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Robust Method for the Automatic Characterization of a Wooden Board'sGeometrical StateLouis Lacasse a; Antoine Tahan a; Zhaoheng Liu a

a Department of Mechanical Engineering, École de technologie supérieure, Université du Québec, Montreal,Quebec, Canada

Online Publication Date: 01 April 2008

To cite this Article Lacasse, Louis, Tahan, Antoine and Liu, Zhaoheng(2008)'Robust Method for the Automatic Characterization of aWooden Board's Geometrical State',Quality Engineering,20:2,221 — 231

To link to this Article: DOI: 10.1080/08982110701733042

URL: http://dx.doi.org/10.1080/08982110701733042

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Robust Method for the AutomaticCharacterization of a Wooden Board’s

Geometrical StateLouis Lacasse,

Antoine Tahan,

Zhaoheng Liu

Department of Mechanical

Engineering, Ecole de

technologie superieure,

Universite du Quebec, Montreal,

Quebec, Canada

ABSTRACT This article presents an algorithm for characterizing and detecting

geometric faults in a wooden board. It is developed for integration into a

quality control system in factories. The industrial environment where this

system will be implemented is characterized by high levels of variation stem-

ming from measurement noise and operating conditions.

Geometrical defects in a board can often be summarized under four types

of deformations: twist, bow, spring, and transversal alignment. A computer

vision system with four cameras is developed and used to obtain a 3D rep-

resentation of the board surface. The surfaces are digitized using ‘‘structured

light’’ active vision techniques. The range of images obtained from the com-

puter vision network can be considered as the input of the proposed algor-

ithm. This algorithm consists of the following five steps: (1) transformation

of the spatial position and orientation of each camera into a common refer-

ence system; (2) data filtering to eliminate aberrant errors originating from

splinters or from tears on the board’s surface; (3) integration of multiple

local surfaces into a 3D global representation of the board; (4) extraction

of significant feature points by means of polynomial surfaces obtained from

linear regression; and (5) characterization and classification of different

geometrical defects using the extracted points. This classification provides the

basis for making a final decision with respect to the surface quality of the

inspected part. Different types of defects combined with different noise levels

were used to validate the algorithm. The results show that high-quality

performance and precision can be achieved with this proposed method.

KEYWORDS algorithm, characterization, inspection, measurement system

analysis, surface defect detection

INTRODUCTION

For many years now, the automation of the manufacturing process has

been a key element for increased productivity. In looking to increase

efficiency and to reduce production costs, certain industrial processes have

tended to integrate technologies originating from computer vision. Areas

Address correspondence to ZhaohengLiu, Department of MechanicalEngineering, Ecole de technologiesuperieure, Universite du Quebec,Montreal, Quebec, Canada H3C 1K3.E-mail: zhaoheng.liu@etsmtl.ca

Quality Engineering, 20:221–231, 2008Copyright # Taylor & Francis Group, LLCISSN: 0898-2112 print=1532-4222 onlineDOI: 10.1080/08982110701733042

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involving surfaces as the inspected elements have

greatly benefited from these developments. Some

good examples of these are textile, pulp and paper,

laminated steel sheets, plastics, and rubber (Tolbas

and Abu-Rezeq, 1997). However, industries requiring

a three-dimensional inspection of products are often

semiautomated using CMM (coordinate measuring

machine) technologies. These are often slow when

compared to manufacturing methods and can there-

fore not be completely integrated into the process

(Harding and Bieman, 1989). Quality control based

on sampling can compensate for the slowness of a

CMM. Nonetheless, a full control that does not

unduly slow down production invariably calls for

the use of other technologies, and robotic vision

technologies take on more importance in such cases

(Hageniers, 2001).

