COMPARISON OF SEGMENTATION METHODS FOR DIGITAL IMAGE ANALYSIS OF CONFOCAL MICROSCOPE IMAGES TO MEASURE TRACHEID CELL DIMENSIONS

COMPARISON OF SEGMENTATION METHODS FOR DIGITAL IMAGE ANALYSIS OF CONFOCAL MICROSCOPE IMAGES

TO MEASURE TRACHEID CELL DIMENSIONS

Mattias K. Moëll

& Lloyd A. Donaldson

SUMMARY

Image analysis is a common tool for measuring tracheid cell dimen- sions. When analyzing a digital image of a transverse cross section of wood, one of the initial procedures is that of segmentation. This in- volves classifying a picture element (pixel) as either cell wall or lumen.

The accuracy of tracheid measurements is dependent on how well the result of the segmentation procedure corresponds to the true distri- butions of cell wall or lumen pixels. In this paper a comparison of seg- mentation methods is given. The effect of segmentation method on measurements is investigated and the performance of each method is discussed.

We demonstrate that automated segmentation methods remove observer bias and are thus capable of more reproducible results. The contrast for confocal microscope images is of such quality that one of the fastest and simplest automatic segmentation methods may be used.

Key words: Segmentation, image analysis, tracheid measurements, con- focal microscopy.

INTRODUCTION

Image analysis has proven to be a useful tool when assessing the morphological char- acteristics of wood tracheids (McMillin 1982; Lee & Rosen 1985; Jagels & Telewski 1990; Evans 1994; Diao et al. 1996; Moëll & Borgefors 2001). Not only has the speed of obtaining such characteristics improved, but image analysis has also allowed the operator bias to be reduced. One of the procedures in an image analysis system for obtaining tracheid morphology is the segmentation process. Segmentation is a pixel classification process to identify different wood anatomical features in a digital im- age. The classification here is focused on identifying wood cell wall pixels. The number of classes is two, that is cell wall and non-cell wall, where non-cell wall includes lumens and ray cells. Groups of pixels forming connected components in the seg- mented binary image can also be classified at the object level (Peachey & Osborne 1990; Diao et al. 1997; Moëll & Borgefors 2001), using size and shape measures to classify non-cell wall objects.

1) Center for image analysis, Lägerhyddv. 17, 752 37 Uppsala, Sweden [E-mail: mattias@

cb.uu.se]

2) New Zealand Forest Research Institute Ltd., Private Bag 3020, Rotorua, New Zealand.

The accuracy of the segmentation process is crucial since measurements are per- formed on the objects created by the segmentation. Thus, the better the cell wall clas- sification the higher the accuracy of the measurements. Wood fiber measurements are of importance to the forest products and paper industries because the morphological characteristics of the fibers significantly affect the properties of wood and paper prod- ucts (Kibblewhite 1980).

The aims of this study are a comparison of segmentation methods and an investi- gation of the effects of segmentation method on measurements of tracheid dimen- sions.

MATERIALS AND METHODS

Sample preparation, confocal microscopy and image acquisition

Samples of Pinus radiata D.Don, Pinus sylvestris L., Pseudotsuga menziesii (Mirb.) Franco, Picea abies Karst. and Eucalyptus delegatensis R.Baker were saturated in water and fixed in formalin aceto-alcohol ( ^FAA ) prior to sectioning with a sledge microtome at a thickness of 60 ^μ m. Sections were stained in safranin (0.1% aq.) for 2–3 minutes, washed, and oven dried before mounting in immersion oil (N

= 1.515) with a coverslip as described by Donaldson and Lausberg (1998). Sections were ex- amined using a Leica TCS / NT confocal microscope using a 16 ^× oil immersion lens.

Confocal microscopy was performed using wavelengths of 568 nm for excitation, and 600 nm for imaging. Digital images were acquired at 1024 ^× 1024 resolution (625 ^× 625 ^μ m) in 8-bit greyscale (0–255 greylevels). Most images examined were single confocal slices approximately 1 ^μ m thick unless otherwise stated. Safranin stain- ing produced a stable fluorescence signal that showed little or no fading over time.

Images were acquired under optimum exposure conditions set by the operator prior to acquisition using a ʻglowoverʼ look-up table. This system displays white pixels (255 greylevel) as bright blue – exposure is set by minimising the number of blue pixels thus ensuring that the full dynamic range (0–255) is utilised without producing an over or under exposure.

