- Email: [email protected]
Calculation of effective pore diameters in porous filtration membranes with image analysis
ARTICLE IN PRESS
Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434 www.elsevier.com/locate/rcim
Calculation of effective pore diameters in porous filtration membranes with image analysis F.H. Shea, K.L. Tungb, L.X. Konga, a
b
Centre for Advanced Manufacturing Research, University of South Australia, Mawson Lakes, Australia R&D Centre for Membrane Technology, Department of Chemical Engineering, Chung Yuan Christian University, Taiwan Received 22 May 2006; received in revised form 24 August 2006; accepted 8 February 2007
Abstract In filtration/separation applications, porous membranes separate particles by a sieving mechanism determined by pore size of membrane and particle size. However, since pores in the membranes have irregular shape and vary in size, the definition of the pore size has been complex and sometimes, even confusing. In this work, we introduced a novel geometric parameter called effective pore diameter to characterize particle permeation performance in porous filtration membranes. The effective diameter of a pore is defined as the maximum diameter of a spherical particle which can pass through the pore in the membrane. We for the first time applied advanced image analysis techniques to automatically measure effective pore diameters and their distribution from scanning electronic microscopic image of the membrane using Euclidean distance transform (EDT). It is found that the effective pore diameter and its distribution are more accurate than the parameters previously used, to evaluate the membrane’s filtration and separation performance and especially, particle permeation performance. r 2007 Published by Elsevier Ltd. Keywords: Effective pore diameter; Porous membrane; Filtration/separation; Particle permeation; Image analysis; Euclidean distance transform (EDT); Virtual circle
1. Introduction Porous membranes have been widely used in various industries, such as modern engineering of chemistry, energy, environmental conservation, bioengineering, medicine, food, and military industries. Filtration and separation are two major applications of porous membranes, such as desalination, wastewater treatment, water purification, and oil/water separation. Filtration is a technique that utilizes a porous barrier (e.g., membrane) to separate suspended or dissolved particles in solution based on the pore sizes of membrane barrier and particles sizes, eliminating the need for centrifugation, solvent phase changes or other product damaging methods. Application of positive or negative pressure differential across a selectively permeable barrier drives the separation in a sieve-like manner. Small particles pass through the barrier Corresponding author. Fax: +61 8 8302 5292.
E-mail address: [email protected] (L.X. Kong). 0736-5845/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.rcim.2007.02.023
with the solvent as filtrate while the large particles are retained. Depending on pore size spectrum, membranes can be used for macrofiltration, microfiltration, and ultrafiltration applications. Characterizing the pore morphology of membranes has been very important for both membrane users and manufacturers, as well as for membrane scientists. They need the information of membrane morphology for choosing an appropriate membrane in a certain application, predicting membrane performance, determining membrane casting conditions, controlling membrane quality, and understanding membrane transport mechanisms [1,2]. Traditional methods used to characterize pore morphology of membranes, such as pore size and pore size distribution, include microscopic method [3], mercury porosimetry bubble pressure and gas transport method [4], gas–liquid equilibrium method (permporometry) and thermoporometry [1]. Some research groups used the concept of active pore size [5,6] to characterize pore
ARTICLE IN PRESS 428
F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
interconnectivity. More recently, some other advanced methods have been developed to characterize the membrane materials of nano pore size with electrochemical and optical single transporter recording [7], fluorescent dextran test [8] and atomic force microscopy [9]. However, the parameters obtained by using the traditional methods [1–4] or even with the more advanced technologies [7–9] do not give direct information about membrane pore structure except the microscopic method and there is a calibration problem commonly involved in all of these methods. Furthermore, how to define the pore size of membranes has been complex and sometimes even confusing since the pores in membranes have irregular shape and vary in size. In this work, we aim to more objectively and efficiently characterize the porous membranes by introducing a new parameter called effective pore diameter. Other than parameters such as pore areas, perimeters, equivalent diameter based on the same areas, shape factors, etc., we will develop an image analysis algorithm in Matlab [10] to calculate the effective pore diameter for all pores and its distribution in polyvinylidene difluoride (PVDF) membrane from its scanning electronic microscopy (SEM) image. The algorithm is based on Euclidean distance transform (EDT) and is the first time to be introduced to objectively characterize membrane materials. 2. Materials and image acquisition The samples used in this study are flat-sheet molded PVDF membranes, which have various pore sizes and irregular shapes. PVDF membranes, in contrast to typical cellulosic membranes, are hydrophobic and resistant to a wide variety of organic solvents as well as most aqueous acids and bases. The images of the membranes with a size of 480 640 pixels are taken by a CCD camera, which is mounted on a SEM and connected to a Pentiums 4 Compaq computer with 512MB RAM in the R&D Research Center for Membrane Technology, Chung Yuan Christian University. A representative image of the PVDF membrane is shown in Fig. 1.