In the forestry industry, the implementation of a

robotic vision is a well-established tool in the opti-

mization of cutting blocks, in the classification of

surface defects, as well as in the presence of discon-

tinuities (Zuech, 2004). The first generation of such

systems uses x-rays to obtain a three-dimensional

representation of the board in order to identify its

internal properties (Bhandarkar et al., 1999). Such a

system, however, requires a lot of power in dealing

with large quantities of data. Surface characteristics

such as knots or in-barks are detected by algorithms

originating from form recognition, while discontinu-

ities such as wanes or splits are generally found with

telemetric data obtained from stereoscopy and lasers

(Truong Pham and Alcock, 1998).

Telemetric technologies were the product of the

convergence of a variety of fields, whereas artificial

intelligence resulted from a need to create three-

dimensional reconstructions. In the 1970s, Marr

(1982) attracted researchers’ attention by stipulating

that a three-dimensional structure can be recon-

structed from two two-dimensional images, much

like the human brain. During that time, different

‘‘shape-from-X’’ (two-dimensional image structure,

shadowing movement structure) techniques and

algorithms were created. The development of these

algorithms can be largely attributed to the develop-

ment of complex mathematics and the technological

advances created by computers. Nowadays, pro-

blems related to stereoscopy have, for the most part,

been solved (Shaw, 2005). Technology is now

ubiquitous in industry, thanks to our computational

ability and the performance of algorithms in the pro-

cessing of images.

In our case study, however, two major constraints

significantly limited the effectiveness of this method.

The first constraint was the work environment. This

system is in fact for use on wooden boards intended

for industrial use in a sawmill. Vibration levels, the

presence of impurities and small particles in the air,

board movement on conveyors, thermal variations,

and the presence of defects and irregularities on

board surfaces lead to measurement discrepancies

that are quite significant, as compared to required

variations. For example, a good quality wood board

should not have a cup measuring over 0.75 mm

(1=3200). According to standard industry practice, this

leads to the definition of higher uncertain measure-

ment limits, which must not exceed one third of

the tolerance. However, the uncertainty of raw data

associated with this type of environment generally

exceeds this value.

The second constraint is the reconstruction of

boards in a continuous fashion (high volume pro-

duction). As with all vision machines, the images

(and data) collected are almost instantaneous. How-

ever, the image must be processed in order to recon-

struct, not the board’s volume at any given time, but

a complete picture of the board over its entire length,

which explains the significance of alignment tech-

niques on various images. This alignment must be

made with the least amount of noise possible in

the system.

The first part of this article looks at different types

of defects, conventions, work hypotheses, and a

system description summary. The second part deals

with algorithm: filtration, alignment, and defect

detection. The third part presents a complete analysis

of the measurement uncertainty caused by the

algorithm. A simulation of various types of defects

with different noise levels will be presented to illus-

trate the performance of the proposed methods.

Finally, a semi-experimental validation of the algor-

ithm will be conducted to evaluate its ability to

correctly classify the board defects.

PROBLEMS

Table 1 represents the various geometrical defects

that allow board classification. These deformations

can occur during the sawing process due to internal

L. Lacasse et al. 222

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constraints in the master workpiece, or during other

processes (e.g., drying). In this study, the longitudi-

nal direction refers to the direction of a board’s

movement (X axis). In sensors 1 and 2, the transver-

sal direction refers to the Y axis, and the depth refers

to the Z axis. For sensors 3 and 4, the transversal

direction refers to the Z axis, and the depth refers

to the Y axis (Figure 1).

The noise refers to the variation levels of raw data

relative to the nominal surface and is quantified by its

standard deviation. It is assumed that any acquisition

errors follow Gaussian distribution, and the impact of

surface finish on the position of our raw data is insig-

nificant. Data are acquired using four pairs of radio

sensors and light sources located on the four longi-

tudinal sides of a board. The travel speed of the

boards on conveyors is 12.7 m=s, the camera acqui-

sition time is 20 to 50ms; the minimum resolution is

30 mm� 6.5 mm on a surface of 600 mm� 450mm;

the total uncertainty, as communicated by the camera

manufacturer (�2r), is 0.8 mm; and the measurement

uncertainty of the distance separating two successive

scans is 300 mm�1 mm.