A control set of images for segmentation comparisons was obtained by manually masking all non-cell wall areas in each image. This produced a near optimum segmen- tation but was too tedious for practical application. The original images were then processed using the various segmentation methods described below.

Manual segmentation methods Manual thresholding based on greylevel

The method of greylevel thresholding groups pixels together within a certain grey- level range. A greylevel threshold is set interactively by the user and all pixels having a higher greylevel than the threshold are classified as cell wall pixels. In confocal microscope images the cell wall contains bright pixels, i.e. pixels with high greylevels.

A comparison was made between two independent observers to measure the level of

operator bias in this method.

Manual thresholding based on texture

In confocal images the cell wall may contain more greylevel variation among pixels than in the empty lumens where there is only random variation, usually removed by signal averaging during acquisition. The texture measures, including variance ( RMS ) and range with either a 3 ^× 3 or octagonal 5 ^× 5 neighborhood, illustrated in Russ (1995) were implemented. The variance value for the central pixel in a neighborhood is the sum of squares of the greylevel difference between the non-central neighborhood pixels and the central pixel.

Where g

is greylevel of the ith non-central neighborhood pixel and g

is the grey- level of the central pixel. The number of pixels in the neighborhood, n, is n

9 and n

21 for the 3 ^× 3 and the 5 ^× 5 octagonal neighborhood respectively. The range value of the central pixel in a neighborhood, g

, is the difference between the highest and lowest greylevel value in the neighborhood

Where g

is the greylevel value of the j

pixel of all the pixels in the neighborhood, j = 1,…,n.

The investigation by Peachey and Osborne (1990) of the Roberts, Sobel, and La- placian edge detectors on a light microscope image of Eucalyptus regnans indicated difficulties in identifying cell boundaries due to poor contrast in the middle lamellae, while easily being able to detect lumen boundaries.

The variance and range operators can be seen as edge detectors; however, in this application they are used as a texture measure in a wood image, rather than as a de- tector for cell wall and lumen boundaries. The aim was to investigate the possibility of using texture for identifying (segmenting) the cell wall component in a confocal image of wood cells. For this purpose we have also included the 3 ^× 3 and the 5 ^× 5 Laplacian filters in this study. Details of the filter masks for the 3 ^× 3 and the 5 ^× 5 Laplacian filters are found in Russ (1995). For the 5 ^× 5 Laplace filter, the 5 ^× 5 Mexi- can hat version was used.

To avoid image border effects, the image border, 1-pixel and 2-pixels thick for the 3 ^× 3 neighborhood and the 5 ^× 5 octagonal neighborhood respectively, was excluded from processing. Because texture is locally variable it was necessary to smooth seg- mented images using a morphological smoothing algorithm (Russ 1995). This has the effect of filling holes within the cell wall while retaining the original size and shape of the cell lumens. Small cell lumens such as those near the latewood boundary tend to be lost by this procedure.

Semi-automatic segmentation methods

Here, semi-automatic refers to manually selecting a training set within an image.

The training set is viewed as the true class, classification is then performed with the use of the training set.

g

max (g

) – min (g

)

Region growing (Masking)

For the region growing method, all pixels in the image with a greylevel within 10% of the selected pixel or pixels (training set) are considered as belonging to the same class as the training set. In this application, the training set was a part of the middle region of one single lumen. Theory and examples of region growing are given in Gonzalez and Woods (1992).

Profile half maximum height

In the profile half maximum height method, a greylevel profile between two points is examined. The two points are chosen as central points of two adjacent lumens, thus giving a lumen-cell wall-lumen profile. The greylevel threshold was set to half of the maximum height of the greylevel profile.

Maximum-Likelihood classification

The maximum-likelihood classification ( ML -classification) of Duda & Hart (1973) was also investigated using the confocal wood images. The training set consists of two classes. The first training class is the main part of one lumen and the second training class contains most of the cell wall around that lumen. Thus based on these two training classes, the ML -method classifies each pixel in the image as either cell wall or lumen.

Automatic segmentation methods Average brightness

The method of average brightness (Donaldson & Lausberg 1998), which is rou- tinely being used at New Zealand Forest Research Ltd. for image analysis of Pinus radiata, was used. This method finds the average cell wall brightness by setting an arbitrary threshold at 5 greylevels and calculating the average greylevel intensity above this threshold. A new threshold is then calculated using the regression equation relat- ing average cell wall greylevel (x

) to the optimum threshold (T). The optimum thresh- old is determined by minimizing the logical XOR error between the test image and its control image over a range of identical images of varying brightness.

