morphology-based macro-scale finite-element timber models

Computer-Aided Design 43 (2011) 72–87

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Computer-Aided Design

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Morphology-based macro-scale finite-element timber modelsRaffaele De Amicis a, Mariapaola Riggio b,∗, Gabrio Girardi a, Maurizio Piazza b

a GraphiTech, Center for Advanced Computer Graphics Technologies, Via alla Cascata 56/c, I-38100 Povo (TN), Italyb Department of Mechanical and Structural Engineering, University of Trento, Via Mesiano 77, I-38100 Trento, Italy

a r t i c l e i n f o

Article history:Received 7 January 2009Accepted 17 September 2010

Keywords:Wood growth layerImage analysisGeometrical modeling

a b s t r a c t

This paper presents a non-invasive technique that can extract an accurate geometrical description ofgrowth layer surfaces in wood. The method has been validated for sawn spruce elements (Picea AbiesKarst.). The aim is to implement a procedure to model domain geometry in the numerical analysis ofwooden elements, taking into account the intrinsic variability of the material. The approach presented bythe authors avoids internal imaging and achieves a digital 3Dmodel of growth layers, using, as input data,images of the ring pattern, which represents the growth surface boundary curves, visible on all the cutfaces of the wooden element.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Wood is a very complex building material, even considering aclear wood element, with no natural defects. The fibrous struc-ture and the layering due to annual rings make wood stronglyanisotropic, with large differences in mechanical properties par-allel and perpendicular to the grain. Furthermore, heterogeneitiesaffect lumber strength and their effects are difficult tomeasure andmodel, due to the variability that occurs within the timber mem-bers. Nevertheless, for the purpose of numerical analysis, wood isoften considered homogenous and isotropic. In some applications,however, numerical modeling of wood should account for mate-rial heterogeneity and for anisotropy. In this case, a possible ap-proach is to have the model closely match the structure of the realspecimen, implementing so-called ‘‘morphology-basedmodels’’. Amorphology-based model draws the parameters of the numericalmodel directly from the physical structure of the material. Ratherthan treating the material as a statistically homogenized contin-uum, it is represented as a collection of discrete elements repre-senting specific structural features.

In this paper, the authors describe their research into amethodology generating the geometry of three-dimensional‘‘morphology-based’’ finite element (FEM) models of woodenelements, taking into account the intrinsic variability of thematerial at the level of growth rings.

Growth layer modeling is a necessary first step in the devel-opment of a more complex description of the material macro-scopic organization. It provides information on two fundamental

∗ Corresponding address: Department of Mechanical and Structural Engineering,University of Trento, Via Mesiano 77, I-38123 Trento, Italy. Tel.: +39 0461 282586;fax: +39 0461 282505.

E-mail address:[email protected] (M. Riggio).

0010-4485/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2010.09.003

aspects that influence the mechanical behavior of wood at thisscale: macroscopic local variation of the orthotropic directions ofthematerial and repetitive variation of stiffness in the radial direc-tion.

Despite simplification (i.e. scale of analysis, mechanical andgeometrical approximation of the layered wood structure), theproposed morphological approach aims at achieving a realisticcharacterization of themechanical behavior ofwoodunder specificload conditions, and in particular, at describing the development ofnon-uniform stress fields caused by the material heterogeneity onthe scale analyzed.

In order to appropriately define the geometry of growth lay-ers in wood, for numerical simulation, a method has been devel-oped, based on the complementary application of known imageanalysis and geometrical modeling techniques, which extracts anaccurate geometrical description of all the growth surfaces in aprismatic wooden element, solely on the basis of the ring pat-tern or boundary curves of the growth layers visible on all six cutfaces.

Image-analysis techniques are applied to highlight thematerialtexture and detect the growth increment boundaries on theelement faces. Subsequent phases are: (a) geometrical descriptionof the boundary curves on the faces, (b) the construction of anappropriate model of the growth surfaces from the boundarycurves.

‘‘Morphological’’ FEM models, using growth layer geometricaldata, have been analyzed and the results experimentally validated.

2. Detection and measurement of growth layers in wood: stateof the art

The three-dimensional structure of wood includes both longi-tudinal cells, running along the trunk, and transverse cells, which

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R. De Amicis et al. / Computer-Aided Design 43 (2011) 72–87 73

form rays that are oriented radially. The longitudinal cells have ayearly variation in density and color that depends on the varyinggrowth rate and leads to concentric growth rings. Thewood formedearly in the growing season, light in weight with large lumina andthin cell walls, is called earlywood or springwood. The primaryfunction of earlywood in the living tree appears to be fluid conduc-tion. The final portion of the growth ring, which is denser, darker incolor, with smaller lumina and thicker cell walls, is called latewoodor summerwood. Because of the increased amount of cell wall sub-stance, latewood has a dominant influence on some of themechan-ical properties of wood. In wood species with gradual changes incell dimension across the ring (e.g. spruce), ring boundaries, be-tween the latewood of one year and the following earlywood, arevery distinct, while the intra-ring boundaries, between earlywoodand latewood of the same year, are less evident.

Different methods for the detection and measurement of theannual rings in wood have been developed for different scopes.

Ringwidthsmaybeused tomatch ring patterns fromone tree toanother, allowing dendrochronological as well as dendroclimaticanalysis. Moreover, due to correlation with density and strength,annual ring width is a parameter used in visual strength grading.

In the case of dendro-analysis, the use of the microscope isthe basic approach, while, in timber strength grading methods,ring width can be measured by hand or found indirectly usingdensimetric profiles [1]. Microscopic analysis is also used tomeasure accurately the width of early- and latewood.

An attempt was made in 1964 to detect growth rings auto-matically with a microphotometer equipped with an automaticrecorder [2]. Today, image analysis techniques are used forcomputerized tree ring width measurement, especially in den-drochronology.