THE ALGORITHM OF GEOMETRICALCHARACTERIZATION

The first part of the algorithm allows us to recon-

struct a digital board. The raw data reach this stage as

a group of points Pi; j where the i index represents

segment numbers and the j index is the surface. Each

i segment possesses its own local coordinate system

that will be transformed into a common global coor-

dinate system using position and orientation infor-

mation of all four sensors. The acquired data will

then be processed in order to characterize the

inspected board into different types of defect such

as cups, bows, crooks, and twists (Figure 2). A brief

description of each step is given below.

Associated Surfaces

The replacement of digital structures with analyti-

cal associated surfaces is a recurring process in each

stage of the board’s reconstruction. This surface

allows us to calculate the residuals present during

filter application and to determine the orientation

and correspondence points during the alignment of

segments, as well as the reference point positions

that allow us to evaluate geometrical characteristics.

This surface analysis was chosen for the type of

geometrical defect that must be detected. In order

to model and identify these types of defects

(Table 1), the surface should have at least a coupling

FIGURE 1 System configuration. FIGURE 2 Data processing diagram.

TABLE 1 Types of Geometrical Defects

Type of

defect Definition Representation

Twist Multiple bends

in a board

Bow Warp on the face

of a board, from

end to end

Cup Hollow across the

face of a board

Crook Warp along the edge

line, also known

as a crown

223 Automatic Characterization

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coefficient, a second-level longitudinal coefficient,

and a second-level transversal coefficient. The model

is illustrated in Eq. (1) with longitudinal axis u, trans-

versal axis v, and depth in relation to stereo sensor, w:

w ¼ CSurf ;1 þ CSurf ;2 � uþ CSurf ;3 � u2 þ CSurf ;4 � vþ CSurf ;5 � v2 þ CSurf ;6 � u � v ð1Þ

Since noise is considered Gaussian, the most effective

method for assessing surface parameters involves the

minimizing of quadratic error.

Filtering

Given the prevailing acquisition conditions, the

data associated with the algorithm may contain a cer-

tain number of discrepancies. These discrepancies

produce a deformation of the associated surface

and can cause a bias when it comes to subsequent

steps in processing, such as the alignment or extrac-

tion of reference points. The filter therefore becomes

a necessary element. Since data filtering should ide-

ally be similar to the algorithm, that is, fast and

robust, the Z score method is considered here.

This method rejects all points with a Z score, Z

(Residual=rResiduals), higher than ZLim or lower than

�ZLim. The residual is the difference between the

actual data point and the corresponding point on

the associated surface. The ZLim parameter is set at

2.5, which represents a reasonable likelihood limit.

To confirm the performance of this filter, we conduc-

ted a test in which a region in space called a disconti-

nuity zone was defined. A meshing of points with a

margin of Gaussian error in depth direction is used

to simulate the data provided by the acquisition sys-

tem. For points located in the discontinuity zone,

many findings with erratic results were added to

simulate discrepancies. Figure 3 shows a typical case

of this discrepancy.

Next, all points were put through two filters whose

filtered points allowed the measurement of the

surface without discrepancy. The standard deviation

of the residuals of the surface filter was compared

to surface residuals obtained when there were no

discrepancies. This comparator is named the

concordance ratio (CR) and is calculated as follows:

CR ¼ rfiltered Residuals

rOrginal Residualsð2Þ

Several discontinuity levels, explained in relation

to noise standard deviationhDiscontinuity

rNoise, were thus evalu-

ated 5000 times in order to ensure reliable results. A

concordance ratio lower than 1 means that the filter

eliminates all points with no discrepancy, causing a

systematic error during tests done to minimize quad-

ratic errors, and a concordance ratio higher than 1

means that the discrepancies have not been elimi-

nated. The results are illustrated in Figure 4. We

noticed that, if the Gaussian hypothesis is valid, the

filter based on a Z score with a ZLim of 2.5 performs

better than another filter (Tukey method; Tukey,

1974). As this test was done using synthetic data,

the Z score method proved to be a good option for

validation during real testing.