Fig. 1. A SEM image of a porous PVDF membrane (at the scale of 37% of original image).
3. Procedures of the membrane characterization In this section, we will firstly discuss image preprocessing techniques to convert the original gray-level image of a membrane to a binary image. Then, a set of conventional geometric parameters and their distributions, such as porosity, pore areas, pore perimeters, shape factors, and equivalent diameters based on the same areas, are measured by using image analysis techniques. Furthermore, a distance transform will be performed on the binary image to compute effective pore diameters and their distribution. The flow chart of the image analysis is shown in Fig. 2.
3.1. Image pre-processing Before analyzing pore parameters of a membrane, image pre-processing is required to convert a SEM image of membrane to a binary image, where all pore regions are shown as foreground, i.e., white pixels and nonpore region as background, i.e., membrane walls. There are mainly two kinds of artifacts in the membrane image. For instance, non-uniformities of pixel intensity (i.e., pixel value) on the membrane surface are obviously observed since illumination is varied; furthermore, the contrast of pixel intensities in pore regions and membrane walls is small. We take the following steps to remove those artifacts in the image and measure the parameters of pores. Step 1: Crop the original image of the membrane (Fig. 3a) so that the figure label and calibration bars are removed and only membrane surface region is left for processing; an image of 409 640 pixels is resulted that is shown in Fig. 3b. Step 2: Adjust the pixel intensity of the cropped image to enhance contrast (Fig. 3c). Step 3: Filter the enhanced image with ‘‘averaging’’ filter to obtain a smoothened image (Fig. 3d) showing pore regions and membrane wall regions with evener pixel intensities. Step 4: Calculate a global image threshold using Otsu’s method [10] which chooses the threshold to convert a graylevel image (i.e., an intensity image) to a binary image (two classes, i.e., black and white) in which the intraclass variance of pixel intensities of the black and white pixels is minimized and the between-class variance is maximized. Step 5: Thresholding the image obtained in Step 3 to a binary image (Fig. 3e) based on the threshold level computed in Step 4, which shows membrane wall regions in white and pore regions in black. Step 6: Complement the binary image that resulted from Step 5 and remove isolated noises in the image (Fig. 3f). In the complement of the binary image, black and white pixels are reversed, i.e., pore regions are shown in white and become foreground while membrane wall regions are shown in black and become background (Fig. 3f). From
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
429
Preparing membrane material
Imaging: SEM and CCD camera
Transferring image of porous PVDF membrane to a computer
Pre-processing images: contrast enhancement, filtering, thresholding, image complementing and morphological operations
Performing distance transform on the binary image of membrane
Calculating the effective pore sizes and their distribution
Calculating other geometric features and their distributions distributions, such as porosity, areas, perimeters, equivalent diameters based on the same area as pore regions, shape factors, solidities and extents of pores
Comprehensive feature set of pores obtained Fig. 2. Flow chart of image analysis of porous PVDF filtration membrane.
Fig. 3f, overall porosity of the membrane surface will be measured. Step 7: Perform morphological operations and labeling each pore region on the image obtained from Step 6 (Fig. 3(g)) There are three purposes in this step. The first is to remove the pore objects, which are connected to the border of the image since those objects are split by the borders of the image frame and their shape parameters are meaningless; the second purpose is to smoothen the pore objects and remove isolated noise pixels; the third purpose is to assign each pore blob a unique label, which will be used in measuring geometric parameters for each pore blob. Step 8: Perform EDT on the image obtained from Step 7 (Fig. 3(h)) and compute the effective pore diameters and distribution, More details about this step are described in the following section.