T = 3.165 + (0.606 ^× x

) + (–0.00174 ^× x

) Greylevel histogram thresholding

The greylevel histogram of a digital image is defined as:

h[i] = the number of pixels with greylevel ≤ i , i = 0,…,255

A good contrast image where two classes of pixels are well defined by greylevels, i.e.

minimal overlap between the classes, should yield a bimodal greylevel histogram.

The class with brighter pixels is centered on higher greylevels than the class with

darker greylevels. The local minimum between the two maxima in a bimodal greylevel

histogram should thus separate two such classes well. This method is called bimodal

greylevel histogram thresholding (Gonzalez & Woods 1992).

In this application, the greylevel histogram was smoothed until it was bimodal using the filter:

h[i] = -1 ^× h[i-1] + 2 ^× h[i] -1 ^× h[i+1]

The image was thresholded at the local minimum between the two maxima.

Shape based thresholding

Another automatic segmentation method in this study was the shape based thresholding of Ranefall et al. (1998), used on confocal reflected light images for the Picea abies studies by Pape et al. (1999), and the Pinus sylvestris studies by Hannrup et al. (2001). This shape-based method selects a global threshold which gives a segmentation containing a small number of compact objects, thus separating out the round and rectangular lumen objects. The threshold is the local minimum between the two maxima in the smoothed bimodal P

A histogram. The P

A histogram is de- fined as:

P

A[i] ⁼ (P[i])

/A[i], i ⁼ 0,…,255

where (P[i]) is the sum for each greylevel

i, of the number of neighbors with grey-l evel > i, and A[i] is the number of pixels with greylevel = i. Here ʻneighborʼ is defined as edge to edge (4 connective) pixel neighbors. The histogram is smoothed with the filter:

P

A[i] = -1 ^× P

A[i-1] + 2 ^× P

A[i] -1 ^× P

A[i+1]

until the histogram is bimodal.

Automatic thresholding in greylevel/texture measure-space

In Panda and Rosenfeld (1978) segmentation is performed using a combination of greylevel and edge value on ʻforward lookingʼ infra-red aerial images. The combina- tion of greylevel and texture was investigated as a method for cell wall classification by these authors. We have investigated the use of the automatic L- and H-methods on wood images. Here the 3 ^× 3 range was used as the texture measure.

The L-method is based on the greylevel histogram of points in greylevel/texture measure-space having low texture values. In our application we have considered low texture values to be texture values less than or equal to 10% of the highest occurring texture value in the image. The aim is that these points should mainly contain lumen and cell wall pixels, and very few pixels from the boundary between lumen and cell wall. The greylevel histogram for these points was calculated, and a threshold was obtained using greylevel histogram thresholding for this conditional histogram.

The H-method is based on points in greylevel/texture measure-space having high

texture values. The threshold of the H-method is the conditional mean of greylevels

of pixels with texture values greater than a certain percentile of the maximum possi-

ble texture value. In our application we consider high texture values as greater or

equal to 85% of the largest occurring texture value in the image.

Fig. 1. Confocal fluorescence micrographs showing the range of species examined in our seg- mentation trials. – A: Pinus radiata. B: Pseudotsuga menziesii. C: Picea abies. D: Pinus syl- vestris. E: Picea abies latewood. F: Eucalyptus delagatensis. – Each image is 625 × 625 μm.

RESULTS AND DISCUSSION

Some of the segmentation methods we have investigated have been used for light microscope images of wood (Lee & Rosen 1985; Gasson 1985; Peachey & Osborne 1990). Lee and Rosen (1985) illustrated greylevel histogram thresholding for a light microscope image of a softwood. With the use of the same software, Gasson (1985) used greylevel histogram thresholding of light microscope images of hardwoods to perform vessel measurements. For light microscope images, Peachey and Osborne (1990) used manual dual thresholding, with two different thresholds set manually, and then post-processed three different classes of pixel groups. Jun et al. (2000) com- pared a region growing method, with a criterion based on image greylevel average and variance, to a threshold determined by cluster analysis. The region growing method was found to be more accurate. In these papers the segmentation result was deter- mined visually rather than pixelwise compared to a control image. Since confocal microscopy allows easy acquisition of good quality images (Donaldson & Lausberg 1998), it is of interest to quantify the results of automated thresholding on confocal microscope images by comparing to a control set of images.