Segment Alignment and ReferencePoints

Segment alignment is the most difficult operation

to perform, given that the coordinate transformation

does not allow for the precise positioning of a given

segment with another. Because of a board’s move-

ment, coordinate transformation at the level of the

FIGURE 3 Discrepancy simulation on a scanned surface.

L. Lacasse et al. 224

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camera’s image conversion is very difficult to

achieve. An efficient strategy was developed in

order to effectively align segments and to obtain

an image of the whole scanned board. An encoder

attached to an upstream conveyor of the scanning

system allowed us to synchronize images with the

board’s movement at a resolution of 1 mm. The sig-

nal activating the cameras allowed us to obtain an

image that overlapped half the preceding image.

Many alignment techniques, such as the iterative

closest point (ICP; Besl and McKay, 1992) and its

variations (Tucker and Kurfess, 2003a, 2003b; Luck

et al., 2000; Langis et al., 2001) have been developed

in the area of imagery and mapping. The disadvan-

tage with these techniques is that they require many

iterations and an estimation of the closest point to

another point or of a surface on which the align-

ment must be done. We therefore decided that the

segments would be aligned by first ensuring an

overlap on half of the preceding segments during

surface digitization. The normalized longitudinal

points used in this step are the segment’s starting

point, the one in the middle of the segment, and

the one at the end. During alignment, the points that

define the segment’s orientation to its longitudinal

points allow for better continuity on the aligned

surfaces (Figure 5).

Next, we used a much thinner alignment in which

the length of overlap was divided into five sections,

with four surface intersections extracted from

segment i and from segment i� 1. Tests revealed

that a number of sections higher than five are

unnecessary (Figure 6). All alignments were made

using the Quaternion method developed by Horn

(1987), which reduces quadratic errors among

aligned points.

Reference points Repk;m are strategic points placed

on a section perpendicular to the longitudinal axis.

The sections are separated from one another by a

30-mm gap. These surfaces are associated with the

filtered points located longitudinally on each side

of the section at less than 300mm (Figure 7). Choos-

ing reference points was obviously motivated by the

geometrical characteristics to be quantified. The

number of points needed to define these characteris-

tics is three points per horizontal face. The median

point quantifies the cup, and it is safe to assume that

this characterizes the hollowness of a board face

(Figure 8).

Quantification of GeometricalCharacteristics

Generally, geometrical defects are quantified by

the distance between a datum and a point represent-

ing an extreme defect. The datum for measuring the

cup defect is a straight line defined in a given cross-

section of the wooden board. For these types of

warping and twisting, the datum is the plan. In each

section, average coordinates are calculated in order

to obtain the board’s median profile. A straight line

passing through the average coordinates is calcu-

lated in order to obtain the cup’s median profile,

which is the distance from the point Repmk;2 to this

straight line. The cup characterizing the board is the

median value of all straightness errors (Figure 9). The

best way to measure the twist is to establish the aver-

age points located at the longitudinal and transversal

extremities. Consequently, four diagrams passing

through three points are constructed, allowing the

FIGURE 5 First alignment representation.

FIGURE 4 Concordance ratio in relation to discontinuity levels.

225 Automatic Characterization

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calculation of four torsion errors. Finally, the biggest

error is chosen to characterize the board’s twist

(Figure 10). In order to determine the best envelope

for illustrating bow variations, a diagram that mini-

mizes quadratic error with a Z axis passing through

designated points at each longitudinal extremity is

used. Next, the distance between the central point

of section Repmk;2 and this diagram is calculated for

each section. Finally, the envelope is obtained with

a difference between maximum and minimum error.

The approach used for the warp is identical to that

used for the bow, except that the associated plane

minimizes quadratic errors on Y axis for warp.