3.2.1. Computing geometric features of pores From the image in Fig. 3f, the porosity of the membrane surface is calculated as the ratio of number of white pixels (i.e., pore regions) to the total image pixels nw r¼ , (1) LW where nw is the number of white pixels while L and W are the length and width of the image in pixels, respectively. From the image in Fig. 3(g), a set of parameters will be measured for each pore blob. Area (Ap) of a pore blob is computed by Ap ¼ m,
(2)
where m is the number of pixels contained in the pore blob. Perimeter (lp) of the pore is computed by n qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ðri ri1 Þ2 þ ðci ci1 Þ2 , (3) lp ¼ i¼1
3.2. Image analysis From the images pre-processed in Section 3.1, a number of parameters and their distributions can be measured using image analysis techniques.
where ri and ci are the row and column of a pixel i on the contour of the pore blob, 2pipn, and n is the number of pixels on the contour of the pore blob. Equivalent diameter (DEq Area ) based on the same area is defined as the diameter of a circle that has the same area as
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
430
Fig. 3. Images obtained in pre-processing: (a) original gray-level image of a membrane sample, calibration bars indicate a length of 10.0 mm; (b) cropped image; (c) contrast enhanced image; (d) filtered image; (e) thresholded image; (f) image after complementing and removing isolated noises from (e); (g) image after morphological operations and (h) Euclidean distance transformed image of (g).
the pore blob: rffiffiffiffiffiffiffiffi 4Ap Eq DArea ¼ . p
(4)
Shape factor (fs) is calculated by fs ¼
l 2p . 4pAp
Solidity (S) is computed as the area of pore blob (Ap) divided by the area of the convex hull of the pore blob (Aconvex), S¼
(5)
Ap . Aconvex
(6)
The convex hull of the pore blob is the smallest convex set that contains the pore blob and is represented as a list of
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
facets, which has a set of vertices, a set of neighboring facets and a half-space. A half-space is defined by a unit normal and an offset [10,11]. Extent (E) is computed as the area of the pore blob (Ap) divided by the area of the bounding box (Ab), the latter is the smallest rectangle containing the pore blob [10,11]: E¼
Ap . Ab
(7)
431
section. The value on the center pixel (i.e., DT(xc, yc)) in the distance transformed image indicates the distance between the center and its closest non-pore pixel. Since the radius of the virtual circle Rv represents the distance between the center pixel and its closet edge point on the pore blob, Rv is calculated as following due to pixel width concern: Rv ¼ DTðxc ; yc Þ 0:5.
(11)
Therefore, the effective pore diameter for this pore blob 3.2.2. Euclidean distance transform (EDT) and effective pore diameter (Deff) In this study, a new parameter, effective pore diameter for each pore, is also extracted. It is defined as the diameter of the largest particle which can pass through the pore in the membrane. In terms of image morphology, the effective pore diameter of a pore can be considered as the diameter of a largest virtual circle that can be encompassed by this pore region. We call it virtual circle because it does not exist in the original image and is very helpful in description of effective pore diameter [12]. In this way, the effective diameter of a pore is equal to two times of the distance between the center of the largest virtual circle and its nearest edge point in this pore region, i.e., the diameter of the largest virtual circle. With the help of distance transform (DT ), a digital binary image that consists of object (i.e., pore in this case) and non-object (i.e., non-pore) pixels is converted into another image in which each object pixel has a value corresponding to the minimum distance from the object pixel to its nearest non-object pixel by a distance function. The interior of a closed boundary is considered as object pixels and exterior as non-object pixels [13,14]. Because of its rotation invariance property, the Euclidean distance function is used. The distance d(p, q) between a pixel p(x, y) in a pore region A and a pixel q(u, v) in the non-pore region Ac is defined by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðp; qÞ ¼ ðx uÞ2 þ ðy vÞ2 ; pðx; yÞ 2 A and qðu; vÞ 2 Ac , (8) where (x, y) and (u, v) are coordinates of pixels p and q, respectively, and Ac is the complement of A. The distance transform assigns a value DT(x, y) to the pixel p(x, y): DTðx; yÞ ¼ minðu;vÞ fdðp; qÞg; qðu; vÞ 2 Ac ,
pðx; yÞ 2 A
and ð9Þ
where DT(x, y) is the minimum distance from the pixel p(x, y) to non-pore pixels in Ac. By repeating the above procedure to all pixels in the pore region, a distance transformed matrix is formed. From this matrix, a local maximum value can be found by searching throughout the pore region A: DTðxc ; yc Þ ¼ maxfDTðx; yÞg;
pðx; yÞ 2 A.
