3D tree-ring analysis using helical X-ray tomography

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ARTICLE IN PRESS Model

ENDRO-25257; No. of Pages 8

Dendrochronologia xxx (2013) xxx– xxx

Contents lists available at ScienceDirect

Dendrochronologia

j ourna l ho me page: www.elsev ier .com/ locate /dendro

riginal article

D tree-ring analysis using helical X-ray tomography

an Van den Bulckea,∗, Erik L.G. Wernerssonb, Manuel Dierickc, Denis Van Looc,ert Masschaelec, Loes Brabantc, Matthieu N. Boonec, Luc Van Hoorebekec,ristof Hanecad, Anders Brunb, Cris L. Luengo Hendriksb, Joris Van Ackera

UGCT – Ghent University, Department of Forest and Water Management, Laboratory of Wood Technology, Coupure Links 653, 9000 Ghent, BelgiumSwedish University of Agricultural Sciences, Centre for Image Analysis, Box 337, SE-751 05 Uppsala, SwedenUGCT – Ghent University, Department of Physics and Astronomy, Proeftuinstraat 86, 9000 Ghent, BelgiumFlanders Heritage Agency, Koning Albert II-laan 19, bus 5, 1210 Brussels, Belgium

r t i c l e i n f o

rticle history:eceived 14 March 2013ccepted 18 July 2013

a b s t r a c t

The current state-of-the-art of tree-ring analysis and densitometry is still mainly limited to two dimen-sions and mostly requires proper treatment of the surface of the samples. In this paper we elaborate on thepotential of helical X-ray computed tomography for 3D tree-ring analysis. Microdensitometrical profiles

eywords:endrochronologyensitometryelical CT

are obtained by processing of the reconstructed volumes. Correction of the structure direction, takinginto account the angle of growth rings and grain, results in very accurate microdensity and precise ringwidth measurements. Both a manual as well as an automated methodology is proposed here, of whichthe MATLAB© code is available. Examples are given for pine (Pinus sylvestris L.), oak (Quercus robur L.) andteak (Tectona grandis L.). In all, the methodologies applied here on the 3D volumes are useful for growthrelated studies, enabling a fast and non-destructive analysis.

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Precise measurements of tree-ring features are key elements inendrochronological studies. To date, the most frequently stud-

ed features are tree-ring width and wood density (e.g. Stockernd Mysak, 1992; Worbes, 1995; Bhattacharyya and Yadav, 1999;herubini et al., 2003; Briffa et al., 2004; Cook et al., 2006;oninsegna et al., 2009; Eckstein and Schweingruber, 2009; Hanecat al., 2009; Rozendaal and Zuidema, 2011; Wils et al., 2011). Bothariables are measured along a radius on a cross-section of a stemr core increment. For ring-width measurements image acquisi-ion is mostly based on the use of a stereomicroscope and a linear

easurement stage connected with a computer, but many otherethods are described in literature (e.g. Polge and Nicholls, 1972;acedo et al., 2002; Mannes et al., 2007; Fonti et al., 2009; Jackson

t al., 2009; Moya and Tomazello Filho, 2009). In most cases, inrder to optimize contrast between growth-ring boundaries, inten-ive surface treatment is required (e.g. Sass and Eckstein, 1994;tehr et al., 1998; Spiecker et al., 2000; Kopp et al., 2005; Fonti

Please cite this article in press as: Van den Bulcke, J., et al., 3D tree-ring ahttp://dx.doi.org/10.1016/j.dendro.2013.07.001

t al., 2009; Gaertner and Nievergelt, 2010).The density of wood on a microscopical scale on the other hand,

s a variable that has widespread applications in and can provide

∗ Corresponding author. Tel.: +32 92646118.E-mail address: [email protected] (J. Van den Bulcke).

orCtatr

125-7865/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.dendro.2013.07.001

© 2013 Elsevier GmbH. All rights reserved.

