Environ. Sci. Technol. 2004, 38, 1161-1169
Bilevel Thresholding of Sliced Image of Sludge Floc C. P. CHU AND D. J. LEE* Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617
This work examined the feasibility of employing various thresholding algorithms to determining the optimal bilevel thresholding value for estimating the geometric parameters of sludge flocs from the microtome sliced images and from the confocal laser scanning microscope images. Morphological information extracted from images depends on the bilevel thresholding value. According to the evaluation on the luminescence-inverted images and fractal curves (quadric Koch curve and Sierpinski carpet), Otsu’s method yields more stable performance than other histogrambased algorithms and is chosen to obtain the porosity. The maximum convex perimeter method, however, can probe the shapes and spatial distribution of the pores among the biomass granules in real sludge flocs. A combined algorithm is recommended for probing the sludge floc structure.
Introduction Morphological information extracted from sliced images, such as porosity and pore size, depends strongly on the image thresholding value. Over the past two decades, algorithms have been reported to determine the optimal bilevel threshold for gray scale images. Several researchers have comprehensively reviewed studies in this area (1, 2). Some indices were proposed to evaluate the performance of image segmentation using bilevel thresholding, including the probability of error (3), uniformity measure (4), shape measure (5), discrepancy (5), and others. Zhang (6, 7) surveyed the methods for evaluating image segmentation. When a priori knowledge of targeted objects is lacking, it is difficult to determine whether the chosen thresholding algorithm yields satisfactory results. In sliced images of bioaggregates, one would commonly noted unimodally distributed gray scale histogram and low contrast in image, which made the thresholding difficult (8). If judged by a group of human experts, a wide range of thresholds can yield acceptable results for bilevel images. Although image analysis has been applied extensively to analyzing the shape, size, number of filaments, and internal structures of biofilms (9) and sludge flocs, whether “optimal” post-processing procedures, thresholding algorithms, and means of evaluating performance exist for this purpose remains unclear. In some literature, the thresholding algorithms were not mentioned (10-16). Cenens et al. (17) proposed an algorithm based on the gray scale histogram for trilevel thresholding of their images, but the evaluation of the performance of the algorithm still depended on the judgment of the researchers. * Corresponding author fax: +886-2-2362-3040; e-mail: djlee@ ntu.edu.tw. 10.1021/es034732d CCC: $27.50 Published on Web 01/06/2004
2004 American Chemical Society
Baveye et al. (18) and Thill et al. (19) both considered the effects of thresholding value on the determination of fractal dimension of floc structure. The results indicated that the obtained dimension was a function of the thresholding value. In the case considered by Baveye et al. (18), the deviation determined by the two adopted algorithms (iterative selection and minimum-error method) was small and acceptable. Thill et al. (19) proposed that selecting the luminescence i gave ∂2D/∂i2 ) 0 as the thresholding value it. Yang et al. (8) discussed the application of five thresholding algorithms on biofilm images. A large deviation of the image quality was evident among the results of five algorithms, and the researchers relied on the judgment of expert biofilm researchers, who manually set the thresholding value to evaluate the algorithms. Baveye (20) later stated that such an evaluation might be inappropriate since the “esthetic considerations” of the observers would result in bias. The thresholding value is often directly selected from the gray scale histogram of the global image because the histogram-based methods are easy to implement and not verycomputationally demanding. This paper first briefly surveys several frequently encountered problems when applying the histogram-based methods for the bilevel thresholding of the microtome sliced images of sludge flocs. Then the individual feasibilities of these methods on probing the geometrical parameters with sludge flocs are evaluated.
