Int J Interact Des Manuf (2012) 6:65–73DOI 10.1007/s12008-012-0140-5

ORIGINAL PAPER

Modeling morphological features of timber from X-raytomographic images

Bruno Simões · Mariapaola Riggio ·Raffaele De Amicis

Received: 7 May 2011 / Accepted: 11 January 2012 / Published online: 1 February 2012© Springer-Verlag 2012

Abstract The use of timber, as engineering material, isinfluenced by the wood heterogeneous structure, which canbe observed hierarchically over a spectrum of length scales.At the macroscopic level, mechanical properties of woodare affected by anatomic characteristics such as annual ringthickness, knots, checks, etc. In some applications, in orderto depict the variability of mechanical properties, numer-ical modeling of wood should account for material heter-ogeneity. In this case, a possible approach is to have themodel closely match the structure of the real specimen, byimplementing so called “morphology-based models”. In thiscase, for the definition of a realistic geometrical domain ofthe numerical model, a description of the investigated struc-tures is necessary. For this purpose, non-destructive imagingtechniques, such as X-ray tomography, can be used. In thispaper, we describe a method by which the morphologicalfeatures of the timber material, at the macro scale, can bemodeled from computed tomography images. Conversion

This research has been supported by the Provincia Autonoma di Trentowith the post-doc fellowship “DIGITimbeR” (DIGital technologies inTimber Restoration) and by the Programme “Marie Curie InitialTraining Network”—Call ID “FP7-PEOPLE-2007-1-1-ITN”—GrantAgreement N◦ 214584-2 (SAGA). The paper is based on furtherdevelopment of the original paper “Use of X-ray tomography andCAD techniques for “morphology-based” wood elements models”presented at the IDMME-Virtual Concept 2010 Conference.

B. Simões · R. De AmicisGraphiTech, Via alla Cascata, 56/C, Trento 38123, Italye-mail: bruno.simoes@graphitech.it

R. De Amicise-mail: raffaele.de.amicis@graphitech.it

M. Riggio (B)Department of Mechanical and Structural Engineering,University of Trento, via Mesiano, 77, Trento 38123, Italye-mail: mariapaola.riggio@ing.unitn.it

of three-dimensional image data into geometrical models,by using state-of-the-art image-based techniques, availablethrough use of commercial software is briefly discussed.A novel methodology is also presented. The implementedmethod allows overcoming the major drawback of traditionalapproaches used for the generation of models from computer-assisted design data, which is the lack of automation in themodel construction pipeline. Advantages and limitations ofthe different methodologies are discussed.

Keywords Wood features · X-ray tomography ·Image analysis · CAD-based modeling

1 Introduction

Because of its natural origin, the physical properties of woodfrequently exhibit an unusually wide degree of variability.The internal structure of wood at the different scales gives riseto anisotropic behavior, with large differences in mechanicalproperties parallel-to and perpendicular-to-grain. In additionto natural variability and anisotropy, wood is also porous andheterogeneous. Heterogeneities derive from growth charac-teristics and take the form of knots, grain deviations, irregu-larities in the rings’ structure, pitch pockets, shakes, etc.

The variability of the properties of wood can be analyzedat the various structural levels of the material organizationby means of so called “morphology-based models”. Theseaccount, in terms of numerical simulation, for details of woodanatomy and variations in structure within specimens.

Different approaches can be followed to model domaingeometry in the numerical analysis of morphology-basedwooden elements, depending on the scale of analysis andthe method adopted for imaging given features.

The authors in [1] present a procedure to achieve a digital3D model of growth layers, using, as input data, images of the

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Fig. 1 Modeling process pathsfrom CT data

ring pattern, which represents the growth surface boundarycurves, visible on all the cut faces of the wooden element.

In [2], the combined use of close range photogrammetry,to map and measure external features, and acoustic tomog-raphy, to detect internal defects of wood, is proposed for onsite characterization of structural timber.

Having in mind the hierarchic organization of wood, theselection of the most relevant non-destructive technique, forimaging heterogeneities in the material, is directly related tothe resolution required.

Techniques for imaging the internal structure of wood,based on different methods using radiations, can be classifiedaccording to the characteristic scale (i.e. frequency, energyor wavelength) of the radiation that interacts with the woodspecimen.

The highest transmitted energy, corresponding to thesmallest wavelength (10−12 m), is obtained with X-raymethods.

X-ray imaging allows creating a precise map of the inter-nal heterogeneities of the sample, through the determinationof the attenuation coefficient of the radiation in a single thinlayer of the sample. The attenuation phenomenon is propor-tional to the mass density of the wood, and, therefore, thedensity variations observed on radiographic images describethe distribution of various anatomic structural elements ofthe specimens under inspection and the water content in thecell wall and in lumina.

X-ray computed tomography (CT) images can be rep-resented in three dimensions as a stack of cross-sectional,two-dimensional images that are reconstructed from tomo-graphic projections. A standard way of representing 3-D

images formed from the reconstruction of tomographic pro-jections, is to divide the reconstruction volume into a regulararray of small voxels (volumetric pixels) and assume that thereconstructed medium is constant inside each voxel [3]. Thismodel then serves as the starting point for different inspectionand evaluation techniques.

The flowchart in Fig. 1 outlines the different alternativepaths that can be followed to obtain a meshed model for finiteelement (FE) analysis from CT data. The traditional approachis to fit contours of image data by using CAD techniques andthen generate volume discretization starting from boundingsurfaces (path 1 in Fig. 1). In the last few years a number ofsoftware solution have been made available on the market forvisualization, image analysis, modeling and meshing of datafrom diagnostic imaging (e.g. MRI, CT, etc.). These softwarepackages have introduced a significant level of automation inthe model construction pipeline, by using voxel-based meth-ods for both surface generation (path 2 in Fig. 1) and meshing(path 3 in Fig. 1).

In this paper a novel methodology for automatic genera-tion of geometries from the CT data of wooden structures isintroduced. This is used to facilitate the implementation ofaccurate CAD-based FE models. A flowchart of the proposedmethod is illustrated in Fig. 2.

2 Materials and methods

2.1 The test material

The specimens used in the investigation were taken fromboth new and old timber samples. The species analyzed is

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Fig. 2 Modeling pipeline according to the implemented method

spruce (Picea Abies Karst.), which is characterized by grad-ual change in cell dimension across the ring; between the ear-lywood, light in weight and paler in color, and the latewood,which is denser and darker. Some of the tested specimensare also characterized by the presence of other macroscopicfeatures: indented rings, which consist in localized circu-lar or lenticular areas with reduced growth, indented towardthe pith [4]; resin pockets, which are plan-convex cavi-ties between growth increments with accumulation of resin;knots, consisting in portions of branches embedded in thewood; and checks, which are ruptures in wood along thegrain, generally developed during seasoning.

Old timbers come from dismissed structural elements,which were affected by biotic decay. In particular, insects(Anobium punctatum—Furniture beetle) have infested sap-wood portions and tomographic images generally appearmore blurred than those of new wood.

The test material has been classified, according to the dif-ferent features of the samples, as following: (a) clear woodelements with large annual rings; (b) clear wood elementswith variable thickness of annual rings (c) elements withdensity variation along the rings, i.e. indented rings, resinpockets; (d) elements with density variation across the rings,i.e. knots, checks; (e) old wood, with biotic decay (insectattacks).

2.2 Data acquisition

The instrumentation used for X-ray tomography is a thirdgeneration spiral system, available at the Forstlichen Ver-suchs- und Forschungsanstalt (Freiburg, Germany) (CT.LOG, MiCROTEC). The rotating part is constituted by a60◦ fan angle X-ray source and a 100 cm long detector array,disposed in an arc focused at the X-ray source.

The reconstruction algorithm interpolates the measure-ments, in order to transform spiral scans to circular one(“interpolated z” algorithm, where “z” is the axis of thescanner translation). Through a filtered back-projection algo-rithm, the attenuation values, measured in each projection,

are mapped in the reconstructed image and associated witha specific cross-sectional pixel size. The resolution of theacquired CT data is 1 × 1 mm in the transversal directionand 5 mm in the longitudinal direction. Finite resolution hascaused some blurring of material boundaries, especially incase of very thin growth layers.

A schema of the process from data acquisition, to datatransformation and interpretation is represented in Fig. 3.

2.3 Segmentation

Segmentation can be described as the process of identify-ing, within an image, which pixels belong to each region ofinterest (RoI), associated to different materials. In this study,macroscopic anatomic structures were grouped in the follow-ing features: earlywood and latewood layers, cavities, knots.Checks, resin pockets and bark were all classified as cavities,considering their role in the mechanic behavior of the mate-rial, even if the density of the last two structures is generallyhigher than that of the surrounding material.

Most image-segmentation algorithms require original datafiles (in this case, density values) to be compressed in therange of 0–255 gray levels. Standard algorithms, availablefrom commercial software (Matlab and ScanIPTM), basedeither on boundary detection or region growing techniques,have been used for segmenting images, following the meth-odological approaches as in the modeling pipeline of Fig. 1.

Following the novel methodology proposed (Fig. 2), seg-mentation is performed on the original binary data, thus main-taining the precision of the acquisition.

Each image of the initial dataset can be viewed as a vec-tor, with one coordinate for each image pixel. Image pixelscan be thought of as real numbers ranging from 0 to 4,000.Considering that typical X-ray CT images have tens of thou-sands of pixels, then we are facing a critical problem whereeach image lies in a very high dimensional space, call itpixel space, P . Therefore, every image I ⊆ P can be highlyexpressive because I is very high dimensional. Besides that,I is also very sparse (of high co-dimension) in P , since a ran-dom choice of values for each pixel will not give anythingclose to an image. Thus, the direct study of I and its seg-mentation is expected to be extremely difficult, unless oneseverely restricts the range of subjects for the images.

The strategy used to segment images without compressingX-ray CT values to RGB values, goes through the analysis ofisopycnic contour maps. An isopycnic map is simply a wayof representing three-dimensional data on a two-dimensionalsurface, where density can be seen as a third dimension. How-ever, applying only this method is still insufficient to modela wood structure from a set of images. For this reason, wehave extended this idea to a new algorithm, built on top ofWilliam V. Snyder’s algorithm 531 [5]. Algorithm 531 isa generic contour plotting algorithm that plots contours by

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Fig. 3 CT acquisition, transformation and interpretation

finding and following a contour from some starting pointuntil it either closes or intersects a boundary. Alternatively itis possible to speed up the algorithm by examining each cellof the grid in turn, checking if contours pass through the celland then drawing line segments within the cell as appropriate.A detailed outline of this algorithm can be found at [6].

The basic idea behind our algorithm can be described asfollows: Let M be an isopycnic contour map composed bythe set of isopycnic curves W with levels ranging from 0 to5. To simplify some notations and avoid further confusion,in this section we will refer to a curve as a finite set of points.We will also use the expression “add f ∈ S to X” to denotethe following update operations:

X ← X ∪ { f } and S← S − { f } (1)

For illustrative purpose, assume Fig. 4 as an example of anisopycnic contour map.

The segmentation algorithm proceeds as following.

Step 1. First, the algorithm removes all points of the isopyc-nic curves intercepting the image border or the wood elementboundary. These points are not necessary because they pro-vide no additional information. Besides that, and from ourexperimental results, we have realized that images may pres-ent similar density values around that area, which may alsolead the algorithm to induce wrong topologies. Formally this

Fig. 4 Isopycnic contour map

step can be described as follows: Let I = { f − f ∩ B|∀ f ∈W } be the set of all continuous curves formed by removingall the intersection points between f and B from every curvef , where B represents the image border or wood elementboundary and f ∈ W . Add f to the set D, which containsall the information to be discarded, and every h ∈ I to theworking list W .

Step 2. We calculate, for every isopycnic curve f ∈ W , thedirection flow vector using tangent vectors or a medial axis

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Fig. 5 Sub-region after Step 1–5

technique, if the curve is closed. This information will beused on later steps.

Step 3. We further remove trivial meaningless features, byusing thresholds for minimal curve lengths and polygonareas. In a formal definition, we assume that N − 1 is thenumber of points of a closed curve f , composed by pointsset {(xi , yi )}, 0 ≤ i ≤ N . We add to D all f ’s such that:

1

2

i=N−1∑

i=0

(xi yi+1 − xi+1 yi ) < β (2)

Analogously, we add to D all open curves g such that #g < α

verifies.

Step 4. During this step, the procedure will discard unneces-sary information, since we only aim some specific wood fea-tures boundaries. Let f(x, y) and g(x, y) be two polygonsdelimited by two closed curves f and g, belonging to the Wand h ∈ W a closed curve such that h ⊂ f (x, y) ∩ g(x, y).

Then we add f and g to the set D and h to a set L , which willhold at the end of the procedure, the final set of boundaries.

Step 5. Add all trivial boundaries to L , which means: add toL all open curves f such that its projection on the flow-asso-ciated axis does not result in singularities, and the closestclosed curve g ∈ D ∪ L does not have the same densitylevel. In Fig. 5 the reader can find two fake boundaries thatare discarded (black lines in lower-right corner).

Step 6. This step is similar to Step 4. However in this stepwe will deal with curves that are actually not closed. Yet,they can be seen as a closed shape, since both extremities areending at some image border. Let f be a curve such that theextremities a and b end up at some borders x and y, where xis not parallel to y or x = y. Then, there is a unique closedshape that can be formed by using those two borders. Assumethat g is the closed form of f . If g is not contained by anyother shape and it contains only one curve h, then add h to D.

Step 7. The algorithm will try to merge a few curves, in orderto reconstruct as best as possible the wood layers. During thatprocess, a new threshold γ is introduced, defining the max-imum distance between the two closest points, belonging totwo different curves. In our implementation γ is directly gen-erated from α. For every pair of {( f, g) | f �= g and g, f ∈W }, we find if possible, two points a, b such that the semi-line passing through them does not intercept any other curvein W ∪ L ∪ D. We sort these pairs (a, b) according to thesmallest angle between the segment ab and both flow vectors.We find the four closest points to a and b such that tangents atthat points intercept a small ball ϕ, which is also interceptedby ab (see Fig. 6).

If these four points are not found after n steps, then weselect the four points f(i+m), f(i−m), g( j−m), g( j+m), wherei, j are the indexes of a and b, and indexes i ± m, j ± m

Fig. 6 Step 5

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Fig. 7 Final image

Fig. 8 Illustrates the curve modeling results using just the B-Splineinterpolation

are clamped to the curve size. We add f and g to D and thenew generated boundaries to L . Figure 7 illustrates some ofthese reconstructions, which are easily identified as straightlines.

Note that these curves are not yet represented as implicitor parametric representations. Currently, they are just a setof lines connecting two consecutive segmented points. Forthat reason, reconstructions are just straight lines. Besidesthat, we know that if the boundary is an isopycnic curve oflevel bigger than 2 (highest density) then it corresponds to apossible knot.

2.4 Geometrical modeling from voxel data

Basically two different approaches can be adopted to gen-erate, from the segmented data, the bounding surfaces:the traditional one is to extract contours from the dif-ferent slices, as shown in Fig. 8, and to loft a surfacethrough these contours. By using commercial software pack-ages (http://www.simpleware.com/, http://www.vsg3d.com/avizo/overview) bounding surfaces can be directly generatedby adopting different voxel-based methods. Stepped surfacescan be straightforwardly modeled from the voxel boundaries.C0 continuous triangulated surface can be extracted, from

the segmented data, using approaches based on the marchingcubes algorithm, described in [7].

The modeling approach based on the two-dimensionalcontouring involves fitting curves around the segmentedcross-sectional data.

Non-uniform B-splines of degree 3 or 4, Spiro splines [8],Akima [9], Composite Beziers and “Almost Vanishing Poly-nomials” [10,11] have been used in this research.

In the following paragraphs we describe the methodsdeveloped for the automatic generation of the fitting curveson the segmented wood feature boundaries.

2.4.1 Selection of control points

In order to generate a mathematical representation for thecontour curves, which so far are just a set of points X ⊂ R2,we need to identify, for each curve, the set of control points.For that we use line simplification algorithms, which can beused to identify the relevance of a point as a control point.Several algorithms are available in our implementation, how-ever by default we use the algorithm suggested in 1972 byUrs Ramer [12] and in 1973 by David Douglas and ThomasPeucker [13]. This algorithm computes a hull, scaled by atolerance factor, around the curve, by choosing a minimumof key points. Some of the advantages of this algorithm are:first, for a n point curve, computation time of the approxi-mation is proportional to nlog2(n). Secondly it is not nec-essary to have a priori knowledge on the curve, and finally,the compression ratio can be easily tuned using the toleranceparameter.

2.4.2 Curve interpolation

As mentioned in Sect. 2.4, several curve representations wereanalyzed. The first to be used was the Composite Bézier.Given a set of (n + 1) control points P0, P1, . . ., Pn , the cor-responding Bézier curve (or Bernstein–Bézier curve) is givenby:

C(t) =n∑

i=0

Pi Bin(t) (3)

where Bin(t) is a Bernstein polynomial and t ∈ [0, 1].A curve that is made of several Bézier curves is called a

composite Bézier curve or a Bézier spline curve. If a com-posite Bézier curve of degree n has m Bézier curves, then thecomposite Bézier curve has in total mn − 1 control vertices.

The effectiveness of B-spline was also investigated. A B-spline is a generalization of the Bézier curve. A B-spline is aspline function (special function defined piecewise by poly-nomials) that has minimal support with respect to a givendegree, smoothness, and domain partition. Specific typesinclude the nonperiodic B-spline (first p + 1 knots equal

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Fig. 9 Circular features modeled with almost vanishing polynomials

0 and last p + 1 equal to 1) and uniform B-spline (internalknots are equally spaced). A B-spline with no internal knotsis a Bézier curve.

The Akima interpolation [9] is a continuously differentia-ble sub-spline interpolation. It is built from piecewise thirdorder polynomials. Only data from the next neighbor pointsis used to determine the coefficients of the interpolationpolynomial. Since there is no need to solve large equationsystems, this interpolation method is also computationallyefficient.

Spiro splines are a novel way of defining curvilinear pathsdeveloped by Raph Levien [8]. These splines are a new typeof path that behaves like springy metal rods, automaticallysmoothing to minimum curvature between their nodes. Thereare no control point “handles” as with Bezier curves. Thesesmooth flowing curves are especially suitable for design-ing fonts. There are five different types of Spiro points: G4Curve Points (continuous up to the fourth derivative), G2Curve Points (continuous up to the second derivative), Cor-ner Points, and two Constraint points (one to be used when thecontour changes from a curve to a straight line, and anotherto be used when the contour changes from a straight line toa curve).

Almost Vanishing Polynomials are implicit representa-tions, rather than parametric forms. In [11], the authors

describe the mathematics behind the polynomials used forthe interpolation of a selected pixel data set, consideredas empirical data with a tolerance describing the absoluteerror on each data. The curves, generated according to thismethod, are obtained using the free software CoCoA [14]and plotted in the range of coordinates delimiting the sam-ple face. The tolerance is defined by a circle, with ray lengthin the range 0–1 (0.25 pixel, in our case) and center in thesampled point.

The resulting polynomials have the property that are ofminimal degree within the error tolerance specified. Thus,the feature will be represented by a perfect shape if it canbe found within the tolerance. Figure 9, which focus on cir-cular details of Fig. 8, illustrates in white the implicit poly-nomial representation and in black the original segmenteddata.

A graphical comparison between all these representationscan be seen in Fig. 10.

2.4.3 Surface reconstruction

Our algorithm can also be automatically applied to a set of X-Ray CT slices. As the reader can observe, Fig. 11 representsa voxel-based curve skeleton interpolated with a B-Splinealgorithm, which can easily be converted to a 3D surface bylofting a profile through the set of curves. However lofting aprofile through a set of curves may not be an easy task if wehave multiple curves at the same level belonging to the samematerial (growth layer, crack, knot, etc.), this is, if some fea-ture shows several branches at some profile section. Thesehard cases are still open problems in geometric modeling.

Figures 12 and 13 are examples containing the representa-tion of several selected features such as: growth layers, ele-ment boundaries, knots, cracks and pith. The interpolationalgorithm used was again the B-Spline.

Fig. 10 Curve interpolation using a Spiro, b Bezier, c Bspline and d Akima algorithms

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Fig. 11 Wood layer

Fig. 12 Wood growth layer, wood element boundary and pith region

Alternatively to lofting, surfaces can be directly mod-eled from the polynomials obtained with the Almost Van-ishing Polynomials algorithm. However, at this stage ofresearch, surface modeling is completely controlled by theuser, without any form of automation.

3 Discussion and future research

Nowadays, different approaches can be followed to extract,from CT data, models of heterogeneous materials, such aswood. While CAD approaches are generally not automated

and time consuming, image-based techniques make it pos-sible to directly generate geometrical and meshed modelsfrom CT images. On the other hand, CAD-based techniquesallow better control of final results and can be adapted to thedifferent geometrical features of the detected morphologies.

The algorithm presented in this article illustrates an exam-ple of a CT image-based technique, with the advantage thatit allows to work directly on the original data. Furthermore,it has several advantages. First it automatically detects pos-sible knots, cracks and other features which exhibit drasticchange of density value. Secondly, it aims at wood struc-tures instead of general image segmentation domains, thus

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Fig. 13 Growth layer, wood element boundary, knot and pith region

providing specific rules to end up with optimized results.Finally, the construction of a voxel-based curve skeleton iscompletely automatic; yet, we can refine it using differentthreshold values.

For what concerns the curve representation, we have iden-tified that, among those curves which can be adopted for mod-eling contours of the segmented data, Spiro spline providesthe most suitable algorithms to describe closed shapes. Dueto its intrinsic roundness properties, it represents very wellfeatures such as resin pockets. However the results are not sopromising with features that approximate line segments, suchas wood growth layers tend to do. On the other hand, Com-posite Beziers probably yield the best results where Spiroalgorithm is presented as the worse approximation, that is,when curves are almost line segments. B-Splines have alsotheir own advantages, such as an excellent representation ofindented layers. Furthermore, they provide a good trade-offwhile describing the set of all features.

Finally, the “Almost vanishing Polynomials” algorithm,which is used to find an implicit representation of minimaldegree that best approximates the set of points by a toler-ance λ, has also some interesting results on wood featuresmodeling. With this algorithm, a geometric representation

shows a tendency to become more symmetric, that is, toapproximate known shapes such as circumferences, hyper-boles, etc.

In future research, an algorithm that selects the best rep-resentation to some specific feature will be considered. Thisapproach will result in a hybrid model to represent the bestapproximation for each feature.

Acknowledgements The authors want to thank MiCROTEC s.r.l., inparticular M. Boschetti, who has provided the CT data.

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