ubstantive information for dendrochronology, dendroclimato-ogy, dendroecology, carbon sequestration, etc. (e.g. Guller et al.,012; Helama et al., 2012; Jyske et al., 2012; Nocetti et al., 2012).herefore microdensitometrical measurements are considered ofigh value (e.g. Schweingruber et al., 1990; Schinker et al., 2003;annes et al., 2007).All steps of the standard two-dimensional densitometry

pproach are given in Schweingruber (1988). Such approach isased on samples of well-defined thickness and to keep biases low,ample preparation has to be done carefully. Different issues haveo be considered when research on cores is required. With standardD densitometry, samples have to be thin to reduce geometricalberrations with X-rays penetrating non-perpendicularly and scat-ering. Furthermore, grain angle deviations and/or ring curvaturere not necessarily taken into account. Even with the techniqueeveloped by Bergsten et al. (2001), orientation of the samples

s still a key issue, as well as deviations from a certain presumedhickness.

Till now, the requirement for sample/surface preparation isften a laborious and time consuming process. Expanding tree-ing analysis to 3D is a feasible option, given the use of X-rayomputed Tomography (XCT). Grabner et al. (2009) clearly state

nalysis using helical X-ray tomography. Dendrochronologia (2013),

hat there is a need of high resolution XCT in dendrochronologynd in wood identification. Bill et al. (2012) illustrated the poten-ial of medical and industrial scanners for dendrochronology ofather large archaeological objects. Gureyev and Evans (1999) have

dx.doi.org/10.1016/j.dendro.2013.07.001


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ARTICLE IN PRESSG Model

DENDRO-25257; No. of Pages 8

2 J. Van den Bulcke et al. / Dendrochronologia xxx (2013) xxx– xxx

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Fig. 2. The structure direction can be estimated manually by measuring the angles �and � for each growth ring. That allows the computation of the actual orthogonal 3Ddo

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ig. 1. Helical XCT allows 3D imaging of highly anisotropic elongated samples, asllustrated by a surface rendering of a pine sample with coordinate axes.

hown that three-dimensional reconstructions of softwood sam-les is possible, using only a small number of conventional X-ray

mages. They have also shown how, in combination with auxiliaryptical photographs, vessel-free density of hardwood samples cane calculated. Unfortunately, many assumptions are involved in therocess and the authors report that it fails for some samples. Theytate that conventional computerised tomography can, in princi-le, provide a three-dimensional reconstruction of an object but

s considered unsuitable for their purpose as the samples have highly anisotropic shape (Barrett, 1990; Gureyev et al., 1996).ecent progress, however, enables to image such samples region byegion and stitch them together or even better image them directlysing the helical scanning set-up such as presented in this paper.urrently, the availability of lab-based equipment (Van den Bulcket al., 2009) as well as access to synchrotron facilities (Mannes et al.,010) has accelerated the use of XCT in wood science, which iseflected in the number of papers applying this technique. In thisaper we elaborate on the concept of ring width as well as micro-ensitometrical profiling in three dimensional space with almosto sample preparation using helical XCT. In a previous paper (Deidder et al., 2011) we have illustrated the use of helical XCT forigh-resolution densitometry and proved that accurate absoluteensity estimates could be obtained. The technique is independentf variations in sample thickness as both density as well as geome-ry are taken into account. Here we also elaborate on the theoreticalramework for 3D tree-ring analysis using the potential of high-hroughput helical XCT, overcoming several of the shortcomings oflassical 2D X-ray densitometry. The growth rings are usually notrthogonal to the transverse direction of the drill cores, e.g. dueo sampling or grain angle, and as a consequence direct measure-

ents of the width at the surface of the samples will be biased.e show how the angle/curvature of growth rings and grain angle

an be corrected using a manual as well as an automated method.urthermore, we exemplify the calculation of vessel-free density.he theory is applied on three different wood species showing thealidity of the concept and potential for future tree-ring research.

rowth-ring geometry

The use of helical XCT in tree-ring analysis necessitates newools and terminology which will be introduced in this section. Aypical scanned sample is illustrated in Fig. 1. For such samples weave a coordinate system where x refers to the tangential direction,

refers to the axial direction and z to the direction from bark to pith.bserve that x, y and z will never exactly match these directions,hich complicates the processing. The coordinates’ axes are also

ndicated in Fig. 2.We let c(z) = (0, 0, z) denote the straight line going through the

iddle of the sample, from bark to pith. At the locations where c(z)


oincides with the surface of an annual ring, we define g(c(z)) as theormal vector of the plane aligned with the growth ring at position(z).