Experimental Section Waste-activated sludge was sampled from the wastewater treatment facility at the Neili Bread Plant, Presidential Enterprise Co., Taoyuan, Taiwan. The total solid content (TS) was measured as 9,350 mg/L. An Accupyc pycnometer 1330 (Micromeritics, UK) measured the true density of the dried solid (FS) in sludge at 1450 kg/m3, with a relative deviation of less than 0.5%. The pH value of original sludge was around approximately 7.0. A particle sizer (LS230, Coulter, USA) estimated the volume-average floc diameter as 73.6 µm. The flocs were carefully collected from the sludge sample, which were first chemically fixed using a formalin buffer at 4 °C for 24 h and embedded by agarose in the cassette. Dehydration was conducted by immersing the flocs subsequently in ethanol/water solution of 50%, 70%, 90%, 95%, and 100% (v/v), respectively. The ethanol was then replaced by xylene/ethanol solutions of 50%, 70%, 90%, 95%, and 100% (v/v). The flocs saturated with xylene were immersed in molten paraffin at 65 °C overnight. Finally the paraffinembedded cakes were cooled to 25 °C in peel-off molds and solidified to form blocks for slicing (21). The block was then sliced into sections of 5 µm thickness using a microtome (Leitz model 1400, Germany). The thin paraffin section was floated on a water bath and then transferred onto a glass slide. The slide was dried in air. Then, the slice was heated in an oven at 70 °C for 10 min to melt the paraffin and then was dewaxed using xylene. Finally, the slice was stained using hematoxylin and eosin (H&E) (22). A phase-contrast microscope (LEICA DME, Germany) and a digital camera (Nikon Coolpix 995, Japan) recorded the image of slices at a constant luminescence light. A confocal laser scanning microscope (CLSM; Leica TCS SP2, Germany) was used to observe the internal floc structure. This microscope was equipped with image processing software, and an argon laser source was used to stimulate fluorescence. The sludge floc was imaged using 20×, 40×, or 60× objectives, depending on the required resolution. The microscope scanned the samples at a fixed depth, and VOL. 38, NO. 4, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Histogram-Based Algorithms for Selecting Bilevel Thresholding Value Otsu’s method
Variance-Based Method Otsu (26)
iterative selection
Iterative Selection Ridler and Calvard (27); Trussell (28)
Moment-Based Method moment preserving Tsai (29) MEM, normal MEM, Poisson P entropy KSW entropy JB entropy MAXMIN MCC ECM Renyi’s entropy
Minimum Error Methods Kittler and Illingworth (30) Pal and Bhandari (31) Entropic Thresholding Pun (32) Kapur et al. (33) Johannsen and Bille (34) Brink (35) Yen et al. (5) Sahoo et al. (36) Sahoo et al. (37)
the obtained image was digitized. Sludge samples were first chemically fixed and then embedded in agarose to perform fluorescence in situ hybridization (FISH). The Supporting Information also lists the procedures for the FISH process. CLSM scanned every slice for three times and then averaged the image for minimizing the luminescent noise.
FIGURE 1. Example image I: (a) original image, (b) inverted image, and (c) the gray scale histograms.
Image Processing In this study, all analyzed images are 8-bit gray scale images. Since the luminous flux per unit under optical microscopy could be spatially inhomogeneous, a “region of interest” (ROI) with more homogeneous luminescent background was defined not only to include sufficient morphological information for analysis but also to prevent unevenness of the luminescent background. Two characteristic lengths of ROI (Lequi) were determined using the projection diameter of the entire floc (region L) and using the gyration radius of scattering aggregates in flocs obtained from small-angle light scattering tests (25) (region S). For data processing, several variables are first defined in eqs S1-S6 of the Supporting Information. The light intensities of all pixels (Hgray(i)) were recorded from the chosen ROI, where their variances (σ2), the kth moments (mk), and other statistical characteristics of intensities could be calculated. Thresholding Using Histogram-Based Algorithms. After the intensity data from the chosen ROI were given, they must be thresholded for image analysis. The thresholding value is often directly selected from the gray scale histogram of the global image because the histogram-based methods are easy to implement and not very computationally demanding. In this study, 12 histogram-based algorithms, listed in Table 1, were chosen to determine the optimal thresholding value. Notably, histogram-based methods do not employ the considerable amount of information in images and have some difficulties in distinguishing foreground from background accurately (38). The histogram-based algorithm section in the Supporting Information briefly introduces these methods. The luminescence of two examples of sliced images of wastewater sludge flocs (Figures 1a and 2a) was inverted (Figures 1b and 2b), and the 12 aforementioned algorithms were applied to determine the thresholding values. Table 2 presents the results. The images in Figures 1a and 2a were bileveled using the obtained thresholding values. Since the microtome-sliced image consisted simply of biomasses and pores, the area fractions of the white parts 1162
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FIGURE 2. Example image II: (a) original image, (b) inverted image, and (c) the gray scale histograms.