ALGORITHM PERFORMANCE

The following assumptions were used during the

evaluation of a single board: (1) The influence of

external factors such as vibration of the acquisition

system and humidity and thermal variation were neg-

ligible; (2) the board was considered perfectly rigid;

(3) measurement noises were Gaussian and were

only manifested in the direction of stereo sensor

fields; (4) no sliding between the board and the con-

veyor; (5) coordinate transformation did not lead to

errors during the acquisition of a board.

The algorithm was processed in a way that

allowed a balance to be maintained between the

FIGURE 7 Reference point section representation.

FIGURE 6 Second alignment representation.

L. Lacasse et al. 226

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ruggedness and execution speed of its components.

The relation between the number of scanned seg-

ments, the noise of raw data, the filter, and associa-

ted surfaces is too complex to be evaluated

analytically This is why a workbench and Monte

Carlo simulations were conducted in order to vali-

date the performance of the proposed methods.

In terms of simulations, the entry parameters are

the level of Gaussian noise on scanned surfaces, the

probability of aberrations and their magnitude,

the dimensions of the board, the geometrical defects,

the probability that a transversal line of raw data

was eliminated, play on the scanned image, the

longitudinal and transversal definition of rough

patches, and crooked movement of the scanned

board (Figure 11).

Stochastic parameters were created artificially

using a MATLAB1 normrnd (l,r) function. Aber-

ration probability was set at an arbitrary rate of 10%

and a magnitude of 1.5 mm. The aberration position

is at the center of the scanned surface on a 60-mm

longitudinal area for each 13-mm transversal. The

probability for a transversal line of raw data to be

eliminated was arbitrarily set at 10%. It was assumed

that movement on the scanned position had a

Gaussian distribution of l ¼ 0 mm and r ¼ 0.5 mm.

Since the board can experience a slight rotation when

it leaves the scanner’s upstream conveyor, this move-

ment will be simulated by an arbitrary rotation of the

scanned segments with a time uncertainty of

� 10� (95%) along all the axes, following a Gaussian

distribution. Thus the standard deviation is approxi-

mately 0.08 radians.

Once all the samples had been taken, the system-

atic error bias and repeatability uncertainty rRep were

calculated with the following equations. The GD

variable represents any geometrical defect, ð ÞData

indicates that the estimator is taken from data

FIGURE 11 Workbench diagram.

FIGURE 10 Extremities that determine twist.

FIGURE 8 Reference point representation.

FIGURE 9 Representation of a cup defect.

227 Automatic Characterization

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measured by the system, and ð ÞNom indicates the

nominal values of defects.

Bias ¼ GDData � GDNom ð3Þ

rRep ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPðGDData � GDDataÞ2

n� 1

sð4Þ

Total expanded uncertainty is evaluated according

to the recommendations set out in the ISO-Guide to

the Expression of Uncertainty in Measurement with: A

U95% ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiBias2 þ r2

Rep

qð5Þ

And finally, an uncertainty ratio:

Ru ¼U95%

GDNomð6Þ

Robustness Study

The robustness study allows us to verify the beha-

vior of the algorithm when faced with parameter

variations. The four parameters studied are the resol-

ution of rough patches, sound on rough patches,

the amplitude of the board’s geometrical defects,

and the length of the board.

Uncertainty Based on Resolution

Resolution is a fundamental parameter that

depends on the acquisition system. The characteriza-

tion of its influence on the algorithm allows us to

determine the level of precision necessary during

the capture of images, as needed. The following test

measures the uncertainty of the measurement of a

scanned board with the following dimensions:

1200 mm� 200 mm� 25 mm with a spring defect

equal to 2.4 mm and a measurement noise level of

rNoise ¼ 3 mm. As shown in Figure 12, uncertainty

decreases in a linear fashion with longitudinal

resolution. In the case of a spring defect, the transver-

sal resolution appears to have no impact on uncer-

tainty. It is important to note here that an increase

in resolution leads to a significant increase in the cal-

culation strength necessary for data processing.