(gv

istance between them as compared with the two-dimensional distance as derivedn the surface of the samples.

The vector field g along c defines a structure direction and can beeen as a generalisation of the structure angle, used to describe therientation of growth rings in planar cross sections (Gureyev andvans, 1999). When the structure direction is defined in the XCTmages, it is possible to measure ring widths correctly even though

does not coincide with the tangential direction and y does notoincide with the axial direction perfectly.

The vector field f indicates the direction orthogonal to adja-ent growth rings, and points out the approximate shortest pathsetween individual growth rings. Using g it is possible to trackaths orthogonal to the annual rings, but any such path will usu-lly leave the imaged sample. It makes more sense to try to measurennual rings widths as well as microdensity along c.

Measuring the structure angle on 2D images is a standard proce-ure in several software packages for dendrochronological analysise.g. Hietz, 2011) and can be used to estimate the location of theith as well as partially correct ring width measurements. With 3D

mages of the growth rings, more information is available and evenetter estimates and corrections can be performed.

We will now describe the methods that we have used to deter-ine the structure direction manually as well as automatically for

ome species. We will later show how it can be used to make accu-ate measurements of ring widths and local density measurements.

anual methodology

The following simple steps can be used to determine g manually,

. the transversal (xz) and radial slice (yz) along c of a reconstructedvolume, I, are loaded and displayed;

. growth ring and grain angles � and �, are indicated on the middlepaths through them as illustrated in Fig. 2;

. from these indications, the structure direction is calculated as across product.

utomated methodology

Estimating the structure direction in softwood samples is equiv-lent to estimating the normals to plane structures in the helicalCT images since the growth rings have a very sharp transition from

atewood to earlywood, locally. There are several options availableor this task and among them we have chosen to use the gradienttructure tensor or second moment matrix,

(x, y, z) (1)


Lindeberg, 2009). This is a better choice than for example the imageradients since the signal that it produces is maximal rather thananishing at the growth rings.


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ig. 3. Showing local anisotropy a for a pine sample. The orientation will be calcu-ated at the locations where the anisotropy has local maxima.

The computation is composed of the followings steps. First, theradient ∇I of the image I is estimated at each point of the imagesing Gaussian derivatives (Lindeberg, 2009).

The gradient gives directions in each voxel and we map these torientations with the outer product to form the structure tensor, aelf-adjoint matrix (Sheldon, 2010):

(x, y, z) = (∇I)T (∇I) (2)

hen each one of the nine components is locally averaged by aonvolution with a Gaussian filter with standard deviation �g. Theominant orientation at each point can then be found as the eigen-ector corresponding to the largest eigenvalue of T. We denote theigenvalues �1 ≥ �2 ≥ �3 and the corresponding orthogonal eigen-ectors ei, i = 1, 2, 3.

To determine where the image contains planar structures (i.e.rowth rings), the anisotropy ratio

= �1

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s most useful (Westin, 1994). A high anisotropy value indicateshat the gradients have only one preferred orientation.

In the following we only need to get the orientation in the mid-le of the volumetric image, i.e. along c(z). We call positions where

has a local maximum Maximally Directed Positions (MDP). At eachDP, the dominant orientation, which can be considered as a rep-

esentative for the structure direction, is then calculated, i.e. e1. Anxample of anisotropy variation is shown in Fig. 3. Note that in thistep we do not detect separate rings, but accurately estimate localrientation.

While the automated method works fine on the samples with-ut vessels, such as pine, some modification was required forpecies with vessels, especially ring-porous species. The vessels inhe oak and teak samples do disturb the calculations, so to run theutomatic method we introduced two preprocessing steps. First theessels were segmented (see ‘Vessel segmentation’) and then theorresponding voxels where filled with the local vessel-free den-ity. As such proper use of the automated methodology describedbove was possible as well.

sing the structure direction

Once that g is determined on c, both ring widths and micro-ensitometry can be calculated more accurately. A re-interpolationrocess is proposed and used for verification. In the followinge assume that the structure direction is determined everywhere

long the central line by interpolation.

ing widths

′


The deviation of g from the tangent of c, dc/dz = c , i.e. (0, 0, 1)ives the error of measured distances. A high deviation means thateasured distances in c are too long. More formally, a step of length

in the c′ direction means a step d〈c, g〉 in the g direction (〈 · , · 〉

tXt

PRESSonologia xxx (2013) xxx– xxx 3

enotes scalar product). To measure the length of a path betweenwo points a and b on c towards the pith we can calculate

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b − a

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∫ b

a

〈c′(z), g(z)〉dz, (4)

here zi = a + i(b − a)/N.Now assume that the position of ring-width boundaries are

etermined, and that their p coordinates are denoted pi, then theistance between adjacent rings is simply dp(pi, pi+1).

ensitometry

When calculating local density, one is faced with the questionow large and what shape the regions should be over which density

s averaged. With the goal of producing a density curve from barko pith, d(c(z)), we would like to average density orthogonal to gather than c. We have used the following formula for local density:

(z) = 1

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0

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0

Pz(r, ϕ)rdrdϕ (5)

here Pz is the plane orthogonal to g at c(z) centered at c expressedn a radial coordinate system with r being the distance from c and ϕhe angle in Pz. The parameter r0 determines the extent of the areashat will be used to obtain average density values. Note that Eq. (5)verages over a disk shaped region for each density value. That ishe preferred way to average in order to reduce the influence ofotations around the z-axis of the drill core and obtain a rotation-nvariant result.

valuation

For visual evaluation we are now able to produce 3D images ofhe sample, where the growth-rings are aligned orthogonal to theentral axis (i.e. c). Therefore we have made use of the followingesampling, which depends on z,

x, y, z) → (c + xu + yv) (6)

here u = u/||u||, u = c′ − Projgc′ and v = u × g. It maps annualings so that they are orthogonal to c. This remapping is used toroduce Fig. 6.

essel segmentation

Helical XCT also allows quantification of vessels, and, takingnto account the limits of resolution, vessel-free density calcula-ions. Vessels have the same density or X-ray absorption as air, son practice almost none in comparison to the wood. To segmenthe vessels the volume is first processed with an edge preservingilateral filter to reduce the influence of noise in the images. Next,he pixels are classified into air and wood. The pixels with air insidehe wood are re-classified as vessels. More information on the exactlgorithms used, can be found in Brabant et al. (2011). Using thislassification, density can be calculated based only on the pixelshich are known to be wood. That provides the vessel-free densityeasurements. An example of labelled earlywood vessels for oak

s shown in Fig. 4.

xperimental


Pith-to-bark samples of three different wood species are usedo illustrate the potential of 3D tree-ring analysis based on helicalCT: Scots pine (Pinus sylvestris L.): a softwood species with sharp

ransition between early- and latewood; oak (Quercus robur L.): a





Fig. 4. Labelled earlywood vessels of oak (colours are random).

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Fig. 5. 3D and 2D views on oak, pine and teak

ing-porous species with large earlywood vessels; teak (Tectonarandis L.): a ring-porous tropical wood species with small vesselssee Fig. 5).

ample preparation

Drill cores of oak and pine have a diameter of 5 mm, whereas theeak sample is rectangular, with a 1 cm × 1 cm square cross-section,awn from a disc. The samples were mounted in special holders,ade of a reference material with a density close to wood cell wall

ensity. By using such material and including the average grey levelf air which is considered zero density, the 16-bit grey values ofeconstructed wood cores can be directly converted to absoluteensities. For more information on this procedure as well as thealibration, see De Ridder et al. (2011). The maximum length of aingle core that can be scanned in one helical scan is approximately5 cm. Up to 7 drill cores or 3 rectangular shaped specimens can becanned in a single operation.

ata acquisition

The scanner used at Woodlab-UGent1 is a setup developed atGCT, the Ghent University Centre for X-ray Tomography.2 The

ystem offers a large range of operational freedom, all combined


n versatile acquisition routines (standard or fast scanning, tiling,elix, etc.). It has a generic in-house developed XCT scanner con-rol software platform (Dierick et al., 2010) that allows full controlf the scanner hardware. Scots pine, oak and teak samples were

1 http://www.woodlab.be.2 http://www.ugct.ugent.be.