(10)
The coordinates (xc, yc) of this maximum represent the center of the virtual circle in terms of definition in previous
Deff ¼ 2Rv .
(12)
This means that the particles with a diameter equal to or less than Deff can pass through this pore. An example of pore blob extracted from Fig. 3(g) is displayed in Fig. 4a, where the pore region shown in gray color for better viewing, has a pixel value of 1 while the pixels in non-pore region (i.e., the membrane walls) have a value of 0. The distance transformed image matrix of the pore in Fig. 4a is displayed in Fig. 4b. The center of the largest virtual circle and its radius are marked in a black box and an arrow in Fig. 4b, respectively. 3.2.3. Calibrations Normally, calibration bars or scale markers are present and clearly visible on all SEM photomicrographs. In the sample image shown in Fig. 3a, calibration bars, which are the little lines, are located in the lower right corner of the image. The distance between the first bar and the last one, which represents 10.0 mm, is measured as 252 pixels. By referencing this calibration rate, the program automatically calibrated the measurements, which were obtained in the previous section, into microns. 4. Results and discussion From the experiments described in Section 3.1, it can be seen that the image pre-processing can be automatically performed and is robust to extract the pore regions without human interaction (Fig. 3b–h). From this membrane image, 437 pore blobs are found. In Section 3.2.1, a set of parameters, including effective diameter, area, perimeter, equivalent diameter based on the same area as each pore blob, pore shape factor, solidity, extent and porosity, are computed to characterize the pore morphologies of the membrane. Their statistical values are listed in Table 1 and distributions are shown in Fig. 5. These parameters, being used together, will give more information about the pore morphologies than when used alone. Some parameters can hardly be extracted by using other methods, such as effective diameter, shape factor, solidity and extent, while some others are very costly to obtain. Especially, we computed the effective diameter of pores (Deff) and its distribution as a new parameter. By using EDT, this algorithm performs a comprehensive search for the largest virtual circle and its diameter throughout each
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
432
Fig. 4. An example of distance transform: (a) an example of pore blob in the binary image of the membrane shown in Fig. 3g; (b) the distance transformed image of (a): the pixel with the highest value marked in the dark black box is the center of the virtual circle, the radius of the virtual circle (shown as a dashed circle) is shown by a black arrow, which represents the distance between the center to its closest edge point.
pore region. Consequently, the effective pore diameters and their distribution in the porous membrane are computed by using Eqs. (8)–(12). The effective pore diameter obtained has a very clear mathematical definition and it simply represents the diameter of the largest particles which can pass through the pore. For the example shown in Fig. 4a, there are 29 pixels belonging to this pore, then the equivalent diameter based on the same area (DEq Area ) is equal to 6.07 pixels by using Eqs. (2) and (4). Comparatively, from the corresponding distance transformed image of Fig. 4a, the pixel with the highest value of 3.00 is found and marked in the dark black box in Fig. 4b. While the pixel is the location of the center of the largest virtual circle (shown as a dashed circle in Fig. 4b) for this pore region, the radius of the circle is 2.5 pixels by using Eq. (11). Therefore, the effective diameter of this pore (Deff) is equal to 5.00 pixels, which means that the particles with a diameter equal to or less than 5.00 pixels can pass through the pore (i.e., can be encompassed by the pore region). However, the particles with the equivalent diameter DEq Area (i.e., 6.07 pixels) cannot pass through the pore (i.e., cannot be encompassed by the pore region). Deff is less than DEq Area . This trend is increased to a great extent when the shape of pore is far away from a circle. When pores are perfect circles, Deff is equal to DEq Area . Our experiment results have shown the trend in Table 1, Fig. 5a and d. From the results obtained above, the effective pore diameter will provide more objective and accurate information about the particle permeability. The membrane performance in both filtration and separation and, specially, particle permeation performance can be better understood and predicted by measuring this parameter and its distribution. Furthermore, the EDT used in this study has rotation invariance property as shown in Eq. (9). With this quality, membrane samples can be imaged at any rotation angle, which makes sampling more convenient. The time spent on both image pre-processing and measurement of all those parameters and their distributions for the membrane is 15.58 s. This indicates the image analysis method is very efficient in characterizing membrane morphologies. The calibration can be done by comparing the measurements in the unit of pixels with the length (in pixels) of the calibration bars. Furthermore, unlike other traditional methods, all of these parameters in Table 1 can be easily measured with this image analysis approach.