Figure 1 shows typical images of the wood species included in this study. From a segmentation point of view we did not find any specific differences among the spe- cies. Segmentation separates the lumen from the cell wall by detecting borders using intensity, i.e. greylevel. The intensity distributions of confocal microscope images are similar for each species although the relative frequencies of wall and lumen pixels may vary, especially between softwoods and hardwoods.

Manual segmentation methods

To investigate the operator bias for manual greylevel thresholding, two observers manually thresholded a set of images. The logical XOR operation was used to obtain the number of pixels which differed between two corresponding observer thresholded images. These results are shown in Table 1. The bias is evident not only in that there is a difference in all but one image, but also that for most images one observer selects a higher threshold than the other. For most images one observer classifies fewer pixels as cell wall pixels, resulting in a thinner cell wall.

The set of images examined contained a range of different species, with both even

and uneven brightness. As shown in Table 1 the largest difference here for a single

image was approximately 23%. The image with the largest difference was an image

with uneven brightness. The reason that some images contain uneven brightness is

that the image contains information from varying depths below the surface of the

section (the section does not necessarily have a flat surface). In a confocal image,

brightness is proportional to depth due to absorption and scattering of light by the

sample (Donaldson & Lausberg 1998). In cases with uneven brightness, it is usually

not possible to segment all cells satisfactorily using a global threshold (the optimum

threshold varies across the image). To choose which cells to be segmented well, and

which not to be segmented at all, is dependent upon subjective decisions by the ob-

server. The differences between the two observers are, in many cases, greater for

Table 1. Comparison of manual thresholds using two independent observers. The differ- ence is given as a percentage of the number of pixels in the image. Image quality is report- ed in terms of uniform or variable brightness.

Image Species and specifications Observer 1 Observer 2 XOR Brightness difference (%)

A1 Douglas fir core wood 45 50 2.0 Uniform A2 Douglas fir core wood 45 60 5.8 Variable A3 Douglas fir outer wood 55 61 1.1 Uniform A4 Douglas fir outer wood 38 60 5.1 Uniform A5 Douglas fir outer wood 45 50 1.6 Uniform A6 Douglas fir outer wood 60 75 3.8 Variable A7 Douglas fir outer wood 55 77 5.8 Variable A8 Eucalyptus delegatensis 54 50 1.6 Uniform A9 Eucalyptus delegatensis 52 55 1.0 Uniform A10 Eucalyptus delegatensis 30 35 2.0 Uniform A11 Eucalyptus delegatensis 45 36 3.7 Uniform A12 Radiata pine core wood 65 70 0.6 Uniform A13 Radiata pine core wood 70 90 2.0 Uniform A14 Radiata pine outer wood 40 52 3.6 Uniform A15 Radiata pine outer wood 45 70 5.8 Uniform A16 Spruce core wood 50 58 3.0 Variable A17 Spruce core wood 33 55 7.7 Uniform A18 Spruce outer wood 45 60 6.4 Variable A19 Spruce outer wood 35 47 11.0 Variable A20 Spruce outer wood 45 30 4.4 Uniform A21 Scots pine core wood 55 70 5.1 Uniform A22 Scots pine core wood 45 53 4.4 Variable A23 Scots pine core wood 65 65 0.0 Uniform A24 Scots pine core wood 35 43 3.1 Uniform A25 Scots pine core wood 30 35 3.0 Uniform A26 Scots pine core wood 35 38 2.0 Uniform A27 Scots pine outer wood 50 60 4.6 Variable A28 Scots pine outer wood 55 80 23.0 Variable A29 Scots pine outer wood 55 74 6.3 Variable A30 Scots pine outer wood 45 60 3.8 Variable Mean 4.4

images with uneven brightness as shown in Table 1. The mean value for the operator differences, 4.4% from Table 1, is an indication of the inter-observer variability or bias. This value can be used when comparing automatic methods. If the automatic method deviates from what is considered a correct segmentation with a smaller error than the inter-observer variability, the automatic method can be considered as a satis- factory method.

Manual thresholding based on texture is also dependent upon subjective decisions

by the observer. Lumen areas generally contain less intensity variation (less texture),

Fig. 2. Segmentation error graphs for comparisons with a control image. The error percentage is the number of pixels difference between a threshold at each greylevel and a control image which was assumed to be an optimum segmentation. – A: Greylevel threshold error. B: Range threshold error. C: Variance threshold error. D: Laplace threshold error. – Greylevel thresholding has a low error level compared to the texture based methods shown for comparison.

