Determination of cotton fiber maturity and linear density (fineness) by examination of fiber cross-sections. Part 1: Comparison of two image analysis systems used in conjunction with optical microscopy

Abstract

Researchers from the United States Department of Agriculture and Texas Tech University have published the establishment of a set of reference cottons with known fiber maturity and linear density (fineness) values. Their work was based on careful analysis of the dimensions of a large number of individual transverse fiber cross-sections viewed under the optical microscope to obtain representative values for a particular cotton. Since this set of reference cottons has a high potential value for instrument developments and the world’s cotton industry in general, it was considered useful to independently test both the processes used and the assigned values for this set of reference cottons. Using independently developed software, a careful cross-section by cross-section comparison with the original data identified that the measured fiber perimeter values were in good agreement. However, cell wall area values and, consequently, the fiber maturity (theta) and fineness values were consistently smaller. The difference ranged from up to 40% for the small cell wall area values down to 15% for the larger cell wall area values, with the average difference being approximately 20%. These differences stem from a different interpretation of the outside boundary of the fiber cross-section by the two image analysis systems due to the limited optical resolution of the captured images. This implies that while the ranking of fineness and maturity values originally assigned to the reference cottons is likely to be correct, there may be a significant systematic error in the assigned values of the cell wall area and hence fiber maturity and linear density values.

Keywords

cotton fiber cross-section perimeter cell wall area linear density fineness maturity optical microscopy image analysis

In cross-section a cotton fiber typically contains a collapsed lumen, as illustrated in Figure 1. During growth, the fiber, which is a single cell, is approximately circular in cross-section. The primary cell wall is formed early in the growth period and then concentric rings of cellulose are deposited starting from the inside surface of the cell wall, that is, the approximately circular lumen is steadily reduced in size as it is replaced by the successive layers of cellulose, which form the secondary wall of the fiber. When the fiber dries the remaining lumen collapses, forming the characteristic irregular kidney-shaped fiber cross-sections visible in Figure 1.

Figure 1.

A typical image of fiber cross-section as observed under the optical microscope using the FIAS system.

From a textile perspective, two parameters of potential interest related to the fiber cross-section are (a) fiber maturity or degree of secondary wall thickening and (b) fiber linear density. (Fiber linear density is often referred to as fiber fineness; however, in this paper to avoid potential confusion with fiber physical cross-sectional dimensions, the term fiber linear density will be used.) For example, immature fibers (i.e. fibers with a thin secondary wall) have been associated with fiber breakage and formation of neps in ginning and textile processing¹ and problems with dye uptake.² Fiber linear density will determine the number of fibers in a yarn cross-section and so may have a direct bearing on the efficiency of the spinning process and the mechanical properties of fine yarns.

A satisfactory, rapid and reliable technique for measuring these two parameters has not until recently been available to industry. Some approaches have included double compression airflow instruments, for example, the FMT instrument (for example, Montalvo et al.³ and Abbott et al.⁴), the maturity module in the Uster AFIS instrument and interpretation of the variation in ribbon width of fiber longitudinal sections.⁵

Recently, this area has been the focus of instrument development at the Commonwealth Science and Industrial Research Organisation (CSIRO) with the Cottonscan™ instrument for direct measurement of fiber linear density^6–9 and the Siromat™ instrument for determining fiber maturity distribution using polarized light microscopy.^10–13 These two technologies are now available in the commercially available Cottonscope instrument.^14–21

A challenge for all instruments in this area has been calibration. Montalvo and Von Hoven^22,23 developed a theoretical model and set of tools for detecting and correcting bias in fiber fineness and maturity results. This work is based on Lord’s micronaire model. This model was then applied to compare the performance of the FMT and AFIS,²⁴ demonstrating that the AFIS exhibited a bias that resulted in a very narrow dynamic range for both fineness and maturity.

A first-principles approach of direct measurements of fiber cross-sections under an optical microscope to create a reference set of cottons with ‘assigned’ values presents considerable technical challenges requiring a skilled operator. It is also very labor and time intensive. Thus, until recently, there have been no reference cottons with agreed assigned values of fiber maturity and fiber linear density. Hequet et al.²⁵ tackled this challenge with an extensive and detailed study to create a reference set of 104 cottons. This study utilized (a) a modified version of the technique for embedding and preparing fiber cross-sections developed by Boylston et al.^26,27 at the United States Department of Agriculture Southern Regional Research Center (USDA-SRRC) in New Orleans and (b) the purpose built FIAS image analysis system developed by Xu and colleagues^28–30 for analyzing images obtained from viewing the cross-sections under the optical microscope. It is interesting to note that Hequet et al.²⁵ aimed to create a reference set with a broad range of average values of fiber maturity ratio and linear density values. The resultant ranges obtained for this set of reference cottons are 0.6–1.1 for average fiber maturity ratio and 120–200 mtex for average fiber linear density.

A later examination of the FIAS image analysis system³¹ has identified that 20–50% of the cross-sections were eliminated by the software as not being suitable for measurement and a visual inspection estimated that 50–90% of these ‘rejected’ cross-sections were immature. This work concluded that the software introduced an ‘immature fiber bias’, resulting in an over estimation of maturity of around 8–9%. More recently, Xu and Guo³² reported an upgrade of the FIAS software to overcome this problem. The early results indicate that using the new upgraded software up to over double the number of cross-sections per slide are accepted by the software as valid measurements, with no significant changes observed in the calculated average maturity values; however, both the skewness and kurtosis of the maturity distributions are quite different. The FIAS system has also been adopted for measuring fiber properties from longitudinal views.^33–35

Given the considerable effort expended in developing this set of reference cottons and its potential value for a range of instrument developments and the cotton industry in general, it was considered useful to embark on an independent process at the CSIRO to attempt to test both the processes used and the assigned values for this set of reference cottons. Some preliminary results from this study have been reported elsewhere.³⁶

Theory: Definition of fiber linear density and maturity

Figure 2 illustrates schematically a generalized fiber cross-section defining the fiber perimeter P and the cell wall area A. (Note that A is not the total area defined by the perimeter, but rather is that area minus the lumen area.) Following the approach developed by Pierce and Lord³⁷ and used by Thibodeaux et al.,³⁸ Hequet et al.²⁵ and Xu and colleagues,^28–30 the degree of secondary wall thickening theta (θ) is defined as the ratio of the cell wall area (A_C) to that of a circle having the same perimeter as the fiber cross-section, that is:

θ = 4 π A_{C} / P^{2}

(1)

Figure 2.

Schematic of a cotton fiber cross-section.

This is scaled to give the maturity ratio M as follows:

M = θ / 0.577 = 4 π A_{C} / (0.577 P^{2})

(2)

Further, the fiber linear density H is given by

H = ρ A_{C}

(3)

where ρ is the cellulose cell wall density.

Thus, accurate determination of the perimeter P and the cell wall area A_C and independent knowledge of cell wall density ρ enable the fiber maturity and linear density to be determined. It is not uncommon in the literature to assume that the cell wall density ρ is constant at 1.52 g/cm³. However, under the optical microscope used in these and similar studies, the observed area is the sum of both the primary and secondary wall and, as noted by Abidi et al.,³⁹ the primary cell wall can represent a significant fraction of the total mass of the cell wall, particularly for immature fibers. Further, the primary cell wall contains only between 35% and 50% cellulose,⁴⁰ with an estimated density of 1.14 g/cm³.⁴¹

Methods

Preparation of fiber cross-sections and optical microscopy

A sample of cotton number 2999, one of the well-blended cottons used by Hequet at al.,²⁵ was used in this study. From the prior study the average cell wall area of this cotton is 89.1 µm² and its average perimeter value is 51.1 µm, giving an average theta value of 0.45, that is, an average maturity ratio value of 0.78. Hequet et al.²⁵ noted that all their cotton samples, including Sample 2999, contained very broad distributions in the cell wall area and perimeter values of individual cross-sections. Hence the use of a range of cross-sections from one individual cotton sample in the current study is not expected to significantly limit the general applicability of any outcomes from the work.

In preparation for cutting fiber cross-sections, the CSIRO followed the detailed technique reported by Boylston et al.^26,27 and used routinely at the USDA to prepare fiber bundles and resin embed the bundle. Given that the aim of the procedure is to obtain quantitative fiber cross-sectional dimensions by viewing the prepared thin fiber cross-sections under the optical microscope, Boylston et al. focused on two critical issues in the development of this procedure. Firstly, alignment of the fiber bundle to minimize systematic errors due to prepared transverse cross-sections not being at ninety degrees to the fiber axis was achieved by packing the aligned fiber bundles inside narrow (1/8 inch internal diameter) tubing prior to embedding. Secondly the embedding medium and sectioning technique were specifically designed to avoid fiber swelling.

It is noted that Hequet et al.²⁵ recently reported a further refinement of this process by mounting the fiber bundle in thinner 1/16-inch internal diameter tubing to further reduce the likelihood of errors due to the fiber axis not being at right angles to the cutting plane during the sectioning process. Note that for all the results reported in this paper the fibers were mounted at the CSIRO following Boylston et al.’s^26,27 original procedure, that is, the fiber bundle was mounted in 1/8-inch internal diameter tubing. This study does not address the likely errors/benefits from adopting the two different tubing sizes for mounting the fiber bundle. Importantly, due to the experimental design and the questions addressed in this comparative study, that is, with shared fiber transverse sections, the conclusions should be independent of any systematic errors arising from this source. Equally, any other potential sampling biases introduced by the Boylston procedure will not affect the current comparative study.

Fiber cross-sections prepared at Texas Tech University (from the CSIRO embedded block) followed the standard technique used at Texas Tech University.²⁵ The optical microscopy system used at Texas Tech University has been described previously.²⁵ It is interesting to note that the original Texas Tech images were 640 × 480 pixels with a resultant resolution of 2.6 pixels per micrometer in both dimensions.

Software

Analysis at Texas Tech used the FIAS software as previously reported.^25,28–30

The CSIRO algorithm was implemented in the Optimas software package. An initial watershed with a pre-flood set at the image mean minus 1.2 times the standard deviation of the image gray levels was performed to isolate fibers and extract the total fiber area (i.e. the sum of the cell wall area A_C and the lumen area A_L) and the perimeter of the cross-section. This was followed by the extraction of intensity histogram information from each cross-section. If the intensity distribution within a cross-section was negatively skewed then it was assumed that this was due to the presence of a lumen and further processing using a threshold equal to the mean gray level within the cross-section minus 1.5 times the standard deviation was used to isolate the lumens. (The optimal values used as multipliers for the standard deviation in the determination of threshold levels were heuristically determined from a number of images prior to the analysis of the entire data set.) The isolated lumen pixels were then set to zero. The cell wall area was calculated by multiplying the total fiber area previously determined by the ratio of pixels above the threshold to the total pixel count within the cross-section. The lumen area was then calculated by subtracting the cell wall area value from the total fiber area. The results were manually post-processed to remove artifacts and failed cross-section outlines using the result images. Perimeter and area information were extracted using standard Optimas functions.⁴² In a similar manner to the FIAS software, an output of the CSIRO software system is a processed image that visually identifies the outer edge of each cross-section and also the lumen as defined by the software. As a quality control step, the analysis procedure included a visual comparison of this processed image with the original image and obvious errors (e.g. due to indistinct or touching cross-sections) were removed from the data set.

In some analyses, area information was also obtained by simply counting the number of whole pixels forming the feature in a binary image. In this case no attempt was made to correct for errors associated with the pixilated nature of the boundary of an object artificially introduced by the digital imaging process.

Utilization of ‘FIAS processed’ images as ‘model’ fiber cross-sections

One output of the FIAS software system developed by Xu and colleagues^28–30 is that for each image frame analyzed it produces a matching ‘processed’ image, as illustrated in Figure 3. One feature of the processed image is that each fiber ‘cross-section’ now has a well-defined sharp boundary. These ‘FIAS processed’ images were used as a useful set of ‘model’ fiber cross-sections for preliminary testing of the CSIRO software. That is, the ‘FIAS processed’ images were used as inputs and reanalyzed using the CSIRO software to extract perimeter (P), cell wall area (A_C) and lumen area (A_L). Matching these values with those obtained from the original analysis using the FIAS system provided a method to compare the output of the two software systems. The use of these ‘model’ cross-sections for this preliminary comparison of the two software systems proved useful in that the additional challenges associated with analyzing objects with ill-defined boundaries were removed.

Figure 3.

The ‘processed’ image from the FIAS software system implemented at Texas Tech University following analysis of the image shown in Figure 1.

Results

A separate software analysis system was developed at the CSIRO to analyze the imaged fiber cross-sections.

A bundle of cotton fibers was embedded into a block at the CSIRO and then sectioned at Texas Tech University. One microscope slide (i.e. one section of the fiber bundle) was imaged at Texas Tech University resulting in the capture of 49 images containing a total of 474 transverse cross-sections. Following data analysis at Texas Tech University using the FIAS analysis software, the microscope slide, Texas Tech images and the ‘FIAS processed’ images were shared with the CSIRO. This sample and data set was used to compare the new CSIRO software image analysis system with the FIAS system developed by Xu and colleagues^28–30 and used by Hequet et al.²⁵ Detailed comparison of the results from the two systems was undertaken in stages to test various aspects of both systems.

Comparison using ‘FIAS processed’ images

The ‘FIAS processed’ images, with well-defined sharp boundaries, were reanalyzed using the CSIRO software to extract the perimeter (P), cell wall area (A_C) and lumen area (A_L).

The CSIRO and FIAS perimeter results are in excellent agreement for the 474 cross-sections, as shown in Figure 4. By comparison, Figure 5 illustrates that the cell wall area values are not in perfect agreement. Two differences are visible in Figure 5. Firstly, the area values reported from the CSIRO software are approximately 5% smaller than the FIAS (Texas Tech) values and, secondly, some scatter (albeit small) around the best fit line is observed.

Figure 4.

Comparison of perimeter values for idealized fiber cross-sections.

Figure 5.

Comparison of cell wall area data for idealized fiber cross-sections.

The CSIRO software uses an area algorithm from the commercial ‘Optimas’ software package. It is documented⁴² that this algorithm uses a smoothing function around a pixilated boundary, which can lead to a small discrepancy. To test the hypothesis that the smoothing function is the source of the 5% difference, Figure 6 shows a plot of a simple count of the number of pixels in the cell wall area as determined by the CSIRO software versus the FIAS area result converted to pixels. A convention used in this and later figures is to use pixels as the unit of cell wall area in cases where the data is based on whole pixel counts and square micrometers when software smoothing of pixilated boundaries is involved. A much closer agreement is observed in this case. This analysis supports the hypothesis that the smoothing function is the source of the 5% difference.

Figure 6.

Comparison of the cell wall area data for idealized fiber cross-sections in pixels. (The CSIRO data are actual pixel counts and the FIAS data are the reported area values in square micrometers converted to pixels using the known pixel size).

Figure 7 shows a comparison between the two software systems of the sum of the cell wall area (A_C) and the lumen area (A_L) in pixels. Two important conclusions can be drawn from the virtually perfect one to one relationship apparent in Figure 7. Firstly, it is further strong supporting evidence for the hypothesis in the previous paragraph, namely that the FIAS software area measurements are based on simple pixel counts. Secondly, the lack of scatter around the best fit line in Figure 7 in contrast to that observed in both Figures 5 and 6 indicates that the scatter in Figures 5 and 6 can be attributed to differences between the two image analysis systems in how they partition this total area (as plotted in Figure 7) between the cell wall area and the lumen area. This is shown clearly in Figure 8, a comparison of the lumen areas from the two systems. The data points in Figure 8 can be considered to fall into four categories, namely:

Figure 7.

Comparison of the sum of the cell wall area and the lumen area reported by the two systems for idealized fiber cross-sections.

Figure 8.

Comparison of lumen area values for idealized fiber cross-sections.

the CSIRO lumen area exactly equals the FIAS lumen area value (321 data points or 68%);

the CSIRO lumen area is exactly half the FIAS lumen area value (96 data points or 20%);

the CSIRO lumen area lies between sets (a) and (b) (25 data points or 5%); and

the CSIRO lumen area is greater than the FIAS lumen area (32 data points or 7%).

Categories (b), (c) and (d), that is, the discrepancies, were somewhat unexpected, particularly given that the input images used for this comparison were indeed ‘FIAS processed’ images with each cross-section now having a well-defined sharp lumen boundary (i.e. images similar to those shown in Figure 3).

A detailed visual examination of the features of the lumens in these input images (i.e. the ‘FIAS processed’ images with the well-defined boundaries) revealed the following.

Cross-sections in Category (b) were uniquely characterized such that the lumen was always exactly one pixel wide at every position along the total length of the lumen. In a random selection of 10 such cross-sections, manual counting of the number of pixels in the lumen in the input image was in agreement with the CSIRO value. It was concluded from this analysis that the algorithm in the FIAS system must mistakenly lead to a double count of the lumen pixels in this specific instance. In Category (c) each cross-section in the input image was characterized by having a partly solid lumen (i.e. width greater than one pixel) combined with a single width component. Thus the application of the explanation for Category (b) to the single width component was able to explain this category. Manual counting of the number of pixels forming the lumen in the input image of a number of cross-sections in Category (c) also confirmed the CSIRO value. No common feature was observed for Category (d) cross-sections and no explanation for the FIAS values was determined for this category. Again manual counting of the number of pixels forming the lumen of a small number of cross-sections in Category (d) was in perfect agreement with that obtained from the CSIRO image analysis system.

It is noted that the observed size of these effects (i.e. differences in lumen area) generally results in only small differences in the reported cell wall area. This is apparent in Figure 6. However, on some individual cross-sections, the error in the cell wall area values may be significant. Individual cross-sections with both a very narrow lumen and low cell wall area, that is, fine immature fibers, will be more susceptible to these anomalies.

Summarizing this section, where ‘FIAS processed’ images with each fiber cross-section having a well-defined outer boundary and lumen were reanalyzed using the new CSIRO software, the following observations/conclusions can be drawn.

There is excellent agreement between the two software systems in the determination of the fiber perimeter values.

Small observed differences between the two software systems in the determination of the cell wall area can been explained as follows.

The CSIRO values are in general 5% smaller due to the CSIRO software using a smoothing function to remove pixilation of the outer boundary of the cross-section instead of counting whole pixels.

Sources of other smaller differences are largely understood and appear to be related to an interpretation in the FIAS software, which miscalculates the lumen area in a limited number of cases. (Manual counting of lumen pixels of a number of fiber cross-sections was consistent with this conclusion.)

Overall, the experience with the ‘FIAS processed’ images and, in particular, the identification and understanding of the sources of the observed differences between the two software systems has built considerable confidence in the new CSIRO image analysis approach.

Comparison using real images

Following the above progress with idealized images, the CSIRO software was applied to the original ‘real’ images captured at Texas Tech University (i.e. corresponding to the ‘FIAS processed’ images used in the previous section). The results for the perimeter measurements on 457 cross-sections (49 images) are shown in Figure 9. The results in general show good agreement. The perimeter values determined by the CSIRO software are on average approximately 4% smaller than those obtained from the FIAS system. (From the original set of 474 imaged cross-sections, the manual/visual quality control step associated with the CSIRO software analysis described in the Methods section identified 17 errors related to the failure of the CSIRO software to either separate touching cross-sections or to ‘open’ a cross-section where the ends had curved around to touch. These were removed from the analysis.)

Figure 9.

Comparison of perimeter values for the original real fiber cross-sections.

A similar analysis for cell wall area is shown in Figure 10. There is a good correlation between the CSIRO and FIAS (Texas Tech) results although the area values (and corresponding theta and maturity values) measured by the CSIRO algorithm are consistently smaller than the FIAS values. This difference ranged between 40% for small area values down to 15% for the largest area values, with the average difference being approximately 20%. Given that the experience with the ‘FIAS processed’ images above had identified some inherent sources of differences between the two software systems (i.e. in the determination of cell wall area), it is reasonable to explore if the current albeit larger differences could arise from the same phenomena. This was tested by removing the known effects as follows. The CSIRO cell wall area values were recalculated by simply counting pixels (thus avoiding the small (approximate 5%) observed correction due to smoothing of the boundary) for a subset of the data where a 1:1 correspondence of pixel lumen areas was obtained in Figure 8. This subset thus specifically eliminates cross-sections where the FIAS system is known to return incorrect lumen and cell wall area results. Figure 11 highlights that the discrepancy between the reported cell wall area values between the two software systems is indeed still present for this recalculated subset of the data, demonstrating that the significant difference between the two results from the two software systems is not explained by these established effects.

Figure 10.

Comparison of cell wall area values for the original real fiber cross-sections.

Figure 11.

Comparison of cell wall area values in pixels for a subset of the original real fiber cross-sections where there is agreement between the two systems for the lumen areas in Figure 8 (i.e. from the analysis of the ‘idealized’ images).

Figure 12 shows a comparison between the two software systems for the areas of the lumens reported from the two software systems for the same subset of the data as used in Figure 11. The CSIRO reported lumen values are on average 20% larger than the values calculated by FIAS. The lumen area values are however small relative to the cell wall area values and so this difference in lumen values cannot explain the differences in the calculated cell wall area values.

Figure 12.

Comparison of the lumen area values in pixels for a subset of the original real fiber cross-sections for the subset of cross-sections used in Figure 11.

Figure 13 is a comparison between the two software systems of the sum of the cell wall area (A_C) and the lumen area (A_L) in pixels for the same subset of the data as used in Figures 11 and 12. In this comparison the summed values returned from the CSIRO software are also consistently smaller than those returned from the FIAS system. This suggests that the major source of discrepancy between the two systems is the determination of the outside boundary of the fiber.

Figure 13.

Comparison of the sum of the cell wall area and the lumen area values in pixels for a subset of the original real fiber cross-sections for the subset of cross-sections used in Figure 11.

In an attempt to discover the source of this difference, the outside edge of the cross-sections in the ‘processed image’ from the CSIRO system were overlaid with the ‘FIAS processed’ image for a number of cross-sections, as illustrated in Figure 14. The pixilation in the original digitally captured unprocessed image is clearly visible in the left hand image in Figure 14. Close examination showed that the outer border determined by the CSIRO algorithm (depicted in light gray) often lies one pixel inside the border determined by the FIAS algorithm (depicted in dark gray or black where the two are co-incident). Further, the outer border determined by the CSIRO algorithm was only rarely observed to be outside the FIAS border. To test if this explanation is able to quantitatively account for the observed differences, Figure 15, shows the relationship between the cell wall area in pixels determined by the CSIRO software versus an ‘adjusted’ FIAS area according to the following equation:

\begin{matrix} Adjusted FIAS Area = FIAS Area - S^{*} (Area associated \\ with outer layer of pixels) \end{matrix}

where S is an empirical scaling factor. This scaling factor can be interpreted physically as the fraction of times that the outer cell wall boundary is removed from the FIAS area. Figure 15 depicts the case where N = 0.86, which then gives a good 1:1 relationship between the ‘adjusted’ FIAS area and the area determined by the CSIRO algorithm. It is interesting that for this value of S the best fit line has a slope of 1.0 and also it has a zero intercept. (As the value of S is moved in either direction from this value of 0.86 (a) the slope of the best fit line deviates from 1.0 and (b) a non-zero intercept emerges.) This value of S is indeed consistent with the observations in Figure 13, that is, that the outer boundary from the FIAS software is generally but not always one pixel outside that defined by the CSIRO software. Thus, this appears to be the explanation for the observed differences in derived cell wall area values. A reassessment of the images observed in the optical microscope suggests that the optical definition of the boundaries is not sufficient to distinguish the relative merits of the two systems in this regard, that is, a combination of the optical resolution and the pixel size in the image capturing camera is a limiting factor in defining the edges of a cross-section, as can be seen in Figure 14.

Figure 14.

For the original cross-section image in (a), (b) is the overlay of the processed image from the two software systems. On the outer boundary of the cross-section, the light gray denotes the edge determined by the CSIRO software, the dark gray the boundary as determined by the FIAS software and the black is where the two software systems overlap.

Figure 15.

A replot of Figure 11 after ‘adjusting’ the FIAS cell wall area values by subtracting a fraction (0.86) of the area associated with the outer layer of pixels.

Figure 16.

Percentage reduction in perimeter associated with erosion of the outside boundary of the cross-section.

It is instructive to explore if the explanation for the observed differences in cell wall area values is also consistent with the much smaller observed differences in perimeter values between the two systems. Using routine image analysis techniques, each cross-section in the FIAS processed images for the complete data set (457 cross-sections) was filled in to form a solid object and then eroded by one pixel. Figures 16 and 17 illustrate the observed percentage changes in perimeter and area values associated with this transformation. The average reduction in perimeter over the whole data set was 3.5% for perimeter and 17.5% for area, that is, (a) the observed changes in perimeter values are indeed much smaller than the corresponding percentage reduction in area values and (b) the percentage changes in both perimeter and area are of similar magnitudes to the observed differences between perimeter and area values reported by the FIAS and CSIRO software.

Figure 17.

Percentage reduction in cell wall plus lumen area associated with erosion of the outside boundary of the cross-section.

Figure 18.

Illustration of the inherent ‘aspect ratio’ associated with a cotton cross-section, with (a) representing a ‘typical’ cross-section, (b) the cross-section ‘straightened’ demonstrating a large aspect ratio and (c) a rectangular approximation to the ‘straightened’ cross-section.

The different order of magnitude change in perimeter and area values under this transformation relates to the inherent shape of cross-sections and can be explained as follows. Conceptually, an individual cross-section can be ‘straightened’, as illustrated in Figure 18, to form a simple geometrical shape without changing either the perimeter or total area values. For virtually all cross-sections (including relatively mature fibers) the aspect ratio (i.e. the ratio of its length to its width) of the ‘straightened’ object is much greater than one. It then becomes clear by example or simple geometry (e.g. using a rectangle as an approximation of the shape of the straighten cross-section) that as the aspect ratio becomes larger an erosion has a much greater effect on area than perimeter. For example, consider a rectangle of original dimensions 10 pixels by 80 pixels (not atypical dimensions for the FIAS system). The original perimeter and area values will be 180 pixels and 800 square pixels, respectively. After an erosion of one pixel the dimensions will become 8 pixels by 78 pixels. The new perimeter is 172 pixels, a reduction of 4.4%, and the new area value is 624 square pixels, a reduction of 22%.

Hence, the explanation that the relatively large cell wall differences reported by the two software systems arises from a shift in the positioning of the outside boundary by one pixel is also consistent with the much smaller observed shift in the perimeter values.

Conclusion

Given the importance of the set of reference samples for fineness and maturity developed by Hequet et al.,²⁵ the CSIRO embarked on a project to independently validate both the previously prescribed technique and reported values. A cross-section by cross-section comparison of the results of analyzing a set of captured images with both the original software (FIAS) and also software independently developed at the CSIRO demonstrated that the CSIRO-measured fiber perimeter values are in good agreement with those obtained with the FIAS. However, the CSIRO cell wall area values are on average approximately 20% smaller. As theta, maturity and average fiber linear density are linear functions of cell wall area, then similar percentage differences in these derived values will also occur. It has been identified that these differences stem from the two image analysis systems having a different interpretation of the outside boundary of the fiber cross-section due to the limited optical resolution of the captured images. This implies that while the ranking of fineness and maturity values assigned to the reference cottons developed by Hequet et al.²⁵ is likely to be correct, there may be some systematic error in the assigned values of cell wall area and hence fiber maturity and linear density values.

Footnotes

Acknowledgments

The authors would like to thank Eric Hequet from Texas Tech University for supplying FIAS data and the shared slide used in this study. Eric Hequet also kindly supplied the images for Figures 1 and , and gave valuable feedback on a draft of the manuscript.

Funding

This work was supported by the Australian Cotton Research and Development Corporation and the Australian Government.

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