Table 1 The parameters computed to characterize membrane pore morphologies
Mean Minimum Maximum Standard deviation
r
Deff (mm)
Ap (mm2)
lp (mm)
DEq Area (mm)
fs
S
E
0.31
0.32 0.14 1.35 0.19
0.26 0.02 2.95 0.39
2.26 0.48 15.36 1.99
0.48 0.16 1.94 0.31
1.89 0.88 8.48 0.91
0.93 0.57 1.00 0.07
0.60 0.34 0.81 0.08
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
433
Fig. 5. The distributions of the parameters of pore morphologies: (a) effective pore diameter, (b) area, (c) perimeter, (d) equivalent diameter based on the same area as pore region, (e) shape factor, (f) solidity, and (g) extent.
5. Conclusions In this work, we employed advanced image analysis techniques to characterize pore morphologies of porous filtration membrane, focusing on measuring the effective pore diameter and its distribution of PVDF porous membrane together with other parameters. The image analysis approach developed in this work allows data-intensive and comprehensive analysis of membrane pore morphologies by computing many parameters including effective pore diameters. It is the effective pore diameters that are actually responsible for the
membrane performance in both filtration and separation, specially, particle permeation performance. It was found that the proposed method is very efficient, fast and accurate and the calibration is simple and straightforward. Acknowledgments Financial support provided for F.H. She to visit Chung Yuan University and work on this project by Australian Academy of Science and National Science Council, ROC, under Scientific Visits to Taiwan Scheme is gratefully acknowledged.
ARTICLE IN PRESS 434
F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
References [1] Nakao S. Determination of pore size and pore size distribution. 3: filtration membranes. J Membr Sci 1994;96(1–2):131–65. [2] Gijsbertsen-Abrahamse AJ, Van der Padt A, Boom RM. Influence of membrane morphology on pore activation in membrane emulsification. J Membr Sci 2003;217(1–2):141–50. [3] Zeman L, Denault L. Characterization of microfiltration membranes by image analysis of electron micrographs. Part I. Method development. J Membr Sci 1992;71(3):221–31. [4] Mietton-Peuchot M, Condat C, Courtois T. Use of gas–liquid porometry measurements for selection of microfiltration membranes. J Membr Sci 1997;133(1):73–82. [5] Cuperus FP, Bargeman D, Smolders CA. Permporometry: the determination of the size distribution of active pores in UF membranes. J Membr Sci 1992;71(1–2):57–67. [6] Mey-Marom A, Katz MG. Measurement of active pore size distribution of microporous membranes—a new approach. J Membr Sci 1986;27(2):119–30.
