Oblique radiographic measurement of knot position and orientation in logs

A novel X-ray scanner system to identify the positions of knots in logs is described. The scanner has a simple, low-cost design that is suitable for use in medium and smaller sawmills. It makes X-ray measurements in an oblique direction as the log moves longitudinally past the X-ray source and line-detector. This unconventional oblique measurement direction creates a more side-on view that better reveals the spatial arrangement of the knots within the log. This view, when combined with the knowledge that all knots start from along the pith and radiate outwards gives sufficient information to identify knot orientations in space. Experimental oblique X-ray measurements on a sample log are described, followed by the processing and analysis of the measured radiographs, and a comparison of the results with independent measurements of knot locations. With the knot identification algorithms developed, knot axial position could be identified within 11 mm, and knot circumferential orientation with a root mean square (rms) error of 7.9°–11.6° when using a single view X-ray scanner, or 5.6°–7.7°


Introduction
When cutting logs into lumber in sawmills, approximately 75% of the total process cost comes from the raw material [1,2].Thus, to maximize the cost efficiency of the production process it is very important to make the most effective use of the input logs.To achieve good material utilization, it is essential to be able to identify and manufacture the highest value products that can be made from the raw material [3].This can only be done effectively if the quality characteristics of the logs entering the sawmill can be assessed reliably and those observations used when choosing the products to be made and the corresponding processing conditions.
Traditionally, log quality assessment was made visually by headrig saw operators, who used their experience to decide how to cut each log.In recent decades, in-line measurement technologies have been introduced to assist with the log quality assessment and to select the most appropriate cutting pattern to achieve the highest value products.The most commonly used measurement technology is laser scanning to measure external shape, from which cutting pattern decisions can be made to achieve product value recovery [4][5][6].However, no interior information is available, so the product value calculation is based only on the enclosed volume within the measured surface shape of the log.There is no ability also to account for the quality of the interior wood.Several studies have indicated that a product value increase of about 5-15% could be achieved by also including within the cutting decision details of the interior of each log [7][8][9].
X-ray measurements have attracted significant interest in recent years because of their ability to probe into the interior of logs and thus to be able to observe the internal features of interest.Such features include knot size and location, the position of the heartwood/sapwood boundary, the ring density and the possible presence of rot and voids [7,8,10].The classical approach is by radiographic scanning [11], which is the same technique as used for medical X-rays.However, radiographic scanning is a 2-dimensional technique and cannot give any depth information.For example, in a radiograph of a log, knots that incline towards the X-ray source appear similarly to those that incline away.Knots with orientation near parallel to the measurement direction are particularly difficult to observe.
The comprehensive solution to the depth identification problem is to do computed tomography (CT) measurements [7,[12][13][14][15][16].This involves making radiographic X-ray measurements from multiple directions and then mathematically combining those 2-D images into a composite 3-D image that contains all the desired depth location information.While this method is certainly effective, it is also very technically demanding and very costly.Very substantial numbers of X-ray measurements must be made at high speed and require very accurate positioning of the log relative to the X-ray source and detector.The irregular shapes of logs and the rough environments of sawmills make this very difficult to achieve.In addition, the very high cost of the equipment creates a substantial impediment to all but the very largest sawmills.
An alternative approach, developed by the author [17], is taken here.It involves modifying the radiographic measurement technique so as to enable the medical approach to X-ray image interpretation to be effective.In the same way as a medical radiographer uses their a priori knowledge of human anatomy to infer the missing depth information from a 2-D radiograph, so it can be similarly possible to use a priori knowledge of tree anatomy to infer knot orientations in 3-D space.Tree anatomy for coniferous species has some primary geometrical features, notably that the knots all start from along the pith and radiate outwards in approximately straight lines [18].The main difficulty with conventional log radiographs is that they are measured perpendicular to the log axis, so the knots are viewed in a plane along the observation direction.This approach effectively maximizes the difficulty in interpreting their orientation in space.Here, it is proposed to relieve the interpretation difficulty by instead making X-ray measurements obliquely to the log axis.This modified approach produces a radiograph that shows the knots with a more side-on view.The oblique view, when combined with the knowledge that all knots start from along the pith and radiate outwards gives sufficient information to be able to identify knot orientation in space.This paper details some experimental oblique X-ray measurements on a sample log, the processing and analysis of the measured radiographs, and a comparison of the results with independent measurements of knot orientations.With the knot identification algorithms developed, knot orientation in space could be identified with a root mean square (rms) error of 5.6°-11.6°,depending on the option chosen.