Errors According to Noise on Rough

Patches

The acquisition system is characterized among

other things by the presence of noise on rough

patches. It is particularly interesting to establish the

relation between the uncertainty of rough patches

and a defect’s measurement uncertainty, as it allows

the determination of the allowable noise for any

given detail. The noise is assumed to be Gaussian,

and it is the standard deviation of the noise that

varies during the following test: dimensions,

1200 mm� 200mm� 25 mm, with a spring defect

equal to 2.4 mm and a typical resolution equal to

0.03 px=mm� 0.15 px=mm. Once again, as shown

in Figure 13, we notice a linear behavior of errors

(95% level) in terms of noise levels. However, it

seems that the algorithm leads to systematic errors

proportional to noise levels. We were expecting

the systematic error to be nil irrespective of the noise

levels, but in this case, error is constantly apparent

below the actual value.

Errors According to a Range of Defects

The influence of two defects, warping and twist-

ing, was examined. This characterization allows us

to verify, under the given conditions, whether the

uncertainty=defect ratio (Ru) diminishes or grows.

In the case of a ratio increase, it allows us to deter-

mine the range in which the algorithm performs sat-

isfactorily. For the configuration of warping and

twisting tests, we used boards with the following

FIGURE 12 Uncertainty on the basis of resolution. FIGURE 13 Errors according to noise.

L. Lacasse et al. 228

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dimensions: 1200 mm� 200 mm� 25 mm, rNoise ¼0:3 mm, with a typical resolution equal to

0.03 px=mm� 0.15 px=mm. The uncertainty ratio

(Ru) decreases under these conditions. With a 5-

mm warp, the ratio is 10.2%, whereas it is 8.5% at

30 mm (Figure 14). We can also clearly see that the

systematic error grows as warp increases, whereas

the repeatability error hardly varies. The contribution

of systematic error to uncertainty is major in this case.

The uncertainty ratio decreases under these con-

ditions. At 1.6 mm of twist, the ratio is 39.7%,

whereas it is 10.47% at 9.6 mm (Figure 15). This

repeatability error is surprisingly stable, whereas

the systematic error follows a tangent that leads us

to believe that the uncertainty error might increase

according to a certain twist range. Once again, it is

the systematic error that seems to have the greatest

impact on algorithm precision.

Errors According to Length

The influence of length on uncertainty is interest-

ing because it allows us to evaluate the impact of a

critical operation of the algorithm: the alignment of

segments. The following test shows the measure-

ment uncertainty on a board with a twist error

proportional to its length, in this case, 1=375th of

its length. Scanning was done on boards with the

following dimensions: 1200 mm� 200 mm� 25 mm,

rNoise ¼ 0:3 mm, with a typical resolution equal to

0.03 px=mm� 0.15 px=mm.

As shown in Figure 16, the repeatability error is

proportional to the length, whereas the systematic

error follows a curvature. This leads us to believe

that systematic errors accumulate as the number of

segment alignments increases. An analysis of the

uncertainty ratio illustrated in Figure 17 shows that

it reaches a minimum level and then increases with

the systematic error effect.

Classification Accuracy

In order to evaluate the ability of the algorithm to

correctly classify the scanned boards, an experi-

mental campaign was done. Real boards of standard

dimensions and known geometrical deviations were

used. Geometrical defects were created in order to

cover all grades. The different grade limits were

taken from the timber classification rules, the Stan-

dard Grading Rules for Canadian Lumber of the

National Lumber Grades Authority (see Table 2 for

FIGURE 16 Errors according to length range.FIGURE 14 Errors according to warp range.

FIGURE 15 Errors according to twist range. FIGURE 17 Uncertainty ratio according to length.

229 Automatic Characterization

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an example of [12 ft� 2 ft� 4 ft] and Table 3 for an

example of [12 ft� 4 ft� 4 ft]).