[7] Hemmler R, Bose G, Wagner R, Peters R. Nanopore unitary permeability measured by electrochemical and optical single transporter recording. Biophys J 2005;88(6):4000–7. [8] Mulherkar P, Van Reis R. Flex test: a fluorescent dextran test for UF membrane characterization. J Membr Sci 2004;236(1):171–82. [9] Hilal N, Al-Zoubi H, Darwish NA, Mohammad AW. Characterization of nanofiltration membranes using atomic force microscopy. Desalination 2005;177(1–3):187–99. [10] MathWorks. MatLab: the language of technical computing. Natick: The MathWorks Inc.; 2004. [11] Russ JC. The image processing handbook. 3rd ed., vol. 1. Raleigh: CRC Press LLC; 1999. p. 771. [12] Alhichri HS, Kamel M. Virtual circles: a new set of features for fast image registration. Pattern Recognit Lett 2003;24(9–10):1181–90. [13] Vincent L. Exact Euclidean distance function by chain propagations. IEEE Comp Vis Pattern Recog 1991. [14] Shih FY, Wu Y-T. Fast Euclidean distance transformation in two scans using a 3 3 neighborhood. Comput Vis Image Und 2004;93(2):195–205.
Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434 www.elsevier.com/locate/rcim
Calculation of effective pore diameters in porous filtration membranes with image analysis F.H. Shea, K.L. Tungb, L.X. Konga, a
b
Centre for Advanced Manufacturing Research, University of South Australia, Mawson Lakes, Australia R&D Centre for Membrane Technology, Department of Chemical Engineering, Chung Yuan Christian University, Taiwan Received 22 May 2006; received in revised form 24 August 2006; accepted 8 February 2007
Abstract In filtration/separation applications, porous membranes separate particles by a sieving mechanism determined by pore size of membrane and particle size. However, since pores in the membranes have irregular shape and vary in size, the definition of the pore size has been complex and sometimes, even confusing. In this work, we introduced a novel geometric parameter called effective pore diameter to characterize particle permeation performance in porous filtration membranes. The effective diameter of a pore is defined as the maximum diameter of a spherical particle which can pass through the pore in the membrane. We for the first time applied advanced image analysis techniques to automatically measure effective pore diameters and their distribution from scanning electronic microscopic image of the membrane using Euclidean distance transform (EDT). It is found that the effective pore diameter and its distribution are more accurate than the parameters previously used, to evaluate the membrane’s filtration and separation performance and especially, particle permeation performance. r 2007 Published by Elsevier Ltd. Keywords: Effective pore diameter; Porous membrane; Filtration/separation; Particle permeation; Image analysis; Euclidean distance transform (EDT); Virtual circle
1. Introduction Porous membranes have been widely used in various industries, such as modern engineering of chemistry, energy, environmental conservation, bioengineering, medicine, food, and military industries. Filtration and separation are two major applications of porous membranes, such as desalination, wastewater treatment, water purification, and oil/water separation. Filtration is a technique that utilizes a porous barrier (e.g., membrane) to separate suspended or dissolved particles in solution based on the pore sizes of membrane barrier and particles sizes, eliminating the need for centrifugation, solvent phase changes or other product damaging methods. Application of positive or negative pressure differential across a selectively permeable barrier drives the separation in a sieve-like manner. Small particles pass through the barrier Corresponding author. Fax: +61 8 8302 5292.
E-mail address: [email protected] (L.X. Kong). 0736-5845/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.rcim.2007.02.023
with the solvent as filtrate while the large particles are retained. Depending on pore size spectrum, membranes can be used for macrofiltration, microfiltration, and ultrafiltration applications. Characterizing the pore morphology of membranes has been very important for both membrane users and manufacturers, as well as for membrane scientists. They need the information of membrane morphology for choosing an appropriate membrane in a certain application, predicting membrane performance, determining membrane casting conditions, controlling membrane quality, and understanding membrane transport mechanisms [1,2]. Traditional methods used to characterize pore morphology of membranes, such as pore size and pore size distribution, include microscopic method [3], mercury porosimetry bubble pressure and gas transport method [4], gas–liquid equilibrium method (permporometry) and thermoporometry [1]. Some research groups used the concept of active pore size [5,6] to characterize pore
ARTICLE IN PRESS 428
F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