Method
Figure 1a shows a plan view of a conventional type of X-ray system for scanning logs.A conveyor system moves a log longitudinally past an X-ray source placed at one side.The X-rays pass perpendicularly through the log and are measured by a vertical line sensor at the other side.Line measurements are made sequentially as the log moves through the X-ray source/sensor arrangement, thereby creating a 2-D radiographic image of the length profile of the log, such as is shown in Fig. 1b.The example radiograph is for a coniferous log, for which the knots grow radially from the center, at orientations close to perpendicular to the pith, either singly or in clusters [18], as schematically shown in the figure.The various knots lie approximately within the X-ray scanning plane, so their angular orientation around the pith is difficult to discern.In addition, knot images easily overlap each other when the knots are present in clusters.
Figure 2a shows the modified X-ray system proposed here.It is generally similar to the conventional perpendicular X-ray system in Fig. 1a, but with the significant difference that the X-ray source and sensor arrangement is aligned obliquely with respect to the log.This change has the effect of imaging the knots within the log with a more side-on view, so that their orientation in space becomes more visible, as shown in Fig. 2b.
The knots appear as dense features within the measured radiographic image.If these features are identified in the oblique view and their angular location in space determined, it is then possible to compute the location and orientation of the corresponding knots within the measured log.As a practical simplification, a knot can be idealized as a circular cone starting from the pith of the log and radiating outward.Five geometrical parameters are needed to describe the basic knot geometry: x = axial location of the pith origin of the knot, φ = circumferential angle of the knot relative to the pith, ψ = longitudinal angle of the knot relative to the pith,.d = diameter of the knot, L = length of the knot.It is the overall objective to be able to identify all five parameters from oblique X-ray measurements.The present work focuses on the first three quantities and gives a path to the remaining two.
The assembly of the X-ray line scans measured as the log moves past the X-ray source/sensor system creates a radiograph of the length profile of the log.In this radiograph the knots appear at angles depending on their angular positions within the log and on the oblique scanning angle.Figure 3  The formulas for the dimensions of the knot image shown in Fig. 3 refer to the case where the knot extends full-length to the outer surface of the log.In that case, R refers to the log radius.For a shorter knot, the value of R used is the radius at the end of the knot.From the geometry of Fig. 3, the imaged knot angle within the radiograph is: where the (R/A) term accounts for the perspective effect of the knot distance variation within the X-ray cone beam caused by the variation in angular position φ.
Equation 1 has two unknowns, the angle of the knot measured circumferentially around the pith, φ and the angle of the knot measured longitudinally relative to the pith normal, ψ.The latter angle is usually small, typically 5°-20° sloping upwards within the tree [18].A few tree species have downward sloping knots, but for logs of a given tree species the angle is fairly consistent.
The two unknowns in Eq. 1 require that two measurements of β be made, from which the knot angles φ and ψ can be determined.This can be done by making (1)  measurements using two X-ray source and sensor systems of the type shown in Fig. 2, aligned perpendicularly to each other.In this case, the knot angle φ can be determined using: where of β 1 and β 2 are the knot orientation angles shown in Fig. 3, observed in each of the two perpendicular X-ray systems used.Equation 2 can be solved iteratively starting from φ = 0.It typically converges rapidly, with 2-3 iterations sufficient.Knot angle ψ can then be determined by inverting Eq. 1 to give: (2) In the case where the longitudinal knot angle ψ is estimated based on the species of the log, the circumferential angle φ could be estimated from a single radiographic measurement using: As before, this equation can be solved iteratively with rapid convergence, starting from φ = 0.If a second orthogonal measurement β 2 is made, the same equation can be used with β 2 replacing β 1 and with 90° subtracted from the converged result.