of the bilevel microtome-sliced images were taken as the values of “areal porosity” (2D). A feasible thresholding algorithm should yield a similar and reasonable estimate of 2D from both original and inverted images, although the two values estimated by histogram-based algorithms will not be identical. The porosity determined from the original images is the area of the light portion as a fraction of the whole area, whereas the area fraction of the dark portion is defined as the porosity of the inverted images. Three situations were found. (i) Some algorithms estimate the porosity from the inverted images approximately 10-20% lower than that estimated from the original images. These include the algorithms associated with Otsu’s method, the iterative selection method, the moment preserving method, and ECM. The deviations are related to the change in the skewness of the histogram peaks. Also, the results determined from these
TABLE 2. Thresholding Values and Porosities Estimated from Figures 1 and 2 original image
Image on Figure S1, E2D ) 0.374; DSC ) 1.402 for the Quadric Koch Island
inverted image
method
it
E2D
it
E2D
categorya
Otsu’s method iterative selection moment preserving MEM, normal MEM, Poisson P entropy KSW entropy JB entropy MAXMIN MCC ECM Renyi’s entropy MAX(Σpp) MAX(ΣpC,p) MIN[Avg(pp/Ap)]
165 166 165 175 132 167 147 168 147 147 164 147 169 170 169
0.761 0.678 0.761 0.002 1.000 0.578 0.999 0.461 0.999 0.999 0.827 0.999 0.336 0.215 0.336
89 89 90 96 122 88 107 89 107 107 90 104 86 85 86
0.578 0.578 0.678 0.960 0.999 0.461 0.999 0.578 0.999 0.999 0.678 0.999 0.336 0.215 0.336
1 1 1 2 2 3 2 3 2 2 1 2 4 4 4
Image on Figure 2 Otsu’s method 122 0.479 iterative selection 122 0.479 moment preserving 115 0.585 MEM, normal 169 3.5 × 10-5 MEM, Poisson 121 0.493 P entropy 117 0.553 KSW entropy 71 0.984 JB entropy 136 0.310 MAXMIN 118 0.537 MCC 62 0.991 ECM 118 0.537 Renyi’s entropy 62 0.991 MAX(Σpp) 114 0.602 144 0.218 MAX(ΣpC,p) MIN[Avg(pp/Ap)] 134 0.333
TABLE 3. E2D and DP,2 Data Determined from Figures S1 and S2 of the Supporting Information
132 131 140 210 127 138 183 149 136 192 136 181 141 111 121
0.452 0.439 0.569 0.996 0.390 0.537 0.982 0.723 0.507 0.990 0.507 0.980 0.602 0.218 0.333
1 1 1 2 1 3 2 3 1 2 1 2 4 4 4
a Category 1: Both porosities are close. Category 2: Estimated porosity >0.95. Category 3: Porosity from original image + porosity from inverted image ) 1.0. Category 4: Identical porosities obtained.
