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Workshop /UFRO 1999 SS.01-04-La Londe-Les-Maures, September 5-12, 1999: Topic 2Modelling the pith location and the ring shape in the stem
using the external tree profile. Case study on Norway spruce
INTRODUCTION
Laurent SA/NT-ANDRE, Renaud DAQUITA/NE, Jean-Michel LEBAN Equipe de Recherches sur la Qualite des Bois (Wood Quality Research Team),
!NRA - Centre de Recherches de Nancy, 54280 CHAMPENOUX (France)
, _ _ _ _ _ EZG'"'
[ -566- )
.
-~cThere is a need in timber production to have the right log for the right product. Achieve this would iricrease the profits but involves a good evaluation of the internal wood properties of the logs. These last 10 years have seen the outcome of new technologies for measuring logs at the sawmill. These devices can be divided into two groups : the optical scanners (shadows 2 or 3 axis, 3D Multipoints) which measure the external log's shape, and the« invasive» scanners (2 axis : X-ray and Gamma-X-ray ; tomographic : X-ray and NMR) which also measure the internal properties of the logs. These new technologies (especially the ray tomographic scanner) offer the opportunities to optimize the sawing pattern (and then maximize the value recovery of the log) according to both the measured external log shape and the internal log features.
The devices already used in the sawmills are the optical scanners (shadows 2 or 3 axis, 3D Multipoints) and the 2-axis X-ray (and Gamma-ray) scanners. The 2 axis X-ray scanners offer the possibilities to have a direct estimation of the internal log features (Grundberg & Gronlund, 1997a, 1997b, 1999 ; Oja et al., 1999) even if the external log shape is coarsely measured (Oja et al., 1998 ; Skatter, 1998). On the other side, a 3D Multipoint optical scanner gives an accurate measurement of the external log shape (often 32 points for describing one cross-section) but there is a need for modeling the internal properties.
Our approach consists in using the external log shape measured with a 3D optical Multipoint scanner and few tree measurements (diameter at breast height, age, total height), to estimate the ring pattern within individual logs. We focused on the ring width (including the tree ring asymmetry), since it gives a good estimation -of the basic density and thus the mechanical properties (Bostrom, 1994).
A preliminary work made on 168 cross-sections sampled in a sawmill has shown two main results (Saint-Andre, 1998b) : first, we can assume that the ring shape is an ellipse, and second the pith is rarely located on the geometrical center of the cross section. One ring is then characterized by 5 parameters (see Figure 1) : Xb and Yb are the coordinates of the center of the ring, a and b are the two axes of the ellipse, and a is the angle between the largest axis of the ring and the largest axis of the cross-section. The ellipticity is defined by the ratio a/b and the eccentricity by the distance between the ring center and the pith (
~
Xb 2+
Yb 2 ).Largest diameter oftheTing
Shape ofthe cross-section
Largest diameter of the cross-se~
Figure 1 : The five parameters used to describe a ring. Xb and Yb are the coordinates of the ring geometric center, a and b are the two axes of the ellipse that represents the ring, and a is the ring orientation.
Workshop IUFRO 1999 S5.01-04-La Londe-Les-Maures, September 5-12, 1999: Topic 2
Using a second sample (374 logs and 285 cross-sections, originating from 72 trees and 36 trees respectively), we hiiv·e
built models for evaluating : (i) the number of rings within the cross-sections (Saint-Andre et al., 1999), (ii) the pith position (Saint-Andre & Leban, 1999a), (iii) the ring width (Daquitaine et al., 1999), (iv) the ring ellipticity and the ring eccentricity (Saint-Andre & Leban, 1999a, 1999b). For the moment, we do not have studied the ring orientation within the cross-section.
The objective of this current paper is to present the whole set of models and how they work together for evaluating the ring pattern within the logs. We will discuss the simulation results in order to illustrate the improvement and the limits provided by this new approach.
MATERIAL AND METHODS Wood sampling
Thirty-six trees have been felled from 4 even-aged and pure Norway spruce stands in the north-eastern part of France (9
trees per stand). A sub-sample of 12 trees was selected for this study according to their size (diameter at breast height
and total height). Within each sampled tree, we cut 3 logs according to their height position within the tree : one at the
bottom (near the ground level), one at the middle and one at the top. Each log is 2 meter long in order to be measured
with the laser scanner built in our laboratory. A synthetic description of the trees and the logs is given in Table 1 and
Table 2.