Experiments
An experimental test setup was constructed corresponding to the schematic diagram shown in Fig. 2. The oblique scanning angle θ = −45°.The X-ray source was a Sourceray model: SB-160-2 K, operating at 160 kVp and 2 mA.The line sensor was a X-scan model: XW8808, 0.8 m long with 768 pixels, corresponding to 0.31 mm spacing within the plane of the log pith.X-ray measurements were made at 126 fps and 2 ms exposure time.The carriage speed, measured using a rotary encoder, was 54.2 mm/s, thus giving a measurement every 0.43 mm of log longitudinal motion.A small dry red cedar (Thuja plicata) log, 1 m long and ~ 158 mm diameter was used as the test specimen.It was scanned four times, each scan after a 90° circumferential rotation from the previous scan.
Figure 4 shows a typical radiograph, made by assembling the line scans made over the length of the log specimen.The particular sensor used here had a prominent artifact that every 16th pixel was faulty, thus producing (3) the regular horizontal lines visible in Fig. 4.This artifact was mathematically removed by replacing the faulty pixel data by the average of the adjacent two well-functioning pixels.
In Fig. 4, areas of high measured radiation intensity appear bright, while areas of low measured intensity appear dark.Since the knots have higher density than the surrounding clear wood, they absorb more X-ray radiation and thus appear darker in the radiograph.However, since they form only a small fraction of the total thickness of the log, the change they cause in the throughthickness density measurement is modest, thus their contrast is low [19].
In addition, the log sample was scanned in an industrial CT scanner.This measurement gave a detailed map of the interior features of the log, which provided a reference data set against which the results of the oblique scanning experiments could be compared,

Calculations
The measured radiographs such as shown in Fig. 4, indicate X-ray attenuation.The quantity of practical interest is the corresponding basis weight (density per unit area).The conversion into basis weight can be done using Beer's Law [20]: where I is the X-ray intensity at a given pixel within the measured radiograph, I 0 is the unattenuated radiation intensity measured at the same pixel while the sensor area was empty, before the entry of the log specimen, and I b is the background reading at the pixel measured when the X-ray source is turned off.Since only relative basis weight information is needed to identify the knot Figure 5 shows the basis weight image corresponding to the radiograph in Fig. 4. In this image, areas of low basis weight appear dark and high basis weight appear bright.The additional lines indicate the location of the log pith and outside surface, estimated from the columns of the basis weight data using [21]: where bw and y, respectively, are the basis weight and row number at a pixel within a column.Σ indicates summation over all the pixels within that column.y c , is the mass centroid of the column, which is estimated to be the row number that contains the pith.y r is the estimated log radius in pixels.The central line in Fig. 5 shows the computed y c and the outer two lines show the computed y c ± y r .
The low contrast in Figs. 4 and 5 creates a serious challenge when seeking to identify the knot areas and highlighting them relative to the adjacent clear wood areas.To identify and segment the knot areas reliably, it is necessary to increase their contrast substantially.A simple size and offset change, such as produced by a conventional brightness/contrast adjustment, will not produce a useful result because it will also substantially multiply the measurement noise.Here, a more customized approach is taken based on the particular features of the basis weight map.The principles and ideas used when developing a suitable algorithm are: • The procedure should as much as possible be selfadaptive, that is, it should adjust its operation based on its own observation of the characteristics of the (6) given data and not require "tuning" by an external operator.• The procedure should seek to minimize the impact of data noise by using aggregate quantities that are an average of many pixels, while avoiding detailed manipulations that involve individual pixels.For example, the log surface identification from Eq. 6 is made by combining all pixels within a column of data.Conceptually the log surface could be found by an edge detection technique, but this approach is avoided here because it involves working with just a few localized pixels.With these thoughts in mind, customized knot contrast enhancement and knot segmentation algorithms were developed as follows.First, to achieve maximum horizontal image consistency, the slope and curvature of the log appearing in the measured radiograph is mathematically straightened.This is done by finding the center pixel y c within each column of the basis weight image using Eq.6 and then shifting the contents of that column vertically so that the center pixel of each column lies along the horizontal centreline of the basis weight map.Practical testing showed that this alignment needs to be done with some care.Simple column shifting by an integer number of pixels produces small vertical artifacts where integer rounding causes rounding up to when it causes rounding down.Thus, the column shifting must be done fractionally by linear interpolation between pixels.On further testing, it was also found that the basis weight increases in the areas of the knots cause small local distortions in the pith line and log radius predicted by Eq. 6.These would then cause corresponding distortions in the mathematically straightened basis weight map.To reduce this effect, the y c values computed from Eq. 6 are first smoothed by averaging each value with those from the 100 columns on each side.The corresponding y r values are similarly averaged to give a smooth outside surface indication.
The horizontally uniform character of the clear wood regions and the relatively small contributions and the knot areas provide a practical opportunity for clear wood subtraction within the straightened basis weight map.The approach taken is to form a vertical (along-column) profile of the clear wood response and subtract it from the basis weight map.To minimize the contributions from the knots, the average of the basis weight profiles across a wide group of columns is used.The width of the column group needs to be much greater than the typical knot width so that the knot contribution to the calculated average profile is small.However, the width should not be excessively large because the clear wood profile does change slowly along the length of the log, and for the best results it should be followed.In the experimental work, 320 columns of data were combined to form a moving average along the length of the test log.This corresponded to an axial distance of 140 mm, which is long compared with the typical knot width, 20 mm, but short compared with the total log length, 1000 mm.Some modest smoothing of the result was useful for reducing local irregularities introduced by the annual growth rings.
Figure 6 shows the knot feature map produced by subtracting the clear wood background from the basis weight map in Fig. 5.The greyscale is substantially multiplied to highlight the knot features.The knots now appear as clearly distinct regions within a substantially dark background.