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e bar = 10 mm, indications at the side in mm.

canned with helical XCT with a scan time ranging from 60 to20 min. Reconstruction is performed with Octopus, a tomographyeconstruction package for parallel, cone-beam and helical geom-try as well as phase correction and retrieval (Vlassenbroeck et al.,007). Helical reconstruction is based on the Katsevich algorithmKatsevich, 2002) implemented on GPU (De Witte, 2010). Beamardening correction was applied, both by hard- as well as softwareltering. The obtained approximate voxel pitch is 35 �m.

isualisation and analysis

Virtual cross-sections as well as 3D wood volumes were ren-ered in VGStudio MAX 2.0©. Manual demarcation of growth ringsnd grain angles as well as volume re-interpolation based on theanual measurements as well as the automated method were

oded in MATLAB© 7.11.0 (R2010b) and all code is available forownload.3 Vessel segmentation is performed in Morpho+(Brabantt al., 2011).

The automated procedure outlined above takes in total 3 mino run on the pine sample. No manual interaction is required evenhough manual validation always should be a concluding step inny analysis.

esults


The three dimensional volumes allow for correcting both ringnd grain angle simultaneously. To obtain a density profile, theverage of each re-interpolated tangential slice (x–y plane) is taken

3 DHXCT, code for dendrological investigations of helical XCT images. Availablender the BSD-license at http://www.cb.uu.se/ erikw/DHXCT/.


http://www.woodlab.be

http://www.ugct.ugent.be

http://www.cb.uu.se/~erikw/DHXCT/

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J. Van den Bulcke et al. / Dendrochr

Fig. 6. Full densitometric profiling (y-axis in kg/m3) for pine (A), oak (B) and teak(C), with indication of the standard deviation (grey surface). The black line in thefull profile figure represents the uncorrected profile, while the red line is the profilewith correction for the structure direction. The uncorrected and corrected detailgive a more detailed view on a selection of the full profile. The blue line in thecorrected detail of oak is the vessel-free density. For teak, the difference betweenc(

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saiiE2pdAsirtvraMcasfiaseaaipa2dftatFuptivodYsThe data acquisition set-up presented here allows feasible scan-

lassical (only correction for the structure angle; green line) and 3D densitometrycorrecting for the structure direction; red line), is given.

rom the entire volume and is considered a true estimate of abso-ute density. Fig. 6 illustrates the results when no correction ispplied and when ring and grain angle corrections are taken intoccount. The zoomed parts of the profiles clearly indicate a nar-ower standard deviation and a more distinct demarcation of theing boundaries. For visual inspection, the respective images areiven as well. It is also possible, within the range of resolution, toalculate vessel-free density. The result of this approach is given


n the corrected profile for oak, where the blue line has an averageensity which is higher than the normal densitometric profile (red

ine), mainly at the level of the earlywood vessels.

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The manual, and for wood species with clear growth rings alsohe automated methodology, enables to retrieve the 3D ring width.ig. 7 illustrates the difference between measuring ring width ofine and teak while correcting for the structure angle only (2D)nd correcting for the structure direction (3D). For the pine sample,bres are more straight than for the teak sample and as such theifference with standard ring width demarcation is rather small<3%), while this is considerable for the teak sample due to theigh tilt of the fibres. For oak, the difference between the 2D andD methodology gives a similar graph compared to pine (data nothown).

iscussion

The helical XCT scanning methodology and accompanying den-itometrical analysis as discussed in this paper, has some cleardvantages. It is not depending on sample thickness and resultsn a density value of the inner structure of the core, without tak-ng edges into account which could be compressed due to drilling.xtractives still need to be removed if required (Bergsten et al.,001; Helama et al., 2010) and the influence of metallic com-ounds should be taken into account, although density changesue to metallic inclusions have indicator value on polluted sites.s discussed by Vansteenkiste et al. (2007), the presence of crystaltructures influences the density measurements too, as they inducencreased diffraction. Due to the partial volume effect, related to theesolution, single crystals can not be segmented and excluded fromhe density analysis. Such an approach would only be possible forery high resolution scans (<2 �m). One option would be to cor-ect for crystal presence by species specific correction. Of course,pplication of a linear correction factor, similar to that described inothe et al. (1998), based on gravimetrically determined densities,

an eliminate some differences too. Compared with the classicalpproach, helical XCT also has the advantage of high-throughputcanning with almost automatic retrieval of a densitometric pro-le with limited operator-time and sample preparation. Obviously,ngled rings and fibres due to natural growth (non circular crossection, impact of roots and buttresses, spiral or interlocked grain,tc.) or non-perpendicular sampling can cause substantial devi-tions in classical 2D densitometry as density is an integrationlong the thickness of the object in the scan process itself. Sim-larly, when profiling for fibre density measurements, the radiallane is of interest (Gureyev and Evans, 1999) and substantial ringngles can distort the microdensity profile. Both approaches areD methods and do not take into account the information in threeimensions. In classical densitometry one normally only correctsor ring angles (or grain angle), but not for different grain direc-ions (or ring angles) along the thickness of the sample. For oaknd pine this is, in these examples, a minor problem, but for teakhe influence is significant as can be seen in the bottom graph ofig. 6. Due to the information available in three dimensions, the vol-mes can be accurately morphed to obtain corrected densitometricrofiles. Also, the occurrence of twist of the core in z-direction dueo stresses in the tree, is not problematic thanks to the processingn 3D. In addition, vessel size quantification and the calculation of aessel-free densitometric profile is also possible, as is exemplifiedn oak. Due to exclusion of the earlywood vessels, it is clear thatensity is still low owing to the presence of mainly parenchyma.et tyloses are difficult to deal with, as they have, in most cases,imilar X-ray density as wood and can not be segmented properly.


ing at a resolution of 20 �m. Standard 2D techniques currentlyllow resolutions of 10 �m, but advances in XCT most likely willllow at least similar and even better resolution in the near future.





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ig. 7. Ring widths for pine and teak corrected for the structure angle only (fullross-section illustrates the ring boundaries (dotted white line) and the ring width

oreover, although current 2D systems have a high precision, theirccuracy can be compromised as structure direction can not beccounted for. Furthermore, sub-voxel resolution can be reachedy interpolation when images are relatively noise-free. For moreetailed analysis one can also do directed high-resolutions scans

n specific parts of interest (Van den Bulcke et al., 2009).Proper conditioning of the cores and subsequent mounting in

he sample holder are the only preparation steps required forrill cores, and thus a clear advantage. Approximately 1 m of drillores can be scanned in half an hour with a resolution of 50 �m.or higher resolutions, such as the ones mentioned in this paper,lightly longer scan times are necessary, yet the development ofew scanners (Masschaele et al., 2013) and optimized protocolsill allow shorter scan times. Reconstruction of the 50 �m volumes

urrently takes no longer than 15 min and conversion of grey valueso absolute densities is only a matter of minutes. Density profiles of

m drill cores can thus be obtained within an hour, without takingnto account the structure direction.


The proposed methodology as such not only increases the pre-ision of local density measurements due to correction of ringnd grain angle, also ring width measurements can be corrected

tue

ig. 8. Filters with a flat shape can not be used to average wood density close to the pithn a cylindrical coordinate system.

and corrected for the structure direction (dotted line). A transversal and radiale double arrows).

imilarly. This is possible with the manual approach, but also forhe automated approach when growth rings are quite clear, whichs often the case for temperate but less straightforward for trop-cal species. The example of teak given in this paper pinpoints athe large differences that can occur if not taking into account theorrection for the structure direction. Note that the relative errorshange between rings, which is particularly more critical than aonstant relative error. At the same time, the new positional infor-ation can also be used to correct the positions of any measured

natomical feature or tissue composition from pith to bark.With the manual approach proper ring indication and good den-

itometric profiling is obtained simultaneously, however it is still aabour-intensive process, scaling with the amount of rings. Also, the

anual correction currently does not take into account curvaturef growth rings, especially important closer to the pith or in mainlyropical species with locally highly curved growth rings. This coulde done by applying the two dimensional method described byothe et al. (1998) in three dimensions. The automated interpola-


ion of the volume to obtain corrected density profiles that can besed for proper ring demarcation would reduce the work consid-rably and could correct for curved features such as growth-ring

where the rings are curved. The figures show filters defined with constant radius


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ARTICLEENDRO-25257; No. of Pages 8

J. Van den Bulcke et al. / Dend

ngles. Curved filters are required in those situations and a some-hat extended description of the samples as well including the

ocal curvature.Close to the pith the ring structure can be modelled as cylin-

rical shells. Then appropriate filters are easily designed. We given example in Fig. 8. More generally, the curvature has to be esti-ated everywhere along the samples. This can be done using

urvature estimators based on local orientation (Rieger et al., 2004;ernersson et al., 2011). For regular samples there is even an

nterpretation of the curvatures. The second principal curvatureirection k2 will point in the fibre direction and the reciprocal ofhe curvature 1/�2 will give the distance to the pith. The curvaturestimation is in general sensitive to the fine structures of the woodo samples less regular than pine would need much preprocessing.

full discussion of these issues is beyond the scope of this paper.

onclusions

The use of 2D X-ray scanning has already been explored androven valuable for wood anatomy and densitometry (e.g. Gureyevnd Evans, 1999; Badel et al., 2006; Helama et al., 2012), yet 3Dcanning and accompanying analysis is less elaborated on (Mannest al., 2010). Current developments in XCT allow us to overcomeome of the problems one might encounter when applying 2D scan-ing, such as the limited field of view, the dependence on samplehickness, ring and fibre angles, etc. The method proposed here,ased on helical XCT, can give an artefact-free mapping of both the

nternal three dimensional structure as well as density. Althoughelical XCT at this resolution is not common yet, XCT is alreadyecoming a routine microscopic technique, several commercialystems are available and many universities and research institutesave one or more XCT scanners at their disposal. The extra expenseo build a helical XCT system compared to a standard XCT systems small. Only an extra elevating stage is required together with

new reconstruction algorithm. Therefore we believe that helicalCT has the potential to be a common technique soon and that theethod in this paper could find a broad use.The methodology elaborated on offers the opportunity to study

ree-ring width and densitometry without cumbersome prepara-ion of the samples and with extraction of valuable qualitatives well as quantitative data, taking into account ring and grainngle. Obviously, the obtained results depend on the achievableesolution and sample size. Automated methods can significantlyccelerate the proper correction of ring and fibre angles and canetect growth ring borders too. Another benefit with automatedethods is that they allow exact reproduction of results and

hat they are objective in the sense that no manual decisions arenvolved.

Helical XCT also opens up perspectives for tropical species, evenf they lack distinct growth rings (e.g. Verheyden et al., 2005; Ohashit al., 2009). Proper analysis of their growth and climate responseenerates valuable environmental information in the frameworkf global change, energy content and climate reconstruction.

There is also a potential for this method in isotope research. Inome cases intra-annual, tangential slices of wood are analysed forsotope ratios (e.g. Verheyden et al., 2004; Pons and Helle, 2011).owever, this involves a microtome that cuts the wood in a certain,xed direction, not taking into account the structure direction, andherefore not perfectly tangential. ‘Screening’ such samples before-and with this methodology would allow to adjust the angle of


he microtome knife during sampling in order to obtain perfectlyangential slices.

Furthermore, from an ecological point of view, volumetric X-raymaging can contribute significantly to the understanding of tree

G

G


rowth, vessel formation, etc. such as investigated in Kitin et al.2004), Garcia-Gonzalez and Fonti (2008), and Fonti et al. (2009).lso, with the improvement of automated demarcation of ring bor-ers using a model with curved rings, even more accurate densityeasurements will become available.In all, helical XCT and both the manual and automated metho-

ology applied on the 3D volumes are useful for density and growthelated studies, enabling a fast analysis resulting in essential data.

cknowledgements

The Special Research Fund of the Ghent University (BOF) iscknowledged for the doctoral grant to Loes Brabant.

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Documents

3D tree-ring analysis using helical X-ray tomography