A B

C D

but cell walls also may contain a reduced texture due to an even intensity distribution in certain areas (Fig. 2). For example, the middle lamella does not always appear very textured in the confocal microscope images. Thresholding a variance or range image therefore requires a low threshold to avoid artificial holes appearing in the cell wall (or middle lamella) of the segmented image. These artifacts increase in proportion to cell wall thickness, becoming a significant problem in latewood images for example.

Such a low threshold will lead to an overestimation of the cell wall. Morphological filters such as open and close, or median based smoothing can be used to fill holes without altering lumen dimensions (Russ 1995). However, segmentation methods

Fig. 3. Representations of a confocal fluorescence image of Pinus radiata in texture space. – A: Range 3×3. B: Range 5×5. C: Variance 3×3. D: Variance 5×5. – Each image is 625 ×625 μm. These texture images show the highest values at the lumen/cell wall boundary and are thus acting as edge detectors. Segmenting this type of image generally produces holes within the central region of the cell wall. These artifacts can be reduced by underestimating the threshold or by morphological smoothing but this can lead to distortion of the true cell wall location and is generally undesirable.

which do not demand the removal of such introduced artifacts are clearly preferred.

Because texture is also high on either side of the lumen boundary, texture based meth- ods do not accurately detect the position of this boundary further contributing to an overestimation of cell wall pixels.

To evaluate the use of manual thresholding based on greylevel or texture, the seg- mented greylevel and texture images of the radiata pine image of Figure 1 were com- pared to the corresponding control segmentation image, and the results are shown in the error graphs of Figure 3. The logical XOR difference or error (the number of pixels difference between the segmented image and the control image), is given for each threshold value from 0 to 255 as a percentage of the total number of pixels. As

– A: Original image (B3). B: Control image. C: Greylevel minimum image. D: H-method image. – Each image is 625×625 μm. The greylevel minimum image is clearly a better seg- mentation than the combined greylevel/texture (H-method) image.

Table 3. Segmentation errors for automatic methods from five radiata pine images with uniform brightness.

Image Method XOR error in percent Average B1 Average brightness 3.8

B2 Average brightness 0.6 B3 Average brightness 1.3 B4 Average brightness 0.8

B5 Average brightness 0.6 1.4 B1 Greylevel histogram min 3.7

B2 Greylevel histogram min 0.9 B3 Greylevel histogram min 1.1 B4 Greylevel histogram min 0.7

B5 Greylevel histogram min 0.7 1.4 B1 Shape based thresholding 8.0

B2 Shape based thresholding 8.0 B3 Shape based thresholding 7.9 B4 Shape based thresholding 7.2

B5 Shape based thresholding 5.4 7.3 B1 L-method 2.5

B2 L-method 2.5 B3 L-method 3.4 B4 L-method 0.7

B5 L-method 1.2 2.1 B1 H-method 3.0

B2 H-method 4.7 B3 H-method 16.4 B4 H-method 3.4

B5 H-method 3.5 6.2

Table 2. Segmentation errors for semi-automatic methods applied to the even brightness radiata pine image of Figure 1

.

Image Method Threshold XOR error in percent B1 Region growing (Masking) NA 6.5 B1 Profile half maximum height 62 9.2 B1 ML-classification NA 5.0

seen from Figure 3

–

the greylevel thresholding of Fig. 3

achieved the least min-

imum error of 1.8% at the greylevel threshold 25. In Figure 3

the minimum errors

were 13.4% and 15.0% for the range 3 ^× 3 and 5 ^× 5 texture filters. In Figure 3

the

minimum errors were 14.9% and 15.2% for the variance 3 ^× 3 and 5 ^× 5 filters, and

in Fig. 3d 19.0% and 13.3% for the laplace 3 ^× 3 and 5 ^× 5 filters. As can be seen in

Figure 3

–

for the 5 ^× 5 filters, a deviation from the optimal threshold value (the

threshold value for which the minimum error is obtained) gives rise to a smaller change in error than for the corresponding 3 ^× 3 filter. However, as seen in Figure 3

, the 5 ^× 5 filter does not always give a lesser minimum error than the 3 ^× 3 filter. Because the texture measures of Figure 3 failed to produce minimum errors less than the inter- observer variability of 4.4%, manual thresholding based on these texture measures is regarded as non-satisfactory.