For this validation, we used 150 boards with

the following typical dimensions: 3658 mm�101.6 mm� 50.8 mm (12 ft� 4 ft� 2 ft) and another

120 boards with 3658 mm� 101.6 mm� 101.6 mm

(12 ft� 4 ft� 4 ft). A noise (rNoise ¼ 0:3 mm) was

added to data numerically after the acquisition and

before treatment. The objective is to validate the

robustness of the algorithm under harsh conditions.

The typical resolution was equal to 0.03 px=mm�0.15 px=mm. A summary of the results is presented

in Tables 3 and 4. Note that the error type underclas-

sification is considered much less critical than the

overclassification type. A comparison of results given

by the proposed method and experimental measure-

ments (with classical instruments) shows a similar

behavior in both cases. We also note that the pre-

cision of the algorithm is very good for most defects.

Therefore, the crook deviation is an exception

attributable to the number of rough patches used

to identify error levels: twice as weak on the edges

as on the surfaces. This causes greater sensitivity in

terms of noise levels of the rough patches on the

edge’s surface and, consequently, a lower evaluation

of the spring. Also, the surfaces associated with the

edge range may have too much freedom. A

second-order coefficient appearing in the associated

surface model has no effect on the measurement

accuracy and could therefore be eliminated in order

to improve the stability on the edge range.

CONCLUSION

This article presented a robust algorithm that

allowed for the real-time characterization of the

geometry of a wooden board by its twist, bow, and

spring levels. The algorithm was developed to allow

its operation in a highly noisy environment. The

main elements of the algorithm were the filter that

allows the elimination of aberrant data, the associa-

ted surfaces that allow the reduction of roughness

of the patches, and the integration of different seg-

ments that allow the board’s reconstruction in its full

length. Sensitivity and convergence analyses were

conducted using synthetic data with characteristics

derived from actual telemetric data. The Monte Carlo

simulations helped to characterize uncertainty with

regards to many of the system’s inherent parameters.

Metrological performances of the classification

were evaluated through a comparison of results

obtained from the proposed method with real

industrial measurements obtained from conventional

measurement techniques. The accuracy and pre-

cision of the algorithm were identified by evaluating

its ability to classify the boards according to NLGA

(National Lumber Grades Authority) standards. The

results showed that the algorithm, even with a noise

level of the same magnitude as the required toler-

ance, performs very well for bow, spring, and

TABLE 3 Classification Performance of the Algorithm

(12 ft 3 4 ft 3 2 ft)—150 Boards

% Proper

classification

%

Overclassification

%

Underclassification

Cup 91.8 0.3 7.9

Bow 94.9 0.5 4.6

Crook 58.1 35.7 6.2

Twist 94.0 2.2 3.8

TABLE 4 Classification Performance of the Algorithm

(12 ft 3 4 ft 3 4 ft)—120 Boards

% Proper

classification

%

Overclassification

%

Underclassification

Cup 92.0 0.5 7.5

Bow 94.5 0.7 4.8

Crook 60.3 32.3 7.4

Twist 95.5 1.8 7.7

TABLE 2 Classification Rules According to a Board’s Geometry: 120 3 400 3 200

Grade Cup Bow Crook Twist

1 < 0:794 mm 132

00h i

<38:1 mm 1 12

00h i

<12:7 mm 12

00h i

<11:906 mm 1532

00h i

2 <0:794 mm 132

00h i

<50:8 mm 200½ � <17:463 mm 1116

00h i

<16:669 mm 2132

00h i

3 <1:587 mm 116

00h i

<76:2 mm 300½ � <25:4 mm 100½ � <23:813 mm 1516

00h i

L. Lacasse et al. 230

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transversal alignment deformations. However,

detecting a crook defect was not as accurate as

detecting other types of defects. This reduced accu-

racy might be related to the geometric complexity

of this type of defect. One of the possible solutions

for improving the accuracy in detecting crook defect

is to consider another associated surface model and

use a better resolution of the reference points.

ABOUT THE AUTHORS

Louis Lacasse is a graduate student at the Ecole de

Technologie Superieure. He received a B.S. in mech-

anical engineering from the same university in 2006.