Results
The next step after highlighting the knot areas in Fig. 6 is to identify their specific locations, orientations and sizes.In keeping with the principles previously outlined, procedures based on the average properties of many pixels were chosen so as to make the results as robust and noise resistant as possible.Conventional edge detection schemes were not pursued because they depend on the values at just a few nearby pixels.Even in the relatively clean knot feature map shown in Fig. 6, the knots display quite jagged edges due to show-though of the annual growth rings of the adjacent clear wood, and thus would give very noisy edge detection results.The first step to identify the knots is to locate their approximate positions within the knot feature map.This is done by passing a 25 × 25 averaging template along the length of the knot feature map at the ± 1/3 log radius positions.These lines intersect most of the knots at some point within their highlighted area.The corresponding basis weight profiles have local peaks at each of these points.The first estimates of the knot positions are the locations of the observed density peaks.
Having located the knots, the next step is to identify their orientations within the knot feature map. Figure 7 schematically displays the computational procedure used.Using the initial knot location estimate as the center position, a rectangular area of pixels is rotated in angular increments, here 5°, around that point and the average basis weight within the rectangle computed at each step.The results are slightly smoothed to remove discretization noise and the direction of maximum basis weight determined.The results can be interpolated to achieve a finer angular resolution, estimated to be about ± 1°.
In addition, by applying Eq. 6 to the pixels along the length and across the width of the rectangular area in Fig. 7, the position of the mass centroid of the knot area can the estimated.By measuring along the identified orientation of the knot by a distance equal to the indicated centroid, a better estimate of the central location of the knot area can be made.A yet further estimate of the knot mass centroid position can then be made.This third estimate is typically quite a good representation of the center of the knot area, so is chosen to be used as the basis for the final knot orientation determination.For this final evaluation, the second Eq. 6 is also used to estimate the length and width of the best-fit knot rectangle.In addition, the axial location of the identified knot along the length of the log is determined by extrapolating the knot orientation line from the final centroid to the pith line of the log.
Figure 8 shows the knot feature maps measured in the four log orientations, 0°, 90°, 180° and 270°.The 0° map corresponds to Fig. 6.Each map is superimposed with the identified best-fit rectangles for each knot.For each rectangle, the side nearest the pith is extended out to mark the intersection point with the pith line.The "x" symbols indicate the starting knot identification points along the 1/3 radius line, the " + " symbols indicate the next estimated knot centroid and "□" indicates the third-estimate centroid positions used for the final knot orientation and dimension calculations.As can be seen, all knot identifications are realistic.
Test calculations using Eqs. 2 and 3 to evaluate the knot circumferential angle φ and axial angle ψ from the observed knot inclination angles β measured in directions 90° apart showed a substantial sensitivity to small measurement errors, causing discrepancies of many tens of degrees in comparison with the reference CT measurements.This behavior occurs because the circumferential and axial knot angles φ and ψ are closely coupled within the equations.Thus, very different combinations of the two angles can correspond to almost the same input data.The error sensitivity within Eqs. 2 and 3 creates the need for an alternative knot angle computation approach.A pragmatic response to the close coupling between the circumferential and axial knot angles φ and ψ is to focus on the more variable of the two, which is the circumferential knot angle φ.This idea is pursued here by noting that within a given tree species, the axial angles ψ of most knots are similar and vary within only a very limited range [18,22,23].Thus, if an average value was assumed in advance, then only the circumferential angle θ would need to be computed.Since ψ is constrained in this way to be in a reasonable range, the resulting θ is likely also to be in a reasonable range.Equation 4gives the solution for circumferential angle θ for the case where the axial angle ψ is given.Table 1 shows the results of using Eq. 4 with the measured knot inclination angles β.The first part of the table uses a knot axial angle ψ = −7° for all knots.The average rms error is 7.9°.The second part corresponds to the case where the knot axial angle cannot be estimated, for which the default value ψ = 0° is used.The resulting rms error then becomes larger, with an average value of 11.6°.
The results shown in Table 1 are attractive because they require the use of only one X-ray scanner.This allows a straightforward and economical X-ray system to be used.
The question arises as to whether the use of two perpendicular scanners might give some advantage through data averaging.This arrangement would ensure that each knot would be observed over a range of angles, one view being more side-on and one more end-on.This should also make the results more independent of knot orientation relative to the scanner.In addition, it may also help with the case where a knot happens not to show up well in a given scan, for example due to knot image overlapping.Table 2 shows the results.It can be seen that using the arithmetic average of two orthogonal scan significantly helps.With ψ = −7° the mean rms error reduces from 7.9° to 5.6° and with ψ = 0° the rms error reduces from 11.6° to 7.7°.The latter is a promising indication because it means that if it should happen that the axial inclination angle ψ is not known for the given log, a null value ψ = 0° would still give a reasonable result.

Discussion
The experiments reported here indicate that the proposed approach to measuring the positions and orientations of knots within a log by oblique X-ray scanning is a very promising one.In this initial study, just one small dry log was measured, so the results must be considered as suggestive rather than definitive.However, the example results do give a good basis for understanding the character and scope of the oblique X-ray scanning measurement concept.This concept is particularly interesting because it is very simple and cost efficient; it needs only one or possibly two simple X-ray sources and line-detectors, both widely available at moderate cost.The computer control system can also be of ordinary type because the required calculations to do the knot identification are modest in scope and can easily be done in real-time.The oblique scanning system has the potential to be practical in medium and smaller size sawmills, where its modest installation and running costs would make it an attractive choice.In the example tests, the measurement accuracy for the knot axial position was found to be ± 11 mm, and for circumferential orientation θ was ± 5.6° to ± 11.6°, depending on option chosen.These accuracy levels should be sufficient in many cases.Greater accuracy could be achieved by the use of a CT scanner system, but at the expense of many times greater installation and operating costs.Likely only the largest sawmills could justify the cost of a full CT system and also have a staff sufficiently specialized to operate it effectively.
In radiographs taken along the length of logs, the fraction of the log diameter taken up by knot material is small, thus the X-ray contrast between the knots and the surrounding clear wood is also small.Because of this, it is necessary to process the measured radiographs to increase the contrast of the knots so that they are more effectively identified and located in space.Algorithms for doing this were designed so as to be as robust and widely applicable as possible, thereby minimizing the need for "tuning" to fit a given measurement condition.In addition, the various procedures used were chosen to involve averages of many measurements from within the radiograph.This was done to minimize the adverse effects of noise on operations that otherwise would involve only a few measurements, for example, conventional schemes for feature edge detection.
Two independent angles are required to describe knot orientation within a log, the circumferential angle θ and the axial angle ψ.Conceptually, both angles could be determined simultaneously from log radiographs taken in two different directions.However, it was found that the two angles contribute in mathematically similar ways to the measured results and so it is difficult to separate them in practice.It happens that logs deriving from a given tree species commonly have similar axial angles ψ, so a significantly stabilization of the knot orientation calculation for θ can be achieved by assuming an average ψ a priori.In the case of the example red cedar log, the axial angle was ψ = −7°.The sign of this angle can be positive or negative depending on the log was scanned from the wide to the narrow end, or vice versa.This direction can readily be identified within the radiograph by observing whether the measured log radius is decreasing increasing along the long length.
It commonly happens in sawmills that different tree species are processed on the same line, and it may also happen that each species has a different axial knot angle.If species identification is not available and if the axial knot angles for the various species greatly differ, then a null choice of ψ = 0° may need to be made.In the example measurements made here, the rms error in circumferential angle θ measurement when using the null choice ψ = 0° was 11.6°.This compares with 7.9° rms error achieved when the actual average axial angle ψ = −7° is used.A further analysis was done to investigate the possible utility of using two perpendicular scanners.This arrangement would ensure that each knot would be observed over a range of angles, with one view being more side-on and one being more end-on.This should make the results more independent of knot orientation relative to the scanner.It may also help with the case where a knot happens not to show up well in a given scan, for example due to knot image overlapping.With ψ = −7°, perpendicular scanning reduced the mean rms error reduced from 7.9° to 5.6° and with ψ = 0° it reduced the rms error from 11.6° to 7.7°.Where the improved accuracy and reliability have sufficient value to justify the increased equipment cost, a two-scanner system would be an appropriate choice.Although not tested here, it is possible that a dual scanner system could give more accurate angle results if the two scanners are set to operate in opposite lengthways directions as well as in orthogonal planes.That way there will be greater diversity in the range of measurement angles used and thus perhaps greater effectiveness in the data averaging from the two measurement planes.