interconnectivity. More recently, some other advanced methods have been developed to characterize the membrane materials of nano pore size with electrochemical and optical single transporter recording [7], fluorescent dextran test [8] and atomic force microscopy [9]. However, the parameters obtained by using the traditional methods [1–4] or even with the more advanced technologies [7–9] do not give direct information about membrane pore structure except the microscopic method and there is a calibration problem commonly involved in all of these methods. Furthermore, how to define the pore size of membranes has been complex and sometimes even confusing since the pores in membranes have irregular shape and vary in size. In this work, we aim to more objectively and efficiently characterize the porous membranes by introducing a new parameter called effective pore diameter. Other than parameters such as pore areas, perimeters, equivalent diameter based on the same areas, shape factors, etc., we will develop an image analysis algorithm in Matlab [10] to calculate the effective pore diameter for all pores and its distribution in polyvinylidene difluoride (PVDF) membrane from its scanning electronic microscopy (SEM) image. The algorithm is based on Euclidean distance transform (EDT) and is the first time to be introduced to objectively characterize membrane materials. 2. Materials and image acquisition The samples used in this study are flat-sheet molded PVDF membranes, which have various pore sizes and irregular shapes. PVDF membranes, in contrast to typical cellulosic membranes, are hydrophobic and resistant to a wide variety of organic solvents as well as most aqueous acids and bases. The images of the membranes with a size of 480 640 pixels are taken by a CCD camera, which is mounted on a SEM and connected to a Pentiums 4 Compaq computer with 512MB RAM in the R&D Research Center for Membrane Technology, Chung Yuan Christian University. A representative image of the PVDF membrane is shown in Fig. 1.
Fig. 1. A SEM image of a porous PVDF membrane (at the scale of 37% of original image).
3. Procedures of the membrane characterization In this section, we will firstly discuss image preprocessing techniques to convert the original gray-level image of a membrane to a binary image. Then, a set of conventional geometric parameters and their distributions, such as porosity, pore areas, pore perimeters, shape factors, and equivalent diameters based on the same areas, are measured by using image analysis techniques. Furthermore, a distance transform will be performed on the binary image to compute effective pore diameters and their distribution. The flow chart of the image analysis is shown in Fig. 2.
3.1. Image pre-processing Before analyzing pore parameters of a membrane, image pre-processing is required to convert a SEM image of membrane to a binary image, where all pore regions are shown as foreground, i.e., white pixels and nonpore region as background, i.e., membrane walls. There are mainly two kinds of artifacts in the membrane image. For instance, non-uniformities of pixel intensity (i.e., pixel value) on the membrane surface are obviously observed since illumination is varied; furthermore, the contrast of pixel intensities in pore regions and membrane walls is small. We take the following steps to remove those artifacts in the image and measure the parameters of pores. Step 1: Crop the original image of the membrane (Fig. 3a) so that the figure label and calibration bars are removed and only membrane surface region is left for processing; an image of 409 640 pixels is resulted that is shown in Fig. 3b. Step 2: Adjust the pixel intensity of the cropped image to enhance contrast (Fig. 3c). Step 3: Filter the enhanced image with ‘‘averaging’’ filter to obtain a smoothened image (Fig. 3d) showing pore regions and membrane wall regions with evener pixel intensities. Step 4: Calculate a global image threshold using Otsu’s method [10] which chooses the threshold to convert a graylevel image (i.e., an intensity image) to a binary image (two classes, i.e., black and white) in which the intraclass variance of pixel intensities of the black and white pixels is minimized and the between-class variance is maximized. Step 5: Thresholding the image obtained in Step 3 to a binary image (Fig. 3e) based on the threshold level computed in Step 4, which shows membrane wall regions in white and pore regions in black. Step 6: Complement the binary image that resulted from Step 5 and remove isolated noises in the image (Fig. 3f). In the complement of the binary image, black and white pixels are reversed, i.e., pore regions are shown in white and become foreground while membrane wall regions are shown in black and become background (Fig. 3f). From
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
429
Preparing membrane material
Imaging: SEM and CCD camera
Transferring image of porous PVDF membrane to a computer
Pre-processing images: contrast enhancement, filtering, thresholding, image complementing and morphological operations
Performing distance transform on the binary image of membrane
Calculating the effective pore sizes and their distribution
Calculating other geometric features and their distributions distributions, such as porosity, areas, perimeters, equivalent diameters based on the same area as pore regions, shape factors, solidities and extents of pores
Comprehensive feature set of pores obtained Fig. 2. Flow chart of image analysis of porous PVDF filtration membrane.