Combined greylevel/texture based thresholding did not achieve any better results than using texture alone. The greylevel minimum image of Figure 4

is clearly a bet- ter segmentation than the combined greylevel/texture (H-method) image (Fig. 4

).

Automatic and semi-automatic segmentation methods

Table 2 shows the errors of segmentation by region growing, profile half maxi- mum height, and maximum-likelihood classification, when applied to the Pinus radiata image in Figure 1

. As seen in Table 2, these errors were not less than the inter- observer bias. The profile method is very location sensitive but irrespective of this it tends to overestimate the correct threshold indicating that the algorithm is biased in favour of lumen pixels.

Table 3 shows the errors of the automatic methods. The least error was achieved with greylevel histogram thresholding for four of the images. For the image B5 of Table 3 the average brightness method gave slightly better results. For all five test images the error of greylevel histogram thresholding was significantly less than the inter-observer variability.

Effect on measurements

As seen from Figures 5–7, different segmentation methods give different cell wall segmentations. The effect of the segmentation differences on morphological meas-

Fig. 5. A comparison of image segmentation using a range of automated, semi-automated and → manual thresholding techniques. – A: Greylevel minimum. B: Average brightness. C: Shape based (P²A). D: Variance 3×3. E: Range 3×3. F: Profile. G: Region growing. H: Control. – Each image is 625×625 μm. Greylevel minimum and average brightness are the best tech- niques both in terms of minimal error and full automation.

Fig. 6. A comparison of image segmentation using a range of automated, semi-automated and → → manual thresholding techniques. In this case the image has variable brightness. – A: Greylevel minimum. B: Average brightness. C: Shape based (P²A). D: Variance 3×3. E: Range 3×3.

F: Profile. G: Region growing. H: Control. – Each image is 625×625 μm. Greylevel mini- mum and region growing (using a training set) are the best techniques both in terms of seg- menting all of the cells and minimising the error. The profile technique consistently overesti- mates the threshold and is very location sensitive.

Fig. 7. A comparison of image segmentation using a range of automated, semi-automated and →→→

manual thresholding techniques. In this case the image contains latewood. – A: Greylevel mi- nimum. B: Average brightness. C: Shape based (P²A). D: Variance 3 ×3. E: Range 3×3.

F: Profile. G: Region growing. H: Control. – Each image is 625×625 μm. Greylevel mini- mum is again the best technique both in terms of minimal error and full automation.

Figure 5 — For legends, see page 279.

Figure 6 — For legends, see page 279.

Figure 7 — For legends, see page 279.

urements was investigated by using Forest Researchʼs routine wood anatomy software on the segmented images. The results are shown in Table 4. This software chooses 50 of the cells to calculate averages of cell wall thickness, lumen diameters, and other parameters. Cell wall and lumen areas are obtained by counting pixels. Selecting 50 cells on the basis of a priori knowledge of cell size gives a more robust system which

Fig. 8. A comparison of confocal images show- ing the effect of section thickness on image reso- lution. – A: A single confocal slice (Z-resolu- tion is approximately 1 μm). B: A maximum intensity projection from a volume 5 μm thick.

C: A transmitted light image (inverted contrast) showing the entire 30 μm thick section.

is less sensitive to sectioning artifacts or other image defects. From Table 4 it can be seen that the measurements from the aver- age brightness and greylevel thresholding images are very similar to the measurements from the control image, deviating by only 1–2 ^μ m for lumen diameter. However, for the texture based methods using variance and range, significant differences occur in comparison to the control image, especially for cell wall thickness. Texture based meth- ods were found to introduce significant ar- tifacts including holes in the central regions of the cell wall and loss of smaller cell lu- mens. Thus poor segmentation will lead to incorrect measurement results even for a robust image analysis system.

Latewood images and projections

Segmentation of latewood images can lead to over-estimation of the cell wall area due to some scattering of light in the cell walls (Fig. 7). This effect is more evident in the smaller latewood tracheids and also for the small hardwood fibers of Eucalyp- tus for example.

A useful property of the confocal micro-

scope is the ability to make projections of

several 2D optical slices. Projections will

in many cases overcome the problem of un-

even brightness mentioned above (Fig. 8).

Table 4. Automatic measurements by Forest Research wood quality image analysis system on some segmented images. Average brightness and greylevel histogram methods perform well over this range of image types. Variable brightness images cause significant problems with all of these methods. The RMS, Range and Profile methods perform significantly worse on latewood images. Measurements that are dependant on cell wall area are more affected by segmentation method than those that are dependant on object shape. Average Grey- Shape RMS RMS Range Range Profile Region Control brightness level 3 × 3 5 × 5 3 × 3 5 × 5 growing Uniform brightness Mean wall thickness μm 3.9 3.6 5.0 4.8 4.9 5.4 5.2 3.5 3.9 3.8 Tangential diameter μm 28.6 27.1 26.9 27.2 27.7 25.8 23.5 28.3 27.5 27.9 Radial diameter μm 45.2 43.6 42.9 44.6 45.3 42.7 38.7 43.7 40.5 41.2 Lumen area μm2 1118.5 1048.9 990.8 1022.3 1050.6 930.6 823.7 1066.4 929.5 959.2 Cell area μm2 1700.3 1570.9 1722.0 1733.0 1772.6 1702.0 1522.8 1568.1 1472.6 1481.1 Wall area μm2 581.8 522.0 731.2 710.7 722.0 771.4 699.1 501.7 543.0 521.9 Coarseness mg/m 0.9 0.8 1.1 1.1 1.1 1.2 1.0 0.8 0.8 0.8 Predicted density*) kg m-3 513.2 498.5 636.9 615.2 611.0 679.9 688.6 479.9 553.2 528.6 Perimeter (lumen) μm 134.3 129.4 125.9 132.1 133.4 120.8 110.1 129.5 119.8 121.8 Perimeter (wall) μm 164.9 158.5 166.0 166.5 168.4 165.0 156.1 158.4 153.5 153.9 Circularity 1.2 1.2 1.2 1.2 1.2 1.1 1.2 1.2 1.2 1.2 Eccentricity 1.6 1.8 1.6 1.7 1.7 1.7 1.7 1.6 1.5 1.5 Black pixels 359759 349340 446302 424406 419882 468933 473007 336328 387558 370359 White pixels 688817 699236 602274 607850 608314 563323 555189 712248 661018 678217 Total pixels 1048576 1048576 1048576 1032256 1028196 1032256 1028196 1048576 1048576 1048576 Threshold 35 39 11 4 5 14 25 44 NA Error -1% -2% 7% 6% 6% 10% 11% -3% 2% Variable brightness Mean wall thickness 3.4 3.2 5.4 4.4 4.6 5.3 4.5 2.3 3.9 3.1 Tangential diameter 29.8 31.0 27.5 27.4 26.6 26.7 23.4 31.1 29.6 30.8 Radial diameter 40.4 41.0 36.8 38.1 36.4 36.3 31.0 41.3 39.6 41.1 Lumen area 994.5 1046.6 844.9 850.6 808.6 799.4 653.7 1062.2 972.9 1052.3 Cell area 1465.6 1496.1 1585.9 1436.2 1418.8 1517.2 1194.0 1375.4 1519.7 1494.4 *) Predicted density overestimates basic density. (continued on next page)

Average Grey- Shape RMS RMS Range Range Profile Region Control brightness level 3 × 3 5 × 5 3 × 3 5 × 5 growing (Variable brightness continued) Wall area 471.2 449.4 741.1 585.6 610.2 717.8 540.3 313.2 546.8 442.2 Coarseness 0.7 0.7 1.1 0.9 0.9 1.1 0.8 0.5 0.8 0.7 Predicted density 482.2 450.6 700.9 611.6 645.1 709.7 678.8 341.6 539.7 443.8 Perimeter (lumen) 123.0 125.5 113.3 117.1 111.8 109.2 94.6 128.6 121.0 125.7 Perimeter (wall) 153.1 154.7 159.3 151.6 150.7 155.8 138.2 148.3 155.9 154.6 Circularity 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 Eccentricity 1.4 1.4 1.4 1.5 1.5 1.4 1.4 1.4 1.4 1.4 Black pixels 337914 315807 490987 421763 443112 489349 466029 239410 378151 311053 White pixels 710662 732769 557589 610493 585084 542907 562167 809166 670425 737523 Total pixels 1048576 1048576 1048576 1032256 1028196 1032256 1028196 1048576 1048576 1048576 Threshold 39.1 49 6 3 3 9 22 76 NA Error 3% 0% 17% 11% 13% 18% 16% -7% 6% Latewood Mean wall thickness 5.1 5.0 3.5 5.8 6.0 7.2 5.6 3.9 5.9 4.6 Tangential diameter 18.4 18.9 18.5 15.0 15.8 15.4 14.3 19.7 17.0 19.3 Radial diameter 17.9 17.9 18.8 14.8 14.9 13.0 13.9 18.9 16.4 18.5 Lumen area 291.3 298.8 305.1 188.7 201.8 171.7 158.4 332.9 250.8 314.7 Cell area 741.2 743.7 599.6 640.8 687.5 753.4 565.1 680.4 765.2 724.0 Wall area 449.9 444.9 294.5 452.1 485.7 581.7 406.7 347.5 514.5 409.3 Coarseness 0.7 0.7 0.4 0.7 0.7 0.9 0.6 0.5 0.8 0.6 Predicted density 910.5 897.4 736.6 1058.3 1059.7 1158.2 1079.5 766.1 1008.4 847.9 Perimeter (lumen) 64.8 65.7 67.1 53.0 54.2 48.9 49.3 70.2 59.5 68.2 Perimeter (wall) 108.9 109.1 97.9 101.3 104.9 109.8 95.1 104.3 110.7 107.6 Circularity 1.2 1.2 1.3 1.2 1.2 1.2 1.2 1.3 1.2 1.3 Eccentricity 1.0 1.0 1.1 1.1 1.0 0.9 1.1 1.0 1.0 1.0 Black pixels 636962 627763 515326 725777 723922 794217 737356 536009 705378 593180 White pixels 411614 420813 533250 302419 300222 233979 286788 512567 343198 455396 Total pixels 1048576 1048576 1048576 1028196 1024144 1028196 1024144 1048576 1048576 1048576 Threshold 46 45 79 3 4 9 26 74 NA Error 4% 3% -7% 14% 14% 21% 15% -5% 11%

Fig. 9. Segmentation error graphs for comparisons with a control image. The error percentage is the number of pixels difference between a threshold at each greylevel, and a control image which was assumed to be an optimum segmentation. This comparison is for the three images in Fig. 8. The effect of image type on threshold error is readily apparent with the transmitted light image showing nearly 20% more cell wall than the single confocal slice.

Fig. 10. A comparison of segmentation error with projection thickness using average intensity and maximum intensity projections. Average intensity projections have a slight advantage over maximum intensity projections for volumes up to 20 μm thick for this particular sample. We found that the best projection method for a particular sample can vary. Projections have an advantage over single confocal slices in cases where variable brightness is a problem provided the thickness of the volume is kept to a minimum.

For some images a maximum intensity projection will give the best results while in other cases an average intensity projection may be best. However, when applied to cross-sectional wood images, a shading effect at the cell wall–lumen border will oc- cur if the tracheids are not perfectly aligned in the longitudinal direction. In such cases, the distinction between lumen and cell wall pixels becomes confused just as it does for images from thick sections by conventional light microscopy (Fig. 8 & 9).

This is less of a problem with average intensity projections (Fig. 10). However in general the sampled volume should be as thin as possible and always less than 10 ^μ m to achieve useful images for cell measurements. A similar effect can be obtained in a single image acquisition by increasing the size of the confocal aperture, which is continuously variable.

CONCLUSIONS

The effect of image segmentation method on wood cell dimension measurements was examined. The results show that segmentation has a significant impact on these meas- urements.

We have demonstrated that automated methods remove observer bias and are thus capable of more reproducible results. The contrast for even brightness confocal mi- croscope images is of such quality that one of the simplest and fastest automatic segmentation methods, greylevel histogram thresholding, may be used. In almost all cases this method produced an error less than the inter-observer bias.

We did not find any specific species dependence for any of these methods. How- ever, we suggest using a greater resolution and magnification for hardwood species because of the smaller fiber dimensions.

Uneven brightness makes the segmentation more difficult and our future work will include a comparison of image analysis methods to handle variations in brightness within an image. Brightness variations can be dealt with by image analysis but this is also affected by sample preparation. Sample preparation should always strive to pro- duce as correct an image of the wood as possible. The better the images input to an image analysis system, the more accurate the output measurements.

ACKNOWLEDGEMENTS

Gunilla Borgefors, Center for Image Analysis, Sweden, and Adya Singh, Forest Research, New Zealand, are thanked for valuable comments on the manuscript. This research was supported by grants from the Swedish University of Agricultural Sciences, and the Swedish Council for Forestry and Agricultural Research through the Graduate School of Wood and Wood Fiber.

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