 3.3Yellow topazio 15 10,517 4180 637 1356 4344 1.52 1.12 1.32 1695.2 3.8 5.2Golden moon 3 3704 603 945 1035 1121 2.05 1.51 1.08 2854.0 19.1 2.4Silver cloud 15 9360 1368 2152 2870 2970 2.45 1.71 1.09 1354.1 3.9 2.8Barre gray 30 20,965 2000 3429 3748 11,788 1.67 3.60 1.13 1692.2 8.6 3.0Lanhelin 30 14,994 1189 2404 2273 9128 3.49 4.76 3.01 1572.4 9.9 2.7Tolga White 30 18,928 373 1247 11,701 5607 1.27 11.15 1.04 1448.6 3.4 1.9Average 2.22 3.73 1.30 1602.7 6.9 3.1Sum 137 87,064 10,891 13,097 25,226 37,850S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 671 ARTICLE IN PRESS4.3. Sample processing timeTo evaluate the effectiveness of the database processing wequantify the duration of the global procedure; that is the CPU-time for the automatic batch processing, and the operator-timefor the manual vector editing. We worked on a Pentium 3 2.2 GHzCPU. The CPU-time depends on the number of pixels in the inputimages and on the number of determined regions. 1–1.5 h of CPUtime per thin section is required for the studied samples.Quantification of the duration of the manual editing session isless straightforward. In general, this parameter depends on threefactors: the total number of grains that must be checked, theaverage quality of the determined regions (the more accurate thisresult the faster the editing) and the ease of visual mineral phasedetermination using the MIS facilities. An editing time between 5and 20 min/cm 2 of thin section is required for the studied rocks.Depending on the rock grain size, a ROI between 1.5 and 4 cm 2was selected for manual editing.4.4. Mode errorsAnalytical errors in modal analysis are commonly classified as(i) sampling errors, linked to the statistical significance of theanalyzed sample, (ii) measurement errors, due to miscalculationin counting areas, and (iii) accidental errors, due to human faultsin assigning mineral phases to grains (Chayes, 1956).In this study the sampling error has been addressed bydetermining the ROI extent vs. mode (Fig. 6). Further statisticalanalyses are beyond the scope of this paper. The measurementerror is null if unbiased procedures are written for measurements.The accidental error is low if the visualization capabilities of theMIS allow robust mineral phase determination. It is well knownthat the attribution of grains to minerals is not alwaysstraightforward even using standard microscopy, and greatlyrelies upon the skill of the petrographer. By comparing ourmethod to the point counting analysis we found that operatorerrors are similar.A small proportion of polygons inside the ROIs are notdetermined, because their size hampers reliable phase attribution(e.g., white regions in Fig. 3f and row 5 in Fig. 4). The averageundetermined area percent (A u ) inside the ROIs is 3.1 (Table 2, lastcolumn). The analyzed rocks contain at least four mineral phases.Assuming that the undetermined areas account for the contribu-tion of all the phases i, proportionally to the measured mode m i ,the error can be calculated for each i phase as A u ?m i .5. Concluding remarksThe presented methodology constitutes a Microscopic Infor-mation System (MIS) which can substitute for a standardFig. 7. Pie diagrams representing measured mode of 90 (out of 137) thin sections linked to reference grid. Legend for mineral phases of pie diagrams is as in Fig. 3f. Piediagrams allow for rapid visual check on the consistency of data between thin sections. (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)Fig. 6. Mode values measured inside ROI vs. ROI extent (mm 2 ) for quartz,plagioclase, K-feldspar and mafic minerals (respectively, Qz, Pl, Kf and Fm). Modeis calculated by averaging measurements performed on 30 thin sections of thesame rock (Barre gray granite, see Tables 1 and 2, Fig. 7) (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.).S. Tarquini, M. Favalli / Computers & Geosciences 36 (2010) 665–674 672 ARTICLE IN PRESSpetrographic microscope in carrying out preliminary thin sectionanalysis. Beyond this case, other MIS constituted by differentkinds of images can be defined: another image acquisition deviceand/or another image processing unit can be used maintaining thegeneral structure and functions of the MIS. The reference gridoptimizes handling of large thin-section databases and is ideal forapplying a database query on the basis of modal or texturalparameters. The result of the queries can be instantaneouslyretrieved and displayed, facilitating the interpretation of dataand/or inspiring further analysis. The MIS is also a suitable toolwith which to arrange a didactic collection of thin sections, or tostore a comprehensive database of all the analyses of apetrographic laboratory.The presented region growing segmentation procedure provedto be an effective tool for the analysis of 137 thin sections fromeight granitoid rocks. This algorithm showed an excellentexportability; once tuned on a granite, it has been successfullyapplied to all the studied samples without further tuning.The use of a MIS provides a means for multiscale analysis ofrock textures, GIS software being ideally suited to combine theinformation derived by different sources at different scales on thesame sample. As an example, the information acquired from athin section with a standard microscope and electron microscopeimages could be fruitfully combined.AcknowledgmentsWe would like to thank Eric Pirard, Sandy Cruden andFrancesco Mazzarini for useful discussions. Constructive reviewsby Michael D. Higgins (to an early draft), Frank Fueten andCaroline Perring are gratefully acknowledged. We would havenever carried out this work without the help of Marc Heinlein, towhom this paper is dedicated.Appendix A. The region growing function f gWe define our pixel connectivity as follows: every square pixelshares one side with 4 pixels and a corner with an additional 4pixels, these 8 neighboring pixels are connected with the centralone.f g is an unseeded function triggered at every image pixel p ithat can work on an arbitrary number of bands n. The regiongrows from the starting pixel p i outwards and then from theedge pixels of the growing area outwards. For every edge pixelf g computes the Euclidean color distance in the n-dimensionalspace between this edge pixel and every connected free pixel.A pixel is free if it is not yet assigned to a region. If this colordistance is lower than a fixed threshold t g , then the free pixel isadded to the growing region, else the propagation from thatedge pixel towards this connection is stopped. The ith (i.e. on p i )run of f g stops when all the edge pixels are dammed by t g . Thethreshold t g is a key value: comparing watershed segmentationto region growing, too low a threshold generates an under-segmentation and too high a threshold generates an over-segmentation in the sense of Barraud (2006). The best value is at g that provides a minimum number of regions without anexcessive merging of actual grains. For our granitoid rockst g =4.1 is adequate. When a single spreading process ends, if theregion is greater than a fixed number of pixels n p , this area isstored as a region, otherwise the loop skips to the next pixel.The threshol...