Table 1 : Synthetic description of the 12 sampled trees.
Diameter at breast height (cm) Total height (m)
Stand Nb of trees Age Min. Average Max. Min. Average Max.
31 3 63 24.8 38.0 45.9 22.9 26.4 28.8
32 3 92 31.5 41.2 47.1 31.5 34.1 37.4
33 3 67 26.1 41.3 49.3 26.8 31.3 34.2
34 3 128 31.4 36.2 39.3 28.2 31.1 33.5
Table 2 : Synthetic description of the 36 sampled logs. The number in brackets gives one standard deviation. Localization Bottom Middle To 0.04 (0.02) 0.28 (0.07) 0.51 0.07 34.9 (7.4) 29.8 (7.6) 23.3 (6.9 Ta er cm.m·1 3.2 (1.9) 0.7 (0.3) 1.0 (0.4 Nb o Growth units 6 (3) 4 (1) 4 1
Two discs were cut at each extremity of the 36 logs. Unfortunately 3 discs among the 72 (2x36) were not usable
essentially because of the occurrence of cracks. The ring shapes (one every 5 rings) were descnbed by 36 points (one
every ten degrees). The large number of radii was necessary to describe accurately the shape of each ring and to calculate the position of the geometric center of the surface delimited by the ring limit (Saint-Andre, 1998a).
Method
The Figure 2 gives a simplified algorithm of the whole method : Inputs
The external log shape is measured with a 3D multipoint optical scanner. The position of36 points per cross-section was
measured at each longitudinal step along the log (in our case every centimeter). Furthermore, we made the assumption
that the flow of information is not interrupted by the harvesting, and the tree measurements ( dbh, h, age) and height of
the log in the tree are available. Processing
For each cross-section, the procedure can be divided into 3 steps:
*
Step 1 : Exploitation of the external log shape measurements :1- Positioning the geometric center of the surface delimited by the shape of the cross-section;
2- Fitting an ellipse on each measured cross-section. The results of this fitting are the two axes of the ellipse (Saint-Andre & Leban, 1999a) ;
3- Knowing these two values, we can therefore calculate the stem irregularity (difference between the actual shape of the cross-section and the fitted ellipse).
Workshop IUFRO 1999 SS.01-04-La Londe-Les-Maures, September 5-12, 1999: Topic 2
Tree Log
Measurement of the external log shape Total Height
L Hlog
Radius (L, 0) Dbh Age
0
Step N°1 : Shape of the stem cross-sectionsJL
Step N°2 : Number of rings
Pith localisation within the cross-sections
0
...
Step N°3 : Ring width, ring ellipticity and ring eccentricity assessment
Figure 2 : Diagram of the method used to estimate ring width when the external shape of the log and some tree
data (height, age, dbh) are measured. In this method, we take into account the ring asymmetry.
*
Step 2 : Evaluation of the number of rings and localization of the pith :1- Number of rings (Saint-Andre et al., 1999). We have used the following model:
1
h
n, =age-rh1(P1 + P2 age)--(p3
+
p4-)ta dbh
with
n,. : number of rings
age : age of the stand
rw : relative height of the log within the stem ta : taper ( cm/m)
dbh : diameter at breast height h : height of the tree
pl=-26.63
p2= 1.11
p3= 12.09 p4=-0.10
2- Evaluation of the pith location within each cross-section (Saint-Andre & Leban, 1999b). We have used the two following models : (i) one for the eccentricity, (ii) and one for the distance to the largest axis (ECC and DLA, see Figure 3). For positioning the pith within each cross-section, we assumed that it was located on the smoothest side (quarter of the cross-section which has the smallest stem irregularity).
Model 1:
ecc=f31.dia+f32.(ell-I)+f33.LN(irr)Model 2 .
:
dla = y1.ecc +y2.(ell-1)
+y3.dia.with
ecc : eccentricity
dia: mean diameter of the cross-section
ell : ellipticity (largest axis divided by the lowest one) of the cross-section irr : stem irregularity
dla : distance to the largest axis
~l=0.056 ~2= 7.338 ~3= 0.205 yl= 0.359 y2= -4.869 y3= 0.012
Workshop IUFRO 1999 SS.01-04 -La Londe-Les-Maures, September 5-12, 1999: Topic 2 DIA= 2
* -
1=-1 -36 ELL=!!._ b 36L
[r(81 )-r .,,1 (81)]2
IRR= i=I 36Figure 3 : Definition of the variables when the cross-section's outline is described by 36 points :
The continuous line is the measured outline of the disc. The dotted line is the fitted ellipse associated to the disc outline. ECC is the distance between the pith and the disc geometric center and DLA
is the distance between the pith and the largest axis of the cross-section.
*
Step 3 : Evaluation of the ring width, the ring ellipticity and the ring eccentricity :1- Evolution of the ring width with the ring age counted from the pith and the height position within the tree (Daquitaine et al., 1999) :
Model :
rw(xa)=
(1-b.e - r .xa). [ a ] c+xa withwith a= a0
+
a1*
ddisc[l + a2.age] and r = r0+
'i*
rhlao=ll,818 rw: ring width (mm)
rh1 : relative height position of the disc within the tree
d.iisc : disc diameter (cm)
age : age of the tree
xa : ring age counted from the pith
a1=3,579 az=-0,004 b=0,872 c=7,338 r0=0,0756 q=0,45
2- Evolution of the ring ellipticity with the ring age counted from the pith and the height position within the tree (Saint-Andre & Leban, 1999a):
13
3 (1- r ) re/l(rxa) = /31.[l + f32·'xa·exp xa ].
~h
with
/31
=
/310
+ /311.rhl ; /32= -
-
1 ; /33=
f330+
/331 ·
-/31
dbhrxa: relative cambial age (ring age I total number of rings in the cross-section) h : total height of the tree (cm)
rw: relative height of the cross-section (height of the cross-section I h) dbh : diameter at breast height of the tree (cm)
ell : ellipticity of the cross-section
PIO= 1.0431 PI l= -0.0094 p3o= -2.569 P31= 0.0211
3- Evolution of the ring eccentricity with the ring age counted from the pith and the height position within the tree (Saint-Andre & Leban, 1999b):
with
recc : the ring eccentricity
rca: relative cambial age (ring age I total number of rings in the cross-section) rh : relative height of the cross-section (height of the cross-section I h)
rnrg : mean radial growth of the cross-section ( dia I number of rings) dia : mean diameter of the cross-section
ell : ellipticity of the cross-section irr: stem irregularity
PIO= 0.061 p11= 5.874 p12= 0.226 p20= 0.833 p21= 0.949
Workshop IUFRO 1999 SS.01-04-La Londe-Les-Maures, September 5-12, 1999: Topic 2
RESULTS
The Table 3 gives the differences between the measured number of rings and the simulated one. Errors range from ...:.7. 6
to +15.5 rings which represent in average less than 6.4% of the measured number of rings. There is no bias (the mean of the differences is close to zero) even if there is a small overestimation for the stands 31 and 34, and a small underestimation for stands 32 and 33. The standard deviation is slightly over 5 rings. These results are in complete accordance with the one we have got during the building of the model (the RMSE was around 5 rings).
Table 3 : Comparison between the simulated number of rings and the measured one.
Stand Mean difference Maximum Minimum Standard deviation
31 -2.2 6.8 -5.4 3.7
32 5.0 15.5 -4.4 6.3
33 1.3 7.38 -2.5 2.6
34 -2.9 0.21 -7.6 3.4
Total 0.5 15.5 -7.6 5.2
The Figure 4 shows four typical examples of the results we gained for the pith localisation. The simulated pith is in
black and the measured one in white. In most cases, the disc eccentricity was well estimated (errors were below 8mm for 69% of the cross-sections) but we lacked in locating the pith within the cross-section (only 33% were at the right position). The worst cases (21 % of the cross-sections) are mostly observed for the butt cross-sections.
The Figure 5 gives, for the same four cross-sections, the simulated ring pattern versus the measured one.
The simulated pith
is located in the
right quadrant
The simulated pith is not located in the right quadrant Error on eccentricity < 8mm 20 15 10 20 -15 -20 33% 20 15 10 10 15 20 2 .5 -10 -15 -20 Error on eccentricity > 8mm . s '·20 • 5 20 15 10 -15 -10 -S '
.
'
·10 -S -10 -15 10% , )Cl.-
-15 10 0 .5 -5 -10 -15 ... :20 10 15 '\ '\ 10 15'
Figure 4 : Simulation of the pith location. The simulated pith is in black and the measured one is in white.
The actual shape of the cross-section is the black line and the fitted ellipse is the dot line.
Workshop IUFRO 1999 S5.0l-04-La Lo11de-Les-Maures, September 5-12, 1999: Topic 2
We can point out three main results :
I. for the butt sections, the main source of errors is the model used for evaluating the ring width (see
cross-section N°3405-l b ). In such case, the ring width is underestimated near the pith and overestimated near the bark ;
2. when the eccentricity is not well estimated, there is an underestimation of the variation of the ring width (or overestimation depending on the error on the eccentricity). This can be seen for the cross-section N°3405-lb and the cross-section N°3437-lb (underestimation);
3. an error on the pith position (wrong quarter of the cross-section) did not lead to a great difference between the
simulated ring width profile and the measured one. An example is given by the cross-section N°3311-1 b : the ring
pattern is different between the simulated cross-section and the measured one but the curves are very similar.
e
.§. 7 ~ 6 ••..
$ .E •..
Disc 3311-Jabeigbt-9,Sm -diam-35,lcm- ar-49 (51 1imulalcd)
o Measuremcms • Sm..Jati>m
lO 60 10 100 110
Ring age coutcd from the pith
Din: JJl 1-lb he ht-l,7111-dJH1 .... S,.Jcm-nbr-60 '2Siandate e' £, •
L
11
:
1
11l1i1i1
e ' .§. • -s :s! ••
..
.
• &..
'Rine •cc: contc:cl fro• the pith
Dilc340>1b
h<;ght-0,9m • cn-«,J an-nbc-121(1281"""1ated)
l:~=:-1
Rmg ~ counted from the pith
Disc3437-lb
loe~l-0,!m--,km-nb<:'l~~-.(~Slmulo!e~
Figure 5 : Result of simulations for 4 typical cross-sections. In white, the actual ring width and in black,
the simulated one. Results are satisfactory for 70% of the sampled discs. A part of the last 30% are butt cross-sections for which the model of average ring width versus ring age is not adapted.
"
..
Workshop IUFRO 1999 SS.01-04-La Londe-Les-Maures, September 5-12, 1999: Topic 2
DISCUSSION AND CONCLUSION
Tree and log measurements
Our method is based on the assumption that the flow of information between the forest and the sawmill is not interrupted by the harvesting. A large amount of data has to be measured on the field and thereafter transmitted to the sawmill : height, age, and dbh of each harvested tree but also the height position of the logs within the trees. At the present time, more and more devices are available for measuring, collecting and transmitting the data (chips, codes barre, radio transmission) and we can expect that these devices will be used in the next future for each harvested stand.
Our procedure is based upon laser measurements and might be sensible to the local removal of bark. This point was not tested in the study : the debarking was hand-made and the wood was not damaged. An industrial log debarking leads automatically to some variations of the stem form that could induce errors on the estimation of the ring pattern (especially for the evaluation of the disc shape and thereafter the disc eccentricity). Further works should be performed in close collaboration to a sawmill in order to improve the method.
The resolution of the log measurements is an important parameter which partly determine the time needed to process the log at the sawmill. The number of points to be measured by the laser scanner for each cross-section has to be important. For example, 36 points are needed for an accurate description of the disc shape and the recent industrial 3D multipoints optical scanners are able to measure up to 32 points per cross-sections every centimeter at a speed compatible with the sawmill process.
Exploitation of the laser measurements
These points are easy to solve and the time needed for the processing is very low. To fit the ellipses, we have used the NLIN procedure of SAS (Sas Institute, 1989). In the case of an industrial application, the algorithms should be embedded in the software that will compute the log data.
