Evaluation of Knots and Fibre Orientation by Gradient Analysis in X-ray Computed Tomography Images of Wood

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Evaluation of Knots and Fibre Orientation by Gradient Analysis in X-ray Computed Tomography Images of Wood

Huber, Johannes Albert Josef, PhD, 1989- (author): Luleå tekniska universitet,Träteknik

Olofsson, Linus (author): Luleå tekniska universitet,Träteknik

(creator_code:org_t)

Barcelona : International Center for Numerical Methods in Engineering (CIMNE), 2023
2023
English.
In: CompWood2023: Computational Methods in Wood Mechanics. - Barcelona : International Center for Numerical Methods in Engineering (CIMNE). - 9788412322279 ; , s. 143-144

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Conference paper (other academic/artistic)

Abstract Subject headings

The mechanical properties of wood are governed by growth-dependent structures on themicro- and macroscopic level, which are subject to natural variation. Numerical modelsof wood on a scale of individual pieces of sawn timber may need to account e.g. for thegrowth ring orientation or the presence of knots and their effects on the local materialorientation, i.e. the variation of the fibre coordinate system (FCS). The FCS is composedof the mutually orthogonal longitudinal (l), radial (r) and tangential (t) directions. Agrowth surface represents a region of equal age, i.e. a former growth front of the tree,and at each point on a growth surface, the r direction consequently represents the surfacenormal. Growth surfaces surrounding a knot are usually approximated by analyticalsurfaces, onto which the l direction is modelled by hydrodynamic flow fields in lateral andby polynomials in the vertical direction, like in [1].A data-driven method used for detecting the location of knots and eliciting the in-planeprojection of the l direction on the surface of sawn timber is optical scanning combinedwith laser tracheid scanning [2]. A disadvantage of this method is that the internalstructure of the scanned timber remains unknown and needs to be extrapolated, againbased on assumptions of growth in wood. X-ray computed tomography (CT) of woodprovides images of the internal density distribution from which features like the pith, thegrowth rings, knots and defects can be extracted by image analysis.In a recent study [3], the local FCSs around knots were reconstructed by density gradientanalysis in CT images, on which finite element models were based for predicting thebending behaviour of sawn timber. Growth surfaces in wood represent regions of nearlyconstant density and can therefore be analysed in CT images by gradient-based methods.The goal of the present study was therefore to study how the gradient of the density fieldderived from CT images of wood can be used to determine growth surfaces, the region ofknots, the border between dead and live knot, and the locally varying FCSs.The material studied was comprised of small log sections of Scots pine (pinus sylvestris)(approximate diameters of 50 mm - 300 mm and length 250 mm) containing knot whorls,which were dried to fibre saturation. CT scans were acquired at a voxel size of 0.5 × 0.5 ×0.5 mm3 yielding a 3D image J(x, y, z). After scanning, the sections were cut throughthe centrelines of the knots and manual measurements were conducted of the dead knotborder, i.e. the position along the boundary of a knot after which a knot died off. At this border, the diameter of the knot stops increasing and the surrounding fibres grow aroundthe knot rather than merging with it. As the tree continues to grow, this will eventuallylead to bark being encased around the knot inside the tree.A purely data-driven analysis was performed based on the partial derivatives Jx , Jy , Jz ,from which the gradient structure tensor (GST) was constructed, see equation 1, where wσ is a Gaussian convolutional kernel. The eigenvalues and eigenvectors of the GSTwere extracted for each voxel and the resulting vector field was used in the subsequentanalyses. Equivalently, second order derivatives were studied to study curvature.The results indicate that gradient-based analyses on CT images of wood can be usedto approximate the locally varying FCSs around knots, see Figure 1 and that they mayfacilitate the determination of the region of dead and live knots.

Subject headings

LANTBRUKSVETENSKAPER -- Lantbruksvetenskap, skogsbruk och fiske -- Trävetenskap (hsv//swe)
AGRICULTURAL SCIENCES -- Agriculture, Forestry and Fisheries -- Wood Science (hsv//eng)
NATURVETENSKAP -- Data- och informationsvetenskap -- Datorseende och robotik (hsv//swe)
NATURAL SCIENCES -- Computer and Information Sciences -- Computer Vision and Robotics (hsv//eng)

Keyword

gradient structure tensor
hessian
partial derivatives
growth surfaces
dead knot
Träteknik
Wood Science and Engineering

Publication and Content Type

vet (subject category)
kon (subject category)

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AGRICULTURAL SCIENCES: AGRICULTURAL SCI ...; and Agriculture Fore ...; and Wood Science

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By the university: Luleå University of Technology

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