algorithms are normally close to each other. The thresholding value determined from the unimodal histogram is generally to the left of the peak, yielding a relatively high porosity. (ii) For other algorithms, such as MEM, KSW entropy, MAXMIN, MCC, and Renyi’s entropy, the estimated porosity generally exceeds 0.95 for all samples. Such algorithms are therefore unsuitable even though they have been reported to perform well in segmenting some images. The narrowness of the unimodal histogram of sliced images may be the main cause of the failure of entropic methods and MEM. (iii) In the Pun (or P) entropy and JB entropy methods, the sum of the two porosities obtained from original and inverted images always equals one. The porosity determined using these two algorithms is apparently unreliable since they always set the thresholding value to divide the area under the histogram into two parts with a fixed ratio of areas. For example, the ratio is 1:1 for P entropy and 6:4 for JB entropy. Therefore, on the basis of the first screening using the inverted images, Otsu’s method, iterative selection method, moment preserving method, and ECM remain on the candidate list for further examination. Feature-Based Thresholding Algorithms. Features of images may provide clues for appropriately selecting the thresholding value. When an image is converted into a bilevel one, blobs can be recognized ,and some features of the blobs such as area and perimeter can be quantified. Statistics concerning these features can be used in thresholding analysis if any of them is a function of thresholding value, as suggested by Rosin (39). The feature-based thresholding
MAX(Σpp) MAX(ΣpC,p) MIN[Avg(pp/Ap)] Otsu’s method iterative selection moment preserving ECM
SD ) 6 (Figure S1b)
SD ) 18 (Figure S1d)
SD ) 30 (Figure S1f)
E2D
DP,2
E2D
DP,2
E2D
DP,2
0.652 0.576 0.373 0.356 0.353 0.362 0.350
na na 1.403 1.416 1.410 1.412 1.418
0.647 0.566 0.333 0.374 0.374 0.407 0.368
na na 1.511 1.584 1.584 1.658 1.583
0.634 0.523 0.265 0.437 0.437 0.463 0.437
na na 1.770 1.819 1.819 1.835 1.819
Image on Figure S3, E2D ) 0.358; DSC ) 1.918 for the Sieroinski Square Carpet SD ) 6 (Figure S3b) E2D MAX(Σpp) MAX(ΣpC,p) MIN[Avg(pp/Ap)] Otsu’s method iterative selection moment preserving ECM R
0.657 0.504 0.358 0.358 0.358 0.366 0.359
SD ) 18 (Figure S3d)
DSC
E2D
1.918 1.918 1.918 1.917 1.919
0.634 0.519 0.356 0.379 0.379 0.407 0.375
SD ) 30 (Figure S3f)
DSC
E2D
DSC
1.916 1.910 1.910 1.900 1.911
0.617 0.496 0.297 0.443 0.435 0.453 0.443
1.931 1.878 1.882 1.873 1.878
2D ) 0.374; DP,2 ) 1.402 for the Quadric Koch Island.
algorithm in the Supporting Information summarized the features of “blobs” chosen to be explored herein, such as perimeter (pp), convex perimeter (pC,p), perimeter/area ratio (pp/Ap), compactness (pp2/4πAp), roughness (pp/pC,p), elongation, and their number. In all of these analyses, the connectivity of neighboring pixels is set to 4; that is, pixels that neighbor each other on the diagonal are not considered to be part of a single blob. Such features were plotted against thresholding values. Two microtome-sliced images sampled (as those in Figures 1 and 2), which yielded typical histogram shapes, were given as examples (Figures 3a and 4a). Figures 3b-d and 4b-d present the change in some of the features of the blobs. Other images were not shown here for brevity sake. For all images, both Σpp and ΣpC,p had maxima, and the average pp/Ap had a minimum. Other parameters did not always show good correspondence (i.e., having an extreme value or an abrupt change in slope) at a particular it and were inappropriate for defining a criterion by which to select thresholding value. We hence limited further discussions on the feasibility of employing the (MAX(Σpp)) method, the (MAX(ΣpC,p)) method, and the (MIN[Avg(pp/Ap)]) method only. When analyzing a series of CLSM images from a single floc, the thresholding values estimated (Figure 5a-f) are all different since the variation of illumination with depth results in varying light intensity. This variation might be caused in part by the opacity of the sample and the attenuation of laser intensity (40), as shown in Figure 5g. The respective thresholding values were determined by the MAX(Σpp), MAX(ΣpC,p), and MIN[Avg(pp/Ap)] methods and plotted against the average luminescence of the images (Figure 6). All three curves were linear, with r 2 ) 0.972, 0.992, and 0.771, respectively. These results suggested that applying the three morphological indices was effective in determining thresholding values because the effects of uneven luminescence could be easily screened off. Among the three methods, the MAX(ΣpC,p) method exhibited the highest r 2 coefficient, meaning that it could best eliminate the luminescence effect. VOL. 38, NO. 4, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Blob features as function of thresholding value (it): (a) example image I; (b) gray scale histogram; (c) Σpp and ΣpC,p vs it; (d) Avg(pp/Ap) vs it; (e) compactness, roughness, and elongation vs it; and (f) number of holes vs it.