Fig. 3f, overall porosity of the membrane surface will be measured. Step 7: Perform morphological operations and labeling each pore region on the image obtained from Step 6 (Fig. 3(g)) There are three purposes in this step. The first is to remove the pore objects, which are connected to the border of the image since those objects are split by the borders of the image frame and their shape parameters are meaningless; the second purpose is to smoothen the pore objects and remove isolated noise pixels; the third purpose is to assign each pore blob a unique label, which will be used in measuring geometric parameters for each pore blob. Step 8: Perform EDT on the image obtained from Step 7 (Fig. 3(h)) and compute the effective pore diameters and distribution, More details about this step are described in the following section.
3.2.1. Computing geometric features of pores From the image in Fig. 3f, the porosity of the membrane surface is calculated as the ratio of number of white pixels (i.e., pore regions) to the total image pixels nw r¼ , (1) LW where nw is the number of white pixels while L and W are the length and width of the image in pixels, respectively. From the image in Fig. 3(g), a set of parameters will be measured for each pore blob. Area (Ap) of a pore blob is computed by Ap ¼ m,
(2)
where m is the number of pixels contained in the pore blob. Perimeter (lp) of the pore is computed by n qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ðri ri1 Þ2 þ ðci ci1 Þ2 , (3) lp ¼ i¼1
3.2. Image analysis From the images pre-processed in Section 3.1, a number of parameters and their distributions can be measured using image analysis techniques.
where ri and ci are the row and column of a pixel i on the contour of the pore blob, 2pipn, and n is the number of pixels on the contour of the pore blob. Equivalent diameter (DEq Area ) based on the same area is defined as the diameter of a circle that has the same area as
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
430
Fig. 3. Images obtained in pre-processing: (a) original gray-level image of a membrane sample, calibration bars indicate a length of 10.0 mm; (b) cropped image; (c) contrast enhanced image; (d) filtered image; (e) thresholded image; (f) image after complementing and removing isolated noises from (e); (g) image after morphological operations and (h) Euclidean distance transformed image of (g).
the pore blob: rffiffiffiffiffiffiffiffi 4Ap Eq DArea ¼ . p
(4)
Shape factor (fs) is calculated by fs ¼
l 2p . 4pAp
Solidity (S) is computed as the area of pore blob (Ap) divided by the area of the convex hull of the pore blob (Aconvex), S¼
(5)
Ap . Aconvex
(6)
The convex hull of the pore blob is the smallest convex set that contains the pore blob and is represented as a list of
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
facets, which has a set of vertices, a set of neighboring facets and a half-space. A half-space is defined by a unit normal and an offset [10,11]. Extent (E) is computed as the area of the pore blob (Ap) divided by the area of the bounding box (Ab), the latter is the smallest rectangle containing the pore blob [10,11]: E¼
Ap . Ab
(7)
431
section. The value on the center pixel (i.e., DT(xc, yc)) in the distance transformed image indicates the distance between the center and its closest non-pore pixel. Since the radius of the virtual circle Rv represents the distance between the center pixel and its closet edge point on the pore blob, Rv is calculated as following due to pixel width concern: Rv ¼ DTðxc ; yc Þ 0:5.
(11)
Therefore, the effective pore diameter for this pore blob 3.2.2. Euclidean distance transform (EDT) and effective pore diameter (Deff) In this study, a new parameter, effective pore diameter for each pore, is also extracted. It is defined as the diameter of the largest particle which can pass through the pore in the membrane. In terms of image morphology, the effective pore diameter of a pore can be considered as the diameter of a largest virtual circle that can be encompassed by this pore region. We call it virtual circle because it does not exist in the original image and is very helpful in description of effective pore diameter [12]. In this way, the effective diameter of a pore is equal to two times of the distance between the center of the largest virtual circle and its nearest edge point in this pore region, i.e., the diameter of the largest virtual circle. With the help of distance transform (DT ), a digital binary image that consists of object (i.e., pore in this case) and non-object (i.e., non-pore) pixels is converted into another image in which each object pixel has a value corresponding to the minimum distance from the object pixel to its nