June 1, 2004
Image Analysis for Cotton Fibers Part II: Cross-Sectional Measurements
Cross-sectional analysis of cotton fibers provides direct, accurate measurements of fiber fineness and maturity, which are often regarded as the reference data for validating or calibrating other indirect measurements of these important cotton properties. Despite the importance, cross-sectional methods of using image analysis have not been broadly applied to cotton quality evaluations because of the tedious procedures for both preparing cotton samples and processing cross-sectional images. This paper illustrates image processing procedures dedicated to cotton cross-sectional analysis for the purpose of increasing the efficiency and accuracy of fiber separation and feature extraction. These procedures greatly improve the automation of processing cotton cross-sectional images and increase the number of analyzable fibers per image. The cross- sectional data of cotton fibers also have good correlations with longitudinal data and data from the Advanced Fiber Information Systems.
A cotton cross section contains measurable information directly related to the maturity of the fiber. Cross-sectional measurements of cotton maturity may be used as a reference when other methods need to be calibrated. Much research has been conducted with image analysis technology to measure cotton maturity and other parameters from fiber cross sections [4-6, 11-15]. The success of a cross- sectional method using image analysis largely relies on two techniques: fiber cross-sectioning and image segmentation. Cross- sectioning is the most import step in obtaining analyzable images of fibers, and grinding and cutting are the two general methods for fiber cross-sectioning. In grinding, a bundle of fibers embedded in a polymer resin and hardener mixture is hardened, ground, then polished, and the surface containing the fiber cross sections is imaged on a microscope by reflected light . There are many different ways of cutting a thin slice of fibers perpendicular to the long axes [1, 3]. A quick embedding method specifically for cotton fibers was established by researchers al the USDA Southern Regional Research Center (SRRC) . A bundle of fibers is embedded in a methacrylate medium, polymerized in a UV reactor, and cut into 1-3 m slices with a microtome. This sectioning method greatly improves the separability and contrast of individual fibers in the image captured by transmitted light.
Image segmentation is a computational process that separates cotton cross sections from the image background and from one another. Segmentation results directly influence the efficiency and accuracy of cross-sectional measurements. Due to variations in the cross-sectional shape and thickness of the sliced samples, fibers in different regions may exhibit different levels of contrast and focus in an image. There are always cross sections that contact or overlap others in the image. Some appear to be damaged due to scratching of the cutting knife. Cotton cross sections can have convex or concave boundaries, and hollow or solid cores, making many powerful segmentation algorithms, e.g., watershed segmentation, invalid for separating touching ones. The image analysis systems for processing cotton cross-sectional images often require operator assistance to draw separation lines between touching fibers, to locate lumens, and to connect broken edges.
In the past several years, we have conducted a research project to develop a dedicated image analysis system for cotton fiber measurements with an emphasis on improving the automation and accuracy of the measuring process, and published a paper presenting the computer algorithms for processing cotton images in longitudinal views . In this paper, we focus on new segmentation algorithms for processing cotton cross-sectional images and experimental results, in comparison with the fineness and maturity data obtained from longitudinal and other tests. The algorithms involve a sequence of pixel manipulations specially designed for handling the problems present in a cotton cross-sectional image.
An 8-bit grayscale image captured by a CCD camera can sufficiently illustrate the cross-sectional features of cotton fibers. Using the cross-sectioning techniques developed by SRRC, one can get a cotton cross-sectional image similar to the one presented in Figure 1a, in which the illumination is rather uniform and many fibers are well separated. Because of differences in mounting orientation in the embedment and in maturity, some fibers in the image have inconsistent intensities of boundaries and lumens, as shown by fibers 1 and 2 in Figure 1a. In order to preserve the details of boundaries and lumens, the threshold used for the binary conversion of the grayscale image should be adjusted dynamically.
FIGURE 1. Gray-scale (a) and binary (b) cross-sectional images of cotton fibers.
As shown in Figure 1b, many fibers contact their neighbors, and the contacting situations depend on the shapes of the cross sections. Reasonable separations of the contacting fibers are the key to correct measurements. With the given cross-sectioning and imaging conditions , a cross section always appears to have a bright cellulosic wall (secondary wall) circumscribed by the dark edges of the fiber and the lumen. The major bodies (cellulosic walls) of two contacting fibers are naturally separated by their dark edges. For these images, background flooding is an extremely robust way to disconnect all the touching fibers and to remove small objects in the background.
Background flooding takes advantage of a regular Visual C++ function, which allows the computer to fill a region with a specified color. If the background of the binary image (Figure 1b) is filled by the black color, all the black edges of the fibers merge with the background, leaving the untouched inner portions in the foreground. Figure 2a displays the inverse image of the binary image in Figure 1b after being processed by flooding the background. Inversing the image keeps the convention that the background is white and the foreground objects are black. Note that fibers bounded by the four sides of the image (e.g., fibers labeled 3 in Figure 1b) have been automatically removed in the process to avoid incomplete fibers. Distorted cross sections arise from fibers with broken edges (see the fibers labeled 4 in Figure 1a) because the flooding erodes the inner portions through the broken channels. Most of the incomplete cross sections can be detected by checking if they are long, thin stripes and do not enclose any hole. Besides the incomplete cross sections, this checking process also helps to remove small solid objects (Figure 2b). Note also that the flooding probably takes away the primary walls of the fibers, which are part of the dark boundaries of the cross sections. The loss of the primary walls can be compensated by adding a 1-pixel (or more) thick layer to the fiber boundaries when taking the perimeter and area measurements.
FIGURE 2. Background flooding (a) and partial fiber removal (b).
The next task is to identify the fiber wall and lumen areas within each cross section. Lumens, varying in size with the degrees of maturity, are the hollow regions normally centered in the cross sections, but are often mixed with other holes, which are caused by scratches or variations in the thickness of cross sections. Those holes should not be counted as portions of lumens. The medial axes or skeletons of the cross sections may provide the best estimates for the locations of lumens. In order to find the skeletons, all the hollow regions inside the cross sections are filled to form solid, black objects, as shown in Figure 3a.
FIGURE 3. Filled (a) and skeletonized (b) cross sections.
A skeleton of an object is defined as a set of points, where each point is at the center of the largest circle that can be fit into the object . The skeletonization method used in this research involves progressive removal of the current boundary pixels from objects. The criterion for differentiating a boundary pixel from an inner pixel is that boundary pixels are those with only three or fewer black neighboring pixels. When a binary image is scanned pixel by pixel, boundary pixels are sought and registered with an intensity value in a gray-scale image created in the same dimensions as the binary image. The boundary pixels are deleted from the binary image, and the modified image is re-scanned for new boundary pixels. The intensity value, starting from 255, decreases with the number of iterative scans, and therefore different layers of boundaries are depicted by different gray scales. The gray-scale image, referred to as a distance map, indicates the thickness of the boundary of an object to its center. As a boundary pixel is removed from the object, the number of its neighbors is also checked. If the pixel has no more than two neighbors, it will be registered by zero (black pixel) rather than the calculated value in the distance map, indicating a found skeleton pixel. This process is repeated until no black pixels exist in the image. Figure 3b displays the distance map and skeletons of the fiber cross sections.
FIGURE 4. Lumens (a) and measurable cross sections (b).
Once the skeletons are formed, the coordinates of a skeletonare used to find holes that fall on the skeleton of the corresponding cross section in Figure 2b. Holes that are not passed through by the skeleton are omitted. Figure 4a presents an image that stores all the identified lumens from Figure 2b. This lumen image is merged with the image in Figure 3a (filled cross sections) using the "XOR" operation [8, 15] to generate a new image containing fiber cross sections with single lumens (Figure 4b). The XOR operation is a logic calculation with which the corresponding pixels in two images are compared. If a pair of pixels is identical, the pixel in the new image is set to black; otherwise it is set to white. One assumption in the paper is that there is always a lumen within a fiber cross section. The reasons for invisible lumens in some cross sections are that the fibers are either so mature that the inner spaces are fully filled, or so immature that the openings are totally collapsed. In these two cases, the skeletons of the cross sections are the best estimate for their invisible lumens. Therefore, the skeletons are inserted into the cross sections that do not possess any holes (see fibers 1, 2, and 3 in Figure 4b). Despite all these considerations, an incorrect identification of a lumen may still occur (see fibers 4 and 5 in Figure 4b). This is mainly because some dead fibers are curled so severely around the long axes that their cross sections are folded into closed objects. Manual editing may be needed to delete these fibers.
TAKING GEOMETRIC MEASUREMENTS
Five geometric features can be directly measured for each fiber cross section, as illustrated in Figure 5. The perimeters of a cross section and its lumen, P^sub c^ and P^sub l^, are obtained by tracing the two concentric boundaries, and the areas, A^sub c^ and A^sub l^, are obtained by counting all the pixels enclosed inside two the boundaries. The wall thickness at one position is measured by the pixels scanned between the boundaries in the direction perpendicular to the skeleton at this position. T is the average of the scanned thickness along the skeleton.
FIGURE 5. Cross-sectional measurements.
TABLE I. Cross-sectional measurements of cotton fibers.
The experiments for the cross-sectional analysis of cotton fibers were conducted in collaboration with the USDA SRRC and the International Textile Center (ITC) of Texas Tech University. Samples of 18 different cotton varieties were collected and cross-sectioned at SRRC and ITC. We obtained 5-12 fields of images for each of the first collection of 11 varieties, and about 300 fields of images for each of the second collection of 7 varieties. Table I presents the averages and coefficients of variance CV (in parentheses) of the cross-sectional data of the first 11 varieties. Due to the difference in the number of available images and the density of embedded fibers, the actual number of analyzed fibers for each variety N varies from 206 to 851. Compared to the other measurements, measurements of cotton perimeters P^sub c^ show relatively low CVs across all varieties. The reason is that the wall area (A^sub c^), thickness (T), and lumens (A^sub 1^ and P^sub l^) are influenced by the growing time of individual fibers, while the cotton perimeters (P^sub c^) arc basically invariant to the growing time. Cotton lumens can also change after growing terminates. The lumens of dead fibers may totally disappear when the tubular fibers collapse, and the lumens of some dead fibers may totally disappear when the fibers collapse. Therefore, only P^sub c^ should be used to describe the fineness of the fibers. For the purpose of characterizing cotton fineness and maturity, the perimeter and area of lumens (A^sub l^ and P^sub l^) are not reliable parameters.
The degree of thickening (T^sub r^) and the circularity (C) are the two independent measures of cotton maturity based on their definitions. Figure 6 shows the data of these two parameters over the 11 varieties. T^sub r^ and C are highly correlated, each of which can be used as a reliable measure of cotton maturity. However, the narrow ranges of C and T^sub r^ in the figure are not sufficient for reflecting the C-T^sub r^ relationship. We have selected the samples with the highest (SG-404) and the lowest (G21) maturity values in Table I to show the C-T^sub r^ relationship over a wider range. Figure 7 displays the C-T^sub r^ data of individual fibers in the G21 and SG-404 samples; there, the maturities of most fibers are visually different. Both plots reveal consistently high correlations and a slight nonlinearity between C and T^sub r^ over the full range of [0, 1]. Because G21 has a lower maturity than SG-404, the C- T^sub r^ data points of G21 concentrate more in the lower range of C- T^sub r^. In fact, the C-T^sub r^ plots of the rest of the samples all exhibit similar features.
FIGURE 6. Correlation between circularity (C) and degree of thickening (T^sub r^).
Figure 8 displays the frequency distributions of the fiber perimeters (P^sub c^) and circularity (C) of three varieties varying in maturity, G21 (low), Amsak (medium), and SG-404 (high). Although G21 and SG404 have similar mean perimeters, the fineness levels of the fibers in G21 are more widely distributed than those in SG-404. On the other hand, Amsak has a lower mean perimeter but a higher concentration in the perimeter distribution than G21 and SA-404. The different maturities of the three varieties are also reflected by the distinct distributions of their circularity data.
FIGURE 7. Circularity (C) and degree of thickening (T ^sub r^) of G21 and SG-404.
FIGURE 8. Distributions of fiber perimeters (P^sub c^) and circularity (C).
FIGURE 9. Variations of perimeter (P^sub c^) with the number of analyzed fibers (N).
For the cottons of the last 7 varieties collected by ITC, 21 subsets of samples were taken for each variety and around 15 fields of images were grabbed for each subset. The number of analyzed fibers of each variety reached more than 12,000, which is useful for examining the variations of the measurements with the numbers of analyzable fibers. Figure 9 shows the fluctuations of the average cotton perimeter (P^sub c^) with the increased number of analyzed fibers (N) in a variety. It seems that P^sub c^ has large variations when the number of the analyzed fibers is low, and fluctuates within small ranges (0.2%) after more than 4000 measurements are taken into account for this variety. To get reliable results for a cotton sample, a minimal number of fibers must be measured.
In the previous paper, we presented the algorithms for implementing transverse scans along the longitudinal axis of a fiber. Each transverse scan yields a width measurement on a fiber ribbon. Cotton fibers are convoluted along their longitudinal axes, and a convoluted fiber's width varies, as projected in a 2D image. Therefore, the scanned width changes with position on a fiber. A high convolution often indicates a low level of maturity in a fiber [2, 10]. For a scanned fiber, the statistics of the width measurements can be used to describe the fineness and maturity of the fiber. Let W^sub mean^ and W^sub sd^ denote the mean and standard deviation of the scanned widths. The maturity M^sub l^ based on the longitudinal measurements can be defined as M^sub l^ = W^sub sd^/W^sub mean^. Figure 10 displays the high correlations of fineness and maturity data of cross-sectional and longitudinal measurements of the last seven variety samples. The cross-sectional data also have reasonably good correlations with the data obtained from the Advanced Fiber Information System (AFIS), as shown in Figure 11, where F^sub Afis^ and M^sub Afis^ stand for the AFIS fineness and maturity, respectively. However, the circularity data in the cross-sectional measurements have a fairly low correlation with the micronaire data (R^sup 2^ = 0.456); this is because a micronaire value is a combined measure of both fineness and maturity .
FIGURE 10. Correlations of cross-sectional and longitudinal data.
FIGURE 11. Correlations of cross-sectional data and AFIS data.
This paper explains our specially designed algorithms for processing cotton cross-sectional images, and the testing results on cotton fineness and maturity data of eighteen varieties obtained from the cross-sectional measurements, longitudinal measurements, AFIS, and micronaire. These algorithms increase the automation and accuracy of separating touching fibers, identifying lumens, and taking measurements pertaining to cotton fineness and maturity. The correlation study shows that the two independent maturity measurements, degree of thickening and circularity, are highly correlated and possess a slightly nonlinear relationship. The perimeter measurement presents the least variability of all the cross-sectional measurements, because fiber perimeters of the same variety do not change with growing time or maturity. All the measurements have more variations when fewer fibers are analyzed and tend to stabilize as the number of analyzed fibers increases. The cross-sectional data of the seven variety samples show high correlations with the longitudinal data, fair correlations with the AFIS data, and low correlations with the micronaire data.
The financial support for this research was provided by the Texas Food and Fiber Commission and the United States Agriculture Department under grant 2003-35504-12855. Special thanks go to Dr. Devron Thibodeaux, USDA Southern Regional Research Center at New Orleans, and Dr. Eric Hequet, International Textile Center of Texas Tech University at Lubbock, for their advice and the cotton samples used in this research.
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Manuscript received April 3, 2003; accepted July 3, 2003.
B. XU AND Y. HUANG
The University of Texas at Austin, Austin, Texas 78712, U.S.A.
Copyright Textile Research Institute May 2004