Many low-level processing techniques can be applied in wood-ring analysis, to eliminate noise and highlight the relevantfeatures of the material texture. Image thresholding and segmen-tation for feature extraction are the most common. Thresholdingcan preserve the connectivity of the detected boundaries of thetree rings and eliminate noise in grey scale images [3,4]. Once thedifferent regions of the image are delineated in low-level process-ing, they can be classified using various high-level processing tech-niques. Edge detection is the most common method for detectingmeaningful discontinuities in grey-scale images. The basic idea un-derlying most edge-detection techniques is the computation of alocal derivative operator (i.e. Canny, Roberts, Sobel, compass, zerocrossing edge detectors). An edge can be defined as the bound-ary between two regions with relatively distinct grey-level prop-erties. In the investigated species, the ring boundaries have verydistinct grey-level properties, while the intra-ring boundaries, be-tween earlywood and latewood of the same year, are less evident,because the contrast depends on the rate of transition. For the pur-poses of dendrochronologists, the intra-ring boundaries are gener-ally ignored. For this reason, and to avoid detection of edges alongprominent rays and other radial features, Conner et al. [3] extractedthe ring boundaries from digital images of wood transversal sec-tions introducing some directional modifications of the Cannyalgorithm [5], based on a priori knowledge of the wood texturestructure. The method, implemented for the detection of ring pat-terns, is not very effective at an abrupt change in boundary di-rection, as often happens in textures on the longitudinal faces,where the more external growth layers are cut along the longitu-dinal–tangential (LT) anatomical direction.

Soille and Misson [6] proposed a mathematical morphologymethod for measuring ring areas, based on the fact that treerings have outstanding anatomical–morphological characteristics(i.e. they can be considered concentric circles, so small parts of treerings can be considered parallel).

Most of the methods, proposed so far, evaluate the ring widthin different orthogonal directions and then average the results,producing large errors in the case of asymmetric growth.

Ring detection on the longitudinal faces of sawn timbers,especially on the longitudinal–tangential planes, is complicated,in comparison with detection on transversal faces, by a lack ofgeneral morphological rules. A method to extract information onthe orientation and on the distance between growth layers visibleon the longitudinal cut faces of boards was developed by Hanburyand Gardeux [7], based on texture analysis.

3. The method

The proposed method semi-automatically detects and modelsthe internal layering of wood by analysis of the external texture onthe cut surfaces of a wooden element.

The scope of the implemented methodology is the definitionof a procedure and of the relevant design tools for modeling thegeometry of the domain in the numerical analysis of wood atgrowth layer scale. We place some limits on the complexity of thethree-dimensional domain, concerning the shape of the elementand the features of the material. In particular, at this stage ofresearch, prismatic clear wood elements (without defects) can beaccurately modeled.

The method is based on two main steps: acquisition andprocessing of images of the wood surface texture; and modelingof the relevant geometric data from the processed images. For this,software has been developed that integrates image-analysis andgeometric modeling techniques in a single architecture.

In order to validate the method, tests were carried out on CADmodels of spruce samples of different size, ring orientation andgrain characteristics. The generated geometrical data, exportedas an IGES file, was examined and compared with the relevantgeometrical features of the real samples.

3.1. Detection of growth surface boundary curves

In this paper, a layer in space containing all fibers producedwithin a growth period is referred to as a growth layer, whilea curved surface in space, with zero thickness, representing theinterface between two consecutive growth layers is referred toas the growth surface (ring or intra-ring boundary surface). Theintersection of the growth surfaces with the element faces arereferred to as boundary curves (Fig. 1).

The method implemented for detection of the set of points onthe boundary curves of the growth surfaces, from the images ofthe ring texture of wooden samples, is a semi-automatic stepwiseprocess that can be summarized as follows:

• Acquisition of the wood surface textures;• Image pre-processing;• Analysis of material texture images, detection of rings and, last,

of intra-ring boundaries;• Post-processing of the detected boundaries.

The choice of the appropriate acquisition method for ring patternsdepends primarily on the size and location of the object ofinterest. A CCD camera can acquire the texture of structural timberelements. In this research, a digital camera (Hasselblad H3DII),with a sensor of 39 megapixels and a macro lens, of focal length118.7mm,was used for testing themethod on structural elements.The macro lens adequately identifies the material texture, suchas the intra-ring pattern. Among the advantages of a large formatsensor is the reduction of image artifacts, in the case of digitalcomposition of different shots of the same element face.

74 R. De Amicis et al. / Computer-Aided Design 43 (2011) 72–87

Fig. 1. Ring pattern (boundary curves), growth surfaces and growth layers definedby NURB curves and surfaces.

A flat-bed scanner was used to perform test on samples oflimited size, to define the minimum needs of a low-cost dataacquisition setup. In this case, textures were digitized at 600 dpiand RGB scale, 48 bit depth.

In principle, the better the input digital image, the simpler andmore reliable will be the image processing. The quality of theacquired image depends on both the acquisition method, mainlythe technique used, the resolution and the lighting conditions,and also on the characteristics of the material texture, especiallythe intrinsic species features (i.e. gradual or abrupt transitionfrom earlywood to latewood) and the quality of the surfaces(i.e. polished, with orwithout stains, dust etc.). The choice of imageresolution determines the accuracy of the digitization processand permits segmentation methods to work appropriately. In thisresearchwe saw that, for clear softwoods, the boundaries betweengrowth layers are the major feature, if compared to other featuressuch as rays, stains etc. Once the textures have been acquired,the application can generate the mapped 3D model of the timberelement.

Using the implemented application, a 3D texturized modelof the prismatic sample is built, once the acquired images ofthe material texture have been imported, for each face of thesample. Image filtering and analysis are then applied directly to thesample images on the 3Dmodel. Each separate face is selected andthe operations described below are applied to the correspondingimage.

The core of the growth layer detection procedure is based onimplementation of the morphological method described by Soilleand Misson for ring measurements [6].

In mathematical morphology [8,9], a grey-level image is seenas a topographical relief, where each pixel is associated with anelevation proportional to its intensity. From this point of view animage of tree rings, on the transversal face of a log, is seen as a highplateau cut by a series of concentric valleys.

In morphology a transformation is given by the relation ofthe image with another set, called a structuring element, whose

shape is chosen according to some a priori knowledge of the imagestructure geometry.

The basic building blocks formanymorphological operators are‘‘erosion’’ and ‘‘dilation’’.