Estimation of the ring pattern
If the tree data are available at the sawmill, the model used for evaluating the number of rings can be used immediately in the industry. Then, by knowing the number of rings and the measured log diameter it is possible to have a good estimation of the average ring width of the log and take it into account to contribute to a better grading.
The procedure for locating the pith is not accurate enough to be applied in the sawmill. However, we can foresee some solutions such measuring the pith position at each extremity of the log (by image analysis) and use this information for calibrating our models and use them for locating the pith within the entire log.
The models that estimate the ring width, the ring eccentricity and the ring ellipticity gave good results. Most of errors occurred for the butt cross-sections which present an irregular shape and a non-typical evolution of the ring width with . the ring age counted from the pith. In such cases, our models have to be improved.
Perspectives and evolution
The knottiness is of major importance when considering the internal properties of a log. This point was not treated in the study and it could be interesting to study the relationships between the external log shape and the knottiness. Grace (1993a, 1993b, 1994) worked with a 2 axes shadows scanner arid developed a method for an automatic grading of the Scots pine logs. One criterion was the surface roughness of the log expressed in «number of bumps per linear meter ». These bumps were probably and mostly induced by the branchiness. In these studies, the results were promising and
. using a 3D multipoint optical scanner would offer much more possibilities.
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France, 68 pp.
W
Grace L.A., 1993a : Using optical log scanners to determine log properties : initial results from SCA's Munksund sawmill. The Swedish University of Agricultural Sciences, Department of forest Products. Report N°232. 56 pp.Workshop IUFRO 1999 SS.01-04 -La Londe-Les-Maures, September 5-12, 1999: Topic 2
W
Grace L.A., 1993b : Evaluating a prototype log sorting system for use in Pine sawmills. The Swedish Universify of Agricultural Sciences, Department of forest Products. Report N°237. 43 pp.W
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W
Grundberg S., Gronlund A., 1997a : Simulated grading of logs with an X-ray log scanner - Grading accuracy compared with manual grading. Scand. J. For. Res., 12(1): 70-76.W
Grundberg S., Gronlund A., 1997b: Modelling of the quality of individual logs. In 2nd Workshop IUFRO WP S5. 01-04. «Connection between Silviculture and Wood Quality through Modelling Approaches and Simulation Software». Berg-en-Dal, Kruger National Park, South Africa, August 26-31, Gerard Nepveu Editor, ERQB INRA-Nancy France, 264-269.lil
Grundberg S., Gronlund A., 1999 : Feature extraction with the aid of an X-ray log scanner. Manuscript. Lulea University of Technology, Division of Wood Technology, Skelleftea, Sweden.W
Oja J., Grundberg S., Gronlund A., 1998 : Measuring the outer shape of Pinus sylvestris saw logs with an X-ray Logscanner. Scand J For Res., 13 : 340-347.W
Oja J., Grundberg S., Gronlund A., 1999 : Simulated control of sawing position based on X-Ray Logscanner measurements. Manuscript. Lulea University of Technology, Division of Wood Technology, Skelleftea, Sweden.W
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Saint-Andre L., 1998a : Excentricite et forme des sections transversales de bois. Definitions, methodologie, exemples sur l'epicea commun (Picea abies Karst.). Ann Sci For, 55 : 899-909.lil
Saint-Andre L., 1998b : Modelisation tridimensionnelle des profils de largeur de ceme dans un billon d'Epicea commun (Picea abies Karst.) compte tenu de la mesure de son enveloppe exteme et des caracteristiques dendrometriques usuelles de l'arbre d'origine. These de doctorat en Sciences Forestieres et du Bois, ENGREF-INRA. Soutenue le 18-dec-1998, !NRA-Nancy, 215 pp.W
Saint-Andre L., Leban J.M., 1999a: An elliptical model for tree ring shape in transverse section. Methodology and case study on Norway Spruce. Accepted in Holz als Roh- und Werkstoff.W
Saint-Andre L., Leban J.M., 1999b : A model for the pith position and the ring eccentricity in transverse sections of Norway spruce logs. Consequences for the board's wood quality. Submitted to Holz als Roh- und Werkstoff.W
Saint-Andre L., Herv~ J-Ch., Leban J-M., 1999 : Modelling the number of rings in individual logs of Norwayspruce.-Accepted in the Scandinavian Journal of Forest Resarch.