Antoine Tahan is a professor in the Department on

Mechanical Engineering, Ecole Technologie Super-

ieure, Montreal, Quebec, Canada. He received his

Ph.D. in Electrical Engineering from the Laval Uni-

versity and he received his Masters Degree in Mech-

anical Engineering from the same university. His

research interests are in the area of industrial stat-

istics: Productivity Improvement, Quality Control

and Tolerances Optimisation. He is Registered Pro-

fessional Engineer in Quebec, Canada and members

of ASME (American Society of Mechanical Engi-

neers), CMVA (Canadian Machinery Vibration

Association) and ASQ.

Zhaoheng Liu is a professor in the Department of

Mechanical Engineering, Ecole Technologie Super-

ieure, Montreal, Quebec, Canada. He received his

Ph.D. and Master degree in Mechanical Engineering

from the University of Sherbooke in 1991 and 1995

respectively. He is Registered Professional Engineer

in Quebec, Canada and members of ASME (Ameri-

can Society of Mechanical Engineers) and CMVA

(Canadian Machinery Vibration Association). His

research interests are in the area of multi-body

dynamics, vehicle dynamics, vibration and computa-

tional geometry.

REFERENCES

Besl, P. J., McKay, N. D. (1992). A method for registration of 3-D shapes.IEEE Transactions on Pattern Analysis and Machine Intelligence,14(2):239–256.

Bhandarkar, S. M., Faust T. D., Tang M. (1999). A system for detectionand rendering of internal log defects using computer tomography.Machine Vision and Applications, 11(4):171–190.

Hageniers, O. (2001). Advantages of 100% inline inspection in automo-tive body assembly. 2001. SPIE Proceedings, 2455:161–165.

Harding, K., Bieman, L. (1989). Moire interferometry gives machine visiona third dimension. Sensors, October 1989, 24–28.

Horn, B. K. P. (1987). Closed-form solution of absolute orientation usingunit quaternions. Journal of the Optical Society of America A (Opticsand Image Science), 4(4):629–642.

Langis, C., Greenspan, M., Godin, G. (2001). The parallel iterative closestpoint algorithm. Proceedings of the Third International Conference on3-D Digital Imaging and Modeling, 28 May–1 June 2001. Quebec City.

Luck, J., Little, C., Hoff, W. (2000). Registration of range data using ahybrid simulated annealing and iterative closest point algorithm. ICRA2000: IEEE International Conference on Robotics and Automation,24–28 April, San Francisco.

Marr, D. (1982). Vision: A Computational Investigation into the HumanRepresentation and Processing of Visual Information. San Francisco:Freeman.

Shaw, M. (2005). Guest introduction: The changing shape of computervision in the twenty-first century. International Journal of ComputerVision, 50:103–110.

Standard Grading Rules for Canadian Lumber, Published by the CanadianLumber Grades Authority, Westminster, British Columbia, Canada,2004, ISBN 0-9736657-O-X.

Tolba, A. S., Abu-Rezeq, A. N. (1997). A self-organizing feature map forautomated visual inspection of textile products. Computer in Industry,32:319–333.

Truong Pham, D., Alcock, R. J. (1998). Automated grading and defectdetection: A review. Forest Products Journal, 48(4):34–42.

Tucker, T. M., Kurfess, T. R. (2003a). Newton methods for parametricsurface registration. Part I: theory. Computer Aided Design, 35(1):107–114.

Tucker, T. M., Kurfess, T. R. (2003b). Newton methods for parametric sur-face registration. Part II: Experimental validation. Computer AidedDesign, 35(1):115–120.

Tukey, J. W. (1974). Nonlinear (nonsuperposable) methods for smoothingdata. Proc. Congr. Rec. EASCON ’74, October 7–9, Washington DC,1974, p. 673.

Zuech, N. (2004). Machine vision in the wood industry. Machine Visiononline. http:==www.machinevisiononline.org=public=articles=archive-details.cfm?id¼2194.

231 Automatic Characterization

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