The eroded and the dilated values of an image at a givenpixel are, respectively, the minimum and the maximum of theimage, in the window defined by the structuring element, whenits origin is at the pixel. Erosion removes pixels to the boundariesof objects in an image, while dilation adds pixels on objectboundaries. The number of pixels added or removed depends onthe size and shape of the structuring element used to process theimage. The ‘‘opening’’ operator allows recovery of most structureslost by erosion, dilating the image previously eroded using thesame structuring element. The dual operator of the morphologicalopening is the morphological ‘‘closing’’, which tends to recoverthe initial shape of the image structures that have been dilated,including in the set of the foreground regions all backgroundstructures that cannot contain the structuring element.

According to [6], ring edges are detected by means of amorphological segmentation, using a watershed procedure, whichgroups the image pixels around the regional minima of the image(the so-called catchment basins) and locates the boundaries ofadjacent groups along the crest lines of the gradient image. Thegradient is a grey-scale image, where each pixel value indicatesthe contrast in the close neighborhood of that pixel. This operationenhances especially the transition from one ring to another,because it has more contrast than the intra-ring boundaries. Thegradient image, the so-called ‘‘mask’’, must then be filtered by a‘‘marker function’’, which marks the relevant image objects andtheir background, and consists in a binary image containing therelevant minima.

Differing from [6], our task here is to highlight both the ring andintra-ring boundaries. For this purpose, two markers are defined(Fig. 2).

First a marker of the earlywood is defined as the output of thefollowing sequence of morphological filtering:

(1) ‘‘Open–close’’ filter by a 3 × 3 square structuring element,in order to filter out minor bright and dark image variations.

(2) ‘‘Opening’’ by a square structuring element to reducediscontinuities along the growth layer boundaries, caused by thepresence of bright streaks in the image. The size of the structuringelement is set according to the width of the largest streak and thenarrowest earlywood region: it must be slightly larger than theformer but smaller than the latter.

(3) ‘‘Black top-hat’’ to extract small elements and details. Itsfunction is to detect contrasted objects on non-uniform back-grounds. It is the difference between the ‘‘closing’’ of the imageand the input image and extracts dark structures. The size of thestructuring element must be set so as to exceed the width of thelargest dark latewood regions.

(4) Threshold of the black top-hat: the threshold output will bethe earlywood marker image.The watershed transformation is then applied to the mask, whileconsidering the earlywood markers as the set of the relevantminima. This operation gives one of the tree ring boundaries.

The secondmarker, defining the latewood regions, results fromthe distance transformof the image obtained by superimposing thefirstmarker and its watershed. The result of the distance transformis a grey level image similar to the input binary image, except thatthe grey level intensities of points inside foreground regions arechanged to show the distance to the closest boundary from eachpoint. The watershed of the mask, taking the marker just created,gives the second boundary in the growth layer.

The quality of results of the edge detection procedure ismainly dependent on the quality of the input image and thecharacteristics of the sample. Good contrast between earlywood


Fig. 2. Block diagram of the proposed image-processing chain for the growth layer boundary detection based on mathematical morphology.


and latewood layers, as well as uniform orientation and spacingbetween layers allow automatic detection, using the techniquepresented, of almost all the growth layer boundaries, and all theirextent. However if conditions are not optimal, discontinuities canoccur in the detected boundaries. In addition, unwanted artifactsresulting from knots, splits, checks and other wood defects canbe present. Therefore post-processing is needed to link growthlayer fragments and to remove unwanted noise from the edgemap.

The implemented edge-linking method is based on the localanalysis of the break points [10]. That is, the characteristics ofthe pixels are analyzed in a small area portion, inside a 12 × 12moving window. The window scans the input grey level edgemap, converting it into three intensity levels using two thresholdvalues. Decisions on linking the edge break points are made basedon their gradient directions. In particular, an edge is linked withits neighbor if the line joining the two edges and the gradientdirection are no more than 45° apart. Further, the edge-linkingmethod proposed by Conner et al. [3] has been integrated inthe implemented application. This is based on some assumptionsthat are generally true in the case of growth layer patterns inradial–tangential (RT) and longitudinal–radial (LR) planes, such asthe nearly constant width of the ring along its length.

Once edge-linking is performed, a snake technique is appliedto increase the continuity of the contours and smooth them. Thealgorithm used for minimizing snake energy for each snake pointis given in [11].

Contours created by means of the snake technique are orderedpoint sets. In a further stage of the implemented methodology, B-spline parametric curves are generated from those point sets.

3.2. Geometrical modeling of growth layers

The output data of the image analysis phase, described in theprevious paragraph, are sets of points which approximate theedges, on the sawn element faces, of thewood growth layers. Fromthese sets of points a geometric model of the growth surfaces isgenerated by means of a semi-automatic process, whose steps canbe described as follows:

1. Generation of parametric curves approximating the sets of datapoints along the boundaries of the growth layers on the elementfaces;

2. Post-processing of the generated curves (for deletion, joiningtwo broken curves andmodifying control point position, aswellas for modeling missing curves);

3. Generation of the surfaces approximating the shapes of thegrowth layers in the sawn element;

4. Post-processing of the generated surfaces (manipulating thecontrol points on the boundary curves);

5. Export of the data.

In order to perform the curve modeling task, from the coordinatesof the ‘snakes’ points, the pixel coordinates in the image space haveto be mapped in the model space.

The snake points describe some but not all the properties ofthe shape of the growth layer boundary curve. The results ofcurve generation, in fact, also depend on the type of constraintsset to define the curve generation process and, therefore, themathematical curve representation.

In order to appropriately represent the natural smoothness ofthe material layers, the most important requirement that has to besatisfied is the C1 continuity of the modeled curve.

As regards the sample data, in principle they should beconsidered as ‘‘hard constraints’’, so that the curve must meetthem, exactly passing through all of them. In this case, the problemis briefly referred to as an interpolating problem. Nevertheless,

the satisfaction of this requirement may produce a curve ofsubstantially different morphology, compared with the expectedone. If a violation of the ‘‘hard constraint’’ requirements is feasibleand the interpolation of the snake point could be considered as a‘‘soft constraint’’, i.e. the distance between the sampled data andcurve is seen as an acceptable placement error, the problem isbriefly referred to as an approximation problem.

In order to identify a curve which satisfactorily fits the shapeof the growth layer, we compared the following mathematicalrepresentations:

• Euler spiral interpolating spline.• Non-rational non-periodic cubic B-spline.• Almost vanishing polynomials.• Composite Bézier.

One of themost sophisticated interpolating splines, based on Eulerspirals, satisfies C1 continuity and effective containment of theeffects of local changes [12]. The curves generated by this methodare obtained using the free library Libspiro [13]. This library takesan array of spiral control points and converts them into a seriesof Bézier splines, which can be plotted in the range of coordinatesdelimiting the sample face.

Non-rational cubic B-splineswith a non-periodic knot sequencehave also used, to keep C1 continuity along the growth layer profile.Knot values are repeated at the beginning and at the end, withmultiplicity equal to the order of the function, and internal knotsequally spaced; in such a case, the resulting B-spline curve alwaysinterpolates the first and last control points.

In [14,15] the mathematics of the polynomials used for thegeneration of the boundary curves is described, from the snakepoint set, considered as empirical data with a tolerance describingthe absolute error at each data point. The curves, generated withthis method, are obtained using the free software CoCoA [16] andplotted in the range of coordinates delimiting the sample face. Thetolerance is defined by a circle, of radius 0 ÷ 1 (0.25 pixels, in ourcase) and centre in the sampled pixel.

The effectiveness of a composite Bézier of degree 3 and C1 con-tinuous at the joining points, for modeling growth layer bound-aries, was also investigated. In this case, the curve control pointsdo not coincide with the whole set of snake points. Control pointsare encoded in Freeman Chain codes [17] and the algorithm pro-posed in [18] is used for detection of the dominant point.

The curvesmodeled according to the abovemethods are shownin Fig. 3. In Fig. 4 the error between the modeled curves and theexperimental data is represented as a Euclidean distance.

In Table 1 the maximum and route mean square (RMS)distance value, as well as the curve length are reported, for eachmathematical representation. Euler spiral interpolating splinesclearly underline the ‘‘scatter’’ of sample points, this shown by thegreater length with respect to the mathematical representationsof others. Almost vanishing polynomials allow generation of verysmooth curves, although the distance between themodeled curvesand the sample data is significant. The length of the compositeBézier, generated using Freeman Chain codes, is considerablyshorter than the Euler spiral interpolating spline, but the RMS isstill significant. The best compromise between smoothness andproximity to the experimental point set is given by the B-splinecurves, in fact the curve length ranks second shortest, whilethe Euclidean distance and RMS are the smallest. Therefore, B-spline curves have been used in the implemented application.Moreover, from the technological point of view, they presentthe additional advantage of being directly compatible with thegeometrical modeler used – Open Cascade- [19].


Fig. 3. (A) Euler spiral interpolating spline; (B) non-rational non-periodic cubic B-spline; (C) composite Bézier; (D) almost vanishing polynomials, superimposed on thedigital image.

Fig. 4. Euclidean distance between the modelled curves and the experimental data shown in Fig. 3.

Table 1Error estimation of the modeled curve.

RMS distance (mm) Max distance (mm) Curve length (mm)

B-spline 0.1213 0.2028 80.6014Composite Bézier 0.4552 1.0357 80.5551Alm. van. polyn. 0.5511 1.3625 78.0708Euler spline / / 85.3111


Fig. 5. User interface for modelling the growth surface boundary curve.

Once the curves have been generated they can be modified bythe user (step 2) (Fig. 5). Curve post-processing is completely con-trolled by the analyst, who can delete curves of low approximationquality, connect disjoined curves, modify the curve shape as wellas model any curves that failed during automatic generation. Toallow curve modification, a ‘‘manipulator’’ is attached to the curvecontrol points.Manipulators (often called ‘‘handles’’ in 2D systems)are small graphic elements in 3D that the user can click and drag,causing changes in the corresponding object. In our case, manipu-lators are used to modify the position of the curve control points,within the plane defined by the relevant element face. The user canmodelmissing curves by directly inserting the curve control pointsalong the relevant ring lines, on the texture of the modeled block.

The growth surface is then generated from its boundarycurves. To do this, each curve is ordered and correlated to thecorresponding one on the adjoining face. Using the algorithm,presented by Stork et al. [20] and Fiorentino et al. [21] the boundarycurves can be given in any order: they are classified and, ifnecessary, reversed and reparameterized. If the distance of twocurves along the common edge is smaller by a factor calculatedas minimum distance of the curves on the same face, the systemconsiders themboth as belonging to the samegrowth layer; so theyare considered as boundary curves of the same surface.

Surface boundaries are generally defined by four curves, two foreach parametric direction. In the implemented application, eachpair of curves has been made compatible in a transparent way forthe user by means of the functions of Open Cascade so that theyhave the same degree and are defined over the same knot vector,i.e. the same number of control points. Open Cascade providesan algorithm, specifically designed to be used in connection withfillets, for the construction of the filled surface from a series ofboundaries which serve as path constraints. The algorithm acceptsthree or four curves as boundaries of the target surface. TheConstrainedFilling class provided byOpenCascademakes availablefunctions for:

– defining the surface boundaries– implementing the construction algorithm– consulting the result.

As the surface filling algorithm in Open Cascade is specificallydesigned for use in connectionwith fillets, this algorithm generallyprovides very good results. The user can in any case, thanksto the visual feedback provided by the application, assess thequality of the generated surface. If the result is not consideredadequate, we can modify the position of the control points on the

boundary curves, using the qualitative information provided by thetexture. This approach is very satisfactory, as demonstrated by theexperimental results.

The implemented application allows direct modeling onlyof three- or four-sided surfaces. In some cases, especially fordiagonal-grained timber elements, it may be necessary to workwith five-sided patches. In this case, it is possible to model the fiveboundary curves and import them into CAD software. Analogouslyit must be noted that in the case of ‘‘tangential’’ specimens, orso-called back-sawn timber with rings roughly parallel to thebroad face, the implemented method for surface generation is notappropriate to define the geometry of the most external layerswhich have only two boundary curves, nor of those layers withtwo boundary curves, in the longitudinal direction, both on thesame element face. The latter limitation is due to the implementedapplication which allows modeling of a single boundary curveon each element face, so two disjoint curves on the same faceare automatically connected and the resulting surface will exhibitunpredictable bulging.