The tests with inverted images could not be used for further examination of the feasibilities of the blob featurebased algorithms since the blobs obtained from the original and inverted images are identical. Table 2 also lists the porosity data from the three feature-based algorithms for completeness. Thresholding of Fractal Objects. The feasibility of the seven remaining algorithms for analyzing the artificial images was evaluated to determine the appropriate algorithms for subsequent analysis. Two synthetic images of a well-known fractal morphologysquadric Koch island (Figure S1a of the Supporting Information, 2D ) 37.45%) and Sierpinski square 1164
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carpet (Figure S3a of the Supporting Information, 2D ) 35.85%)swere prepared (41). As depicted in Figures S2a and S4a of the Supporting Information, the gray scale histogram included two discrete peaks. We added Gaussian noise on each pixel with a prescribed standard deviation (SD). When the SD increased, the two peaks on the bimodal histogram merged into a single peak (Figures S2f and S4f of Supporting Information), similar to that in Figure 2a. The images with noise then could not be directly bileveled. Table 3 shows the estimated 2D data with various SD based on the seven remaining algorithms. Most of these algorithms overestimated 2D. The results obtained from
FIGURE 4. Blob features as function of thresholding value (it): (a) example image II; (b) gray scale histogram; (c) Σpp and ΣpC,p vs it; (d) Avg(pp/Ap) vs it; (e) compactness, roughness, and elongation vs it; and (f) number of holes vs it. histogram-based algorithms are quite similar to each other. Notably, Otsu’s method, iterative selection, and ECM yielded relatively stable performance on the porosity estimation. Otsu’s method is simpler to implement than the other two methods. Meanwhile, all the feature-based algorithms poorly estimated 2D. Besides the aeral porosity, the pore size distribution could be obtained by blob analysis. Restated, once the bilevel images were obtained, the boundaries of all pores on the image could be built up, where their equivalent diameter (dp,i) was estimated. The box-counting analysisis one of the most widely used methods for characterizing fractals. If the surface of one fractal
object is covered by triangular patches with a characteristic side length of ROI (lequi), then the box-counting fractal dimension (DP,2) is modified from Baveye et al. (18) as follows:
DP,2 ) - lim
lequif0
log N(lequi) log lequi
(1)
where N(lequi) is the number of triangular patches. In practice, the limit lequi f 0 cannot be approached. DP,2 is estimated by measuring the dependence of N on lequi when the characteristic length is larger than some cutoff length, which is the size in pixels of the original sliced image. The value of VOL. 38, NO. 4, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 5. Blob features as function of thresholding value (it): (a-f) example CLSM images in series (interval ) 6 µm). (g) The average luminescence of different slices. DP,2 of a pore with smooth and flattened perimeter equals to 1. The Supporting Information also briefly summarizes the way to determine DP,2 from a quadric Koch island as an example. Table 3 shows the estimated DP,2 for the noised Koch island All algorithms overestimated this fractal dimension of noised Koch island. This deviation increased with the magnitude of the noise. Using the MIN[Avg(pp/Ap)] method, the lowest DP,2 among other methods can be found, at which the contribution of the noise (or small pores) is minimal. Meanwhile, both the MAX(Σpp) and the MAX(ΣpC,p) methods could probe the small pores in the images. At high resolution, the perimeters increase dramatically, which leads to unreasonable DP,2. Assuming that the cross section of sludge floc can be described as a Sierpinski carpet (Figure S3a of the Supporting 1166
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Information), the Sierpinski carpet fractal dimension (DSC) can be determined to quantify the “disappearing rate” of remaining area. On a Sierpinski carpet, the remaining area (βR) decreases as the image resolution is increased and smaller pores can be detected (41). The Supporting Information also briefly lists the method to estimate the Sierpinski fractal dimension of the example image I. The seven algorithms in general underestimated the Sierpinski fractal dimension (DSC) (Table 3). The results obtained from histogram-based algorithms are quite similar to each other, as noted in the preceding paragraph. Again, both the MAX(Σpp) and the MAX(ΣpC,p) failed to estimate the DSC. The failure of MAX(Σpp) and MAX(ΣpC,p) methods for estimating the fractal dimensions reflects their capability to probe the detailed structure, while these blobs were filtered
out by the histogram-based algorithms. Figure S8 of the Supporting Information displays the bilevel images obtained using the MAX(ΣpC,p) method. Although the small pores occupied an insignificant fraction of the area, they contributed most of the total perimeter and convex perimeter. The effects of small blobs were largely canceled when the MIN[Avg(pp/Ap)] method was employed. Therefore, for a deterministic fractal object, like Koch curve or Sierpinski carpet, the porosity and the fractal dimensions of pore structure could be determined using Otsu’s method and the MIN[Avg(pp/Ap)] method. Both the MAX(Σpp) and MAX(ΣpC,p) methods could neither estimate the porosity nor the fractal dimensions. However, based on image from a real floc, the latter two methods could detail the pore structure to build up the floc model. This point is discussed in the next session.
Probing the Floc Structure
FIGURE 6. Thresholding values it determined from the three criteria vs average luminescence of image µT.
On the basis of the above discussions, Otsu’s method could estimate the porosity and the fractal dimension of the internal pore structure, while the MIN[Avg(pp/Ap)] method could provide the fractal dimension data. When the real floc was analyzed, the small blobs to be filtered out in the preceding section are the detailed pore structures we want to probe.
FIGURE 7. Morphologies of example image I obtained respectively from Otsu’s method and the MAX(ΣpC,p) method: (a) original image, (b) bilevel image using Otsu’s method, (c) bilevel image using the MAX(ΣpC,p) method, (d) blob size distribution obtained from Otsu’s method, and (e) blob size distribution obtained from the MAX(ΣpC,p) method. VOL. 38, NO. 4, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 8. Morphologies of example image II obtained respectively from Otsu’s method and the MAX(ΣpC,p) method: (a) original image, (b) bilevel image using Otsu’s method, (c) bilevel image using the MAX(ΣpC,p) method, (d) blob size distribution obtained from Otsu’s method, and (e) blob size distribution obtained from the MAX(ΣpC,p) method. The spatial distribution of texture or the local statistics of luminescence of the sliced images are normally more complex and irregular than those of the two synthetic images. The MAX(Σpp) and MAX(ΣpC,p) methods then become the better way of probing. Meanwhile, in images with a narrowly distributed histogram, the outcome of the MIN[Avg(pp/Ap)] method is sensitivity to the applied thresholding value. For example, the curve of pp/Ap versus i in Figure 2d has six local minima that are close to each other. Figures 7 and 8 show two images thresholded using Otsu’s method and the MAX(ΣpC,p) method. The frames of the floc matrix are presented using Otsu’s method (as demonstrated in Figures 7b and 8b). The morphology of the pores, however, could not be determined since the boundaries of the interstices among the biomass granules did not form loops (discrete pores with closed boundaries). That is, when Otsu’s method was used to produce bilevel images, the smaller pores (or detailed porous configuration) were filtered out. Applying the algorithms based on the MAX(Σpp) and MAX(ΣpC,p) methods, instead of detecting the overall porosity, can help determine the spatial distribution of small pores or interstices among the granules, just as in Figures 7c and 8c. That is, a much more detailed local structure appeared. Figures 7d,e and 8d,e compared the pore size distribution obtained from Otsu’s method with that obtained using the MAX(ΣpC,p) 1168
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method. Apparently, most small pores in the sliced images (labeled as “M” in Figure 7e) were included in the largest pores (labeled as “G” in Figure 7d), and only very small pores were shown to be embedded in the granules of biomass (labeled as “D”). The histogram-based, Otsu’s method is feasible to estimate the floc interior porosity, but the featurebased, MAX(ΣpC,p) method is suitable to probe the detailed structure in sludge floc. A combined algorithm should be applied for probing the floc interior at various scales.
Supporting Information Available Figures and tables. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review July 8, 2003. Revised manuscript received November 23, 2003. Accepted November 25, 2003. ES034732D
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