Conclusions
A low-cost, radiographic system for identifying knot radial and longitudinal positions within a log has been demonstrated.It uses oblique scanning of the log to gain a more revealing view of the knots within the log than are available from conventional perpendicular scanning.The best results are achieved with knots that are aligned perpendicularly to the X-ray propagation direction.Thus, to achieve a uniform measurement accuracy for knots with arbitrary alignment, a dual axis scanning system is suggested, where two perpendicular X-ray scanners are used.In the example tests, for a single axis arrangement the rms error for the knot axial position was found to be 11 mm, and for circumferential orientation θ was 11.6° when the log species is not known in advance (assuming knot angle ψ = 0°), reducing to 7.9° when the log species is known in advance (putting knot angle ψ = −7° in this case).The use of two perpendicular scanners reduced the rms error in knot angle θ to 7.7° for the unknown species (ψ = 0) case, further reducing to ± 5.6° for the known species (ψ = −7°) case.
A radiographic X-ray scanning system of the type proposed here may be used for purposes beyond knot location identification.In common with conventional perpendicular X-ray scanning systems, under-bark log diameter, radial position of hardwood/sapwood boundary, ring spacing and the presence of rot and voids can all potentially be observed.
Figure1ashows a plan view of a conventional type of X-ray system for scanning logs.A conveyor system moves a log longitudinally past an X-ray source placed at one side.The X-rays pass perpendicularly through the log and are measured by a vertical line sensor at the other side.Line measurements are made sequentially as the log moves through the X-ray source/sensor arrangement, thereby creating a 2-D radiographic image of the length profile of the log, such as is shown in Fig.1b.The example radiograph is for a coniferous log, for which the knots grow radially from the center, at orientations close to perpendicular to the pith, either singly or in clusters[18], as schematically shown in the figure.The various knots lie approximately within the X-ray scanning plane, so their angular orientation around the pith is difficult to discern.In addition, knot images easily overlap each other when the knots are present in clusters.Figure2ashows the modified X-ray system proposed here.It is generally similar to the conventional perpendicular X-ray system in Fig.1a, but with the significant difference that the X-ray source and sensor arrangement is aligned obliquely with respect to the log.This change has the effect of imaging the knots within the log with a more side-on view, so that their orientation in space becomes more visible, as shown in Fig.2b.The knots appear as dense features within the measured radiographic image.If these features are identified in the oblique view and their angular location in space determined, it is then possible to compute the location and orientation of the corresponding knots within the measured log.As a practical simplification, a knot can be idealized as a circular cone starting from the pith of the log and radiating outward.Five geometrical parameters are needed to describe the basic knot geometry:x = axial location of the pith origin of the knot, φ = circumferential angle of the knot relative to the pith, ψ = longitudinal angle of the knot relative to the pith,.d = diameter of the knot, L = length of the knot.It is the overall objective to be able to identify all five parameters from oblique X-ray measurements.The present work focuses on the first three quantities and gives a path to the remaining two.The assembly of the X-ray line scans measured as the log moves past the X-ray source/sensor system creates a radiograph of the length profile of the log.In this radiograph the knots appear at angles depending on their angular positions within the log and on the oblique scanning angle.Figure3schematically shows a typical knot image within a radiograph.The physical dimensions are:

Fig. 1
Fig. 1 Perpendicular X-ray scanning of a log a plan view, b log radiograph

Fig. 2 Fig. 3
Fig. 2 Oblique X-ray scanning of a log: a perspective view, b log radiograph

Fig. 5
Fig. 5 Basis weight map of test log measured at 0° log orientation

Fig. 6
Fig. 6 Knot feature map of test log created by subtraction of clear wood background

Fig. 7 Fig. 8
Fig. 7 Rotation of a rectangular area of pixels to find the direction of maximum mass density