4. Verification and applicability of the method

In order to validate themethod, testswere performed on sprucesamples.

The robustness of the method for growth surface modeling isstrictly connected to the quality of the approximation of theirboundaries by means of B-spline curves. Therefore the qualityof models of both growth surfaces and curves were separatelyverified. The verification analysis was based on the comparisonof the width of rings measured both on the real sample andfrom the generated parametric curves. Ringwidthsweremeasuredon the real sample by means of an optical dendrochronologydevice: a measuring stage Lintab 3.2 r⃝ equipped with a LeicaMS5 r⃝ microscope. The ring-widthswere recorded bymeans of theTSAP r⃝ software.

The distances between the B-spline curves approximating thedetected boundariesweremeasured, after exporting the geometricmodel, as an IGES file, in commercial CAD software. In order totest the effectiveness of the automatic procedure for growth layerboundary detection and modeling, the analyzed output data arethose obtained after automatic generation of the B-spline curves,avoiding any manual post-processing of the model.

The accurate measurement of both ring and intra-ring widthswas carried out only on the RT plane. For this purpose, the test wasdone on a portion of a disc from a spruce log.


Fig. 6. Model of a ‘‘Type A’’ element and cross-section location.

The sample was prepared to ensure high quality output digitalimages: the surface of the stem cross section disc was sanded withan orbital sander and successively finer grades.

To assess the effectiveness of the method in detecting growthsurface boundary curves on the long faces, a visual estimate wasmade by superposing the detected edges on the digital image of areal sample.

Spruce elements of different size and grain characteristic, withgrowth rings oriented in a generic direction with respect to thegeometrical axis of the specimen, were used to test the robustnessof the surfacemodeling phase. Samples were labeledwith a capitalletter to denote their size (A, B andC) and anumber for the differentgrain characteristics (1 and 2). A first series of tests was carried outon small samples (‘‘Type A’’: 8 × 8 × 20 cm; ‘‘Type B’’: 10 × 15 ×

20 cm). As regards the grain characteristics, two classes of sampleswere considered: (1) ‘‘clear’’ elements with straight grain andwith‘‘cross-grain’’, that is, with the anatomical longitudinal directionnot coincident with the geometrical axis, and (2) elements withknots and extreme local fiber deviation.

Subsequently tests on timber in structural dimensions (‘‘TypeC’’: 9 × 9 × 170 cm) were carried out. In this case, to minimizethe presence of extreme local fiber deviation such as around knots,some limits on knot number and size were set. Size limits forknots comply with the visual strength grading standards stated in

UNI 11035-1/2 [22,23], which sets limits to macroscopic strength-affecting characteristics for timber, in order to assign timberelements to a given strength class. The tested element was in classS1, where the limit for single knots is the ratio A of the minimaldiameter to the width of the element face, in S1 equal to or lessthan 1/5; while knot clusters are evaluated using the ratio Ag ofthe sum of the minimal diameters of all the knots, in a 150 mmrange, to the width of the element face. For elements of S1 class, Agis equal to or less than 2/5.

Graphical data were compared with the relevant featuresobserved on the corresponding sample. For this purpose, themodels were imported into 3D CAD software. Cross-cutting planeswere modeled in order to visualize the layer pattern in variouscross-sections along the virtual specimens. Similarly, the realsamples were cut at the same distance along the longitudinal axisand the cross-sections were acquired and imported into the CADmodel, in order to superimpose real on virtual sections. Two crosssections, at one and two-thirds of the length of ‘‘Type A’’ and ‘‘TypeB’’ samples, were considered (Fig. 6), while the ‘‘Type C’’ elementwas cross cut at the mid-span as well as at and besides the knots,where knots had no more effect on local fiber orientation (Fig. 7).

The distances between the modeled surfaces were measuredfrom the obtained cross-sections of the model, along the samelines where the measurements on the real sample were taken.Measurement lines were traced, approximately perpendicular tothe growth ring, at the center of the cross section, as shown in Fig. 8.

5. Analysis of results

Fig. 9(a) shows the portion of the log disc used for assessingthe accuracy of the curve modeling phase; the reference linefor measurement is also represented. Fig. 9(b) and (c) show thesuperimposition, on the image of the disc sample, of theautomatically detected ring and intra-ring curves, respectively.

In Fig. 10 ring widths measured by means of the imple-mented method are compared with those measured with thedendrochronology apparatus. Errors between the ring-widthsmeasured on the model and on the real sample were expressed asthe ratio between the two values (Fig. 11).

As shown in Fig. 9(b) and (c), the method was able to detectmost ring boundaries; but it could not detect very narrow ringboundaries, especially in a series of narrow layers. As regardsaccuracy in detecting the intra-ring boundaries, results shownin Figs. 12 and 13 report a systematic error, which is most

Fig. 7. Model of a ‘‘Type C’’ element and cross-section location.


Fig. 8. ‘‘Type C’’: modelled curves and reference line superimposed on sample faces, at (a) 14.7 cm, (b) 53.7 cm, (c) 122.7 cm and (d) 147.7 cm from the initial face.

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Fig. 9. Automatic detection of ring and intra-ring boundaries: original image (a), superimposed detected ring (b) and intra-ring (c) edges.

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Fig. 10. Comparison between ring-width series of Picea Abiesmeasured manually with the Lintab 3.2 r⃝ and those computed from the automatically detected rings.


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Fig. 11. Relationship between ring widths measured manually with the Lintab 3.2 r⃝ and those computed from the automatically detected rings.

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0.40

0.60

0.80

1.00

1.20

1.40

1.60

Fig. 12. Comparison between latewood width series of Picea Abiesmeasured manually with the Lintab 3.2 r⃝ and those computed from the automatically detected rings.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Fig. 13. Relationship between latewood widths measured manually with Lintab 3.2 r⃝ and those computed from the automatically detected rings.


Fig. 14. Automatically extracted boundary curves superimposed on the originalimage on an LT texture of Picea Abies.

probably due to the fact that the boundary between earlywood andlatewood in spruce is not abrupt and was differently detected bythe microscopic interpretation and by the implemented automaticprocedure. We note that the Leica MS5 microscope has up to320x magnification, which is insufficient to define clearly theearlywood–latewood boundary, on the basis of the differencesin cell wall and lumina sizes, according to Mork’s method [24].Therefore, in the twomeasurement procedures, a different portionof so-called transition-wood is included in the detected latewoodportion.

Visual analysis shows that the results obtained on the longi-tudinal faces of spruce samples are comparable with those forthe transverse plane (Fig. 14). Some problems occur in detectingintra-ring boundaries, especially in the case of very different spac-ing between layers. This depends on the fact that the morphologi-cal segmentation, used for edge detection, is applied to the entire

Table 2Errors between the ring-widths measured on the real samples and on the model.

Element type Mean Std. dev.

Type A-1, sample with straight-grain 0.989 0.124Type A-1, sample with diagonal-grain 1.266 0.638Type A-2, sample with a knot 1.218 0.645Type B-1, sample with straight-grain 0.978 0.173Type B-1, sample with diagonal-grain 1.032 0.158Type B-2, sample with a knot 0.992 0.112Type C 1.457 1.056

image. At each filtering step, a unique structuring element is used,whose size is set according to themaximal–minimal size of the rel-evant image structures (in this case the earlywood and latewoodregions). On the longitudinal faces of the wooden element in par-ticular, the width of the growth layers, tangentially cut, can varyconsiderably. In this case, a piecewise segmentation, on image re-gions with uniform texture characteristics, should overcome thisproblem.

As when assessing the quality of the curves approximating thegrowth layer boundaries on the external faces of the element,surface modeling was evaluated by comparing the width of ringsmeasured both on the real sample and from the curves resultingfrom the intersection of themodeled surface and the cutting plane.In this case, good results were obtained for type ‘‘A’’ and ‘‘B’’samples, as shown in Fig. 15 and Table 2. In particular, Fig. 15represents the mean value of the ring width measured in themodel, at the 1/3 and 2/3 length positions, versus that measuredin the real sample. In Table 2 the error between the ring-widthsmeasured on the real samples and on the model was calculatedas a percentage of the real sample widths. Some problems occurfor surfaces where the boundaries consist of more than fourcurves, as is typical for some growth layers in diagonal-grainedelements. In this case the surfaces cannot be generated directlyin the implemented application; the results, however, have beenanalyzed generating the surfaces with commercial CAD software,after exporting the boundary curves. The main problems occurredin samples with knots (‘‘Type A-2’’ and Type C).

Fig. 16 shows the error distribution along the length in the‘‘Type C’’ element. The error is expressed by the distance, in mm,between the real and the corresponding modeled curve takenalong the reference lines approximately normal to the ring curves,

0

0.5

1

1.5

2

2.5

3

3.5

4

Fig. 15. Relationship between ring widths measured manually with Lintab 3.2 r⃝ and those computed from the models.


0

0.5

1

1.5

2

2.5

3

Fig. 16. ‘‘Type C’’: error distribution along the element length: scheme of the element and position of the cross-sections (top).

as shown in Fig. 8(a)–(d). We measured only one of the four ringboundary curves. In Fig. 8(a)–(d), pictures of the sections of sampletype ‘‘C’’, at 14.7, 53.7, 122.7 and 147.7 cm from the initial face,are shown and the reference line and modeled curves used for themeasurements are superimposed.

The method, at the current stage of research, cannot predictdeviation of the layers in the element, around the wood knot. Inthis case, distortion is due to the knot-bump causing growth layersto bulge from the cylindrical form of the stem. Thus errors dueto method accuracy derive, basically, from the limit of the NURBSmathematics in modeling abrupt slope changes, such as thosenear knots. Moreover, errors obviously occur where ‘‘extraneousobjects’’, like the knots themselves, are located.

6. ‘‘Morphological’’ FEM analysis of wooden elements

In previous research, definition of the geometry ofmorphology-based models used different approaches, corresponding to thescope of the analysis and the relevant structural level of thematerial organization. For calculation of the properties of woodcells, realistic geometries were obtained by Astley et al. [25] andPersson [26] frommicrographs of transversal sections of the woodtissue. In the longitudinal direction, however, the geometry wassimplified by extruding the cell wall pattern.

At macroscopic scale, one of the first attempts to analyze woodelements by means of 3D FE models was made by Al-Dabbaghet al. in 1972 [27], who represented latewood and earlywood witha simplified layered model of different stiffness and anisotropiccharacteristics.

A realistic description of the grain pattern and knots in boardswas provided by Cramer and McDonald [28]. However, theresulting model is two-dimensional and can describe the behaviorof boards, but not of thicker elements such as beams.

In Perré and Turner [29], a bidimensional mesostructuremodel is proposed to capture drying effects in softwood due tomaterial variation across the growth rings. Nairn [30] proposed the‘‘material point method’’, to simulate transverse fracture in woodat the scale of the growth ring. Two-dimensional morphologies ofgrowth rings were modeled from the digital images of transversesections of solid wood.

Differing from the cited works, the methodology we proposein this paper lets us model realistic, three-dimensional geometriesof the wood structure. The aim of the proposed approach is toanalyze the effects of material layering and orientation on stressdistribution in a 3D field.

6.1. Application of themorphological approach: FEM analysis of woodin transverse compression

The effectiveness of the proposed methodology in supportingthe mechanical characterization of wood was experimentallyvalidated [31]. For this purpose, ‘‘morphological’’ FEM models ofwooden elementswere implemented. Subsequently, the capabilityof the model to depict the effects of material layering andorientation on woodmechanical behavior was verified, comparingnumerical results with those obtained from mechanical tests.

The level of magnification of the model permits effectivestudy of the behavior of wood under specific load conditions. Inparticular, morphological models were implemented to study thebehavior of specimens loaded in transverse compression.

The earlywood/latewood alternation and ratio are importantparameters in explaining the differences in behaviour of woodunder transverse compression [32,33]. Under both radial andtangential compression (with load directed perpendicular ortangential to the growth rings), the behavior of wood can beexplainedwith the ‘‘weak layer’’ and the ‘‘spaced column’’ theories,respectively [32]. Accordingly, a relatively weak earlywood layercontrols most of the deformation in radial compression while, inthe case of tangential compression, the load is distributed betweenearlywood and latewood in proportion to the relative stiffness ofthe materials.

In the implementedmodel, the behaviour ofwood in transversecompression is analyzed at an intermediate angle of load on thering, with the aim of evaluating how the differences in stiffness ofthe two materials and their orientation give rise to the develop-ment of a non-uniform stress distribution.

Besides the radial alternation of stiffness, another source ofmesoscale wood variability is variation of the anatomical direc-tions. Indeed, growth layers follow the stem taper and, within eachlayer, the fibres can twist, leading to the so-called spiral grain [34](Fig. 17). In the model studied, the behavior of wood in transversecompression is analysed at an intermediate angle of load to grain(gross fiber direction). We note that at this level of analysis, theanisotropy due to microscopic material characteristics, such as themicrofibril angle, is not taken into account.

In the proposed ‘‘morphological’’ approach, FEM models ofwood are implemented, considering an orthotropic material,whose material axes vary locally, according to the topology ofthe adopted finite element. A general purpose FEM analysis code(Ansys) was used, and a routine was implemented to assign localmaterial directions from the triad computed for each finiteelement, with the X-axis connecting the first two nodes, lying


Fig. 17. Spiral grain: fiber direction within the growth layer.

Table 3Assumed stiffness properties (MPa) of early-wood and latewood, at 12% M.C.

Elastic constant Earlywood Latewood

EL 7710 23900ER 150 670ET 200 1091

GLR 675 1172GLT 397 1315GRT 30 65

µTL 0.006 0.0425µRL 0.009 0.0135µRT 0.26 0.39

along one of the two parametric directions of the growth surface.In the case of spiral grain, the axis defining the local longitudinaldirection rotates by an angle αt (in Fig. 17), which is the meanvalue of the grain angles measured on the longitudinal faces of thespecimen, from the inclination of shrinkage splits or grooves drawnusing a scribe.

The species chosen for investigation is spruce (Picea AbiesKarst.), characterized by a gradual variation of material propertieswithin the annual growth layer. This choicewas determined by therelatively good availability of data on the mechanical properties ofthe two seasonalmaterials for this species. However, data reportedin the literature (i.e. [35–38,25,26,39]) are difficult to compare,due to the differing sets of conditions of the timber (moisturecontent, density, species). In our research we chose to adoptparameters for the earlywood and latewood materials, based onthe values determined by Persson [26], considering only two intra-ring materials (the so-called transition wood is mostly included inthe detected latewood portion) (Table 3).

Further, amodelwhere timber is analysed as homogeneous andorthotropic with respect to a Cartesian system of coordinate axesattached to the element was analysed. In this case,

Table 4Assumed stiffnessproperties of spruce(MPa).

EL 10400ER 236ET 387GLR 650GRT 29GLT 597µRT 0.42µTL 0.017µRL 0.018

The Young modulus as well as the rigidity of clear sprucewood, in the three anatomical directions, were experimentallydetermined, bymeans of load tests, according to EN 408 [40], usingspecimens taken from the same log. The stiffness matrix used forthe homogeneous model is reported in Table 4.

Mechanical tests were then carried out, in order to compareresults of both the proposed morphological FEM model and thesimplified model of wood. For this purpose, transverse compres-sion tests were performed on a cubic specimen (20× 20× 20 cm),in which the longitudinal and transversal material directions donot coincide with the element geometrical axes.

The test method included two phases. In the first phase, loadswere applied within the elastic limit; the test was repeated severaltimes, each time fitting four strain gauges on the four unloadedfaces of the specimen, at different positions (Fig. 18), in order tomap the stress distribution. HBM (DD1 type) mechanical straingauges, with a gauge length of 25 mm and accuracy of 2.5 ×

10−3 mm, centred at the points {A, B, C}×{1, 2, 3, 4, . . . , 6} in thegrid in Fig. 18, were used tomeasure vertical strain during loading.A further test was carried out to failure, in order to qualitativelyanalyze the failure mode of the specimen.

Fig. 19 shows the diagrams of the numerical and experimentaldisplacements for each mapped point in the specimen. Numericalresults are presented for both theproposed ‘‘morphological’’model(model 2) and for themodel of timber considered as homogeneousand orthotropic with respect to the geometrical direction of theelement (model 1).

As can be observed, the numerical results of the latter modelaverage the displacement values at all locations, while themorphological model depicts well the strain variation within thespecimen. In the latter case, the accuracy of the prediction isstrongly dependent on the parameters assumed for modelling theintra-ring materials, which we took from the literature and werenot experimentally determined.

In the FEM analysis, a concentrated 25 kN load is considered,corresponding to 80% of the experimental load at the proportionallimit. Even limiting the analysis to the linear range, the failure

Fig. 18. Sampled points on the test specimen (compression test). Grid for the placement of the strain gauges on the transversal faces (1st and 3rd) and the longitudinal faces(2nd and 4th).


-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

-0.25

-0.2

-0.15

-0.1

-0.05

0

Fig. 19. Scheme of the numerical and experimental displacements found at the various sampled points on the test specimen, represented in the grid {A, B, C} ×

{1, 2, 3, . . . , 12} in Fig. 18. Numerical results of the ‘‘morphological’’ model (1) and of a simplified homogeneous model (2).

initiation locus, corresponding to the area of tension stressconcentration, is closely identified. This can be observed byqualitative comparison of the pictures of the transversal faces ofthe specimen after destructive compression tests with the plots of

the Z-component of stress (perpendicular to the applied load) inthe numerical model (Fig. 20).

In particular, it can be observed that the actual position of theinitial cracks in the real specimen is close but not coincident with


Fig. 20. (a) Transversal faces of the specimen after destructive compression test; (b) FEM analysis: Z-component of stress.

that predicted by the numerical simulation. This is because in themodel the properties of the intra-ring materials are consideredconstant for all layers; but this is a simplification of the real mate-rial, where variability also occurs between different growth incre-ments, and failure initiates in the more stressed and weaker layer.

While failure initiation can be pinpointed by a linear elastic‘‘morphological’’ model assuming local variation of the orthotropicdirections, for crack propagation analysis, methods based onfracture mechanics should be adopted. However, this impliesknowledge of material parameters, such as the fracture toughness,at either medium or large scale, according to the type of model.

The lack of a standard method for determining the fracturetoughness of wood as well as the influence of condition factors,such as species, orientation, grain angle and moisture state onthe measurement of this parameter, limits the applicability of theproposed morphological models beyond the linear range.

7. Conclusions and further developments

We present here a methodology based on the integration ofknown computer vision and geometrical modeling techniqueswith the aim of implementing a novel procedure to model domaingeometry in the numerical analysis of wooden elements, takinginto account the intrinsic variability of the material. The proposedapproach yielded very interesting and promising results: it allowsspatial modeling of the material layers, using as input data onlyimages of the ring texture at the cut surfaces. We had good resultsusing low-cost image acquisition devices, even though for in situsurveys we recommend the use of high resolution CCD cameras.

The method has been implemented, so far, to be applied towooden samples with specific geometrical and anatomical charac-teristics. It allows effectivemodeling of straight-grained and cross-grained prismatic clear wood elements, with rings generically ori-ented with respect to the geometrical axes of the element.

Today, the applicability of the method to structural size timberis limited by the current restrictions of the implemented applica-tion. In particular, it is hampered if surfaces with less than three

and more than four boundary curves or with two disjoint curveson the same face have to be modeled. Moreover, the presence ofknots and strong distortion of material layering, which is unavoid-able in structural size elements, is not currently considered. There-fore, in future research, we will refine the methodology describedto take account of different sources of variability of the materialat the macroscale, to achieve a more predictable model for largetimber elements.

To allow the adoption of the proposed methodology forcharacterization of a timber element in service, the currenthardware could be coupledwith other portable input sources, suchas sonic tomography devices, which could be used to detect localfeatures such as large knots.

The geometric data, defining the wood growth surfaces, aregenerated within the implemented application and exportedas IGES files. Therefore only data relative to the surfaces andassociated edges and vertices are imported in the finite elementmethod (FEM) program. The solid model to be meshed can then begenerated either through a top-down approach, following a CSGscheme, or through a bottom-up procedure, from its boundaries.

Alternatively to FEM analysis, the NURBS approximating thewood growth surfaces could be used as basis functions in anumerical model based on the isogeometric analysis method [41].The advantage of the isogeometric method is that the basisfunctions represent geometrical objects with a higher degree ofprecision and smoothness than those obtained with simplepiecewise-polynomial C0-continuous basis functions, as com-monly used in finite element analysis.

The results of morphology-based FEM analysis, using geomet-rical data obtained from the implemented methodology, confirmthe effectiveness of the proposed approach in highlighting localphenomena and failure initiation loci, in wood specimens underspecific loading conditions. Modeling the intra-ring layers, i.e. theinterface between earlywood and latewood of the same year, is ofgreat interest for wood species having significant changes in cellpattern across the ring.


The effectiveness of the analysis at the proposed scale can befurther improved through specific investigation of the mechanicalproperties of intra-ring materials.

Acknowledgements

This research has been partially supported by the FundingAgency EU Marie Curie, by the project titled ‘‘SAGA: ShApesGeometry Algebra’’.

The second author was partially supported by the Provincia Au-tonoma di Trento, by the post-doc fellowship titled ‘‘DIGITIMBER(DIGItal technologies in TIMBEr Restoration)’’.

The authors are grateful to D. Minh-Son, former researcher atthe GraphiTech Foundation, and to the student M. Santini, for theircontributions to the research.

The authors also thank Hasseblad A/S for allowing them to testits products for the purpose of the presented research.

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Raffaele De Amicis is the Director of GraphiTech. Since 2005 he belongs tothe Experts Board Member Panel for Mathematics and Information Technologyand Industrial and Information Engineering of the CIVR, Italian Committee forEvaluation of Research of theMinistry of Education. He holds aM.Eng. inMechanicalEngineering and a Ph.D. on Surface Modeling in Virtual Environments fromthe University of Bologna, Italy. He has been research fellow at the IndustrialApplications Department of the Fraunhofer Institute for Computer GraphicsResearch (IGD) in Darmstadt, Germany and senior researcher at the InteractiveGraphics Systems Group, at TUD—Technical University of Darmstadt. He has beeninvolved in several projects funded by the European Commission, NATO/OTAN—North Atlantic Treaty Organization, Government Institutions and by industries. Hisinterests are in CAD, virtual reality, virtual engineering, geovisual analytics, scienceand technology policy. He also serves as Consulting Professor, in computer graphics,at the Department of Information and Communication Technology at the Universityof Trento, Italy.

Mariapaola Riggio is a post-doc fellow at the University of Trento. She receivedher Ph.D. in Structural Engineering in 2007 at the University of Trento. In 1997she received a master’s degree in Architecture from the University of Florence,Italy with a thesis on Architectural Restoration. In 1999 and in 2000 she workedat the Fraunhofer-Institut IGD of Darmstadt, Germany on the application ofdigital techniques for architecture. Her current research interests are modeling,preservation and control of old timber structures. In particular she has focusedher research on mechanical characterization of timber elements using novel digitaltechnologies.

Gabrio Girardi has been working in the GraphiTech Foundation since 2005. Heholds a M.Eng. in Engineering; He graduated with a thesis on ‘‘Texture-based 3Dmodelling of timber elements’’. In the past few years he has been involved in alarge number of industrial and European projects dealing with the application of3D computer graphics in the product development process aswell as in the CulturalHeritage domain.

Maurizio Piazza is Full Professor at the Department of Mechanical and StructuralEngineering, University of Trento. He has carried out research activities in fieldstypical of the structural design and of the structural rehabilitation, initially atthe Istituto di Scienza e Tecnica delle Costruzioni of the University of Padova(1978/1992), then at the Department of Mechanical and Structural Engineeringof the University of Trento. The research has been and is mainly devoted tothe themes of steel structures, composite steel–concrete and timber–concretestructures, and timber structures. As regards the latter theme and in particularexisting timber structures, the research areas deal with traditional connections,mechanical characterization, static and seismic behavior, rehabilitation proceduresas well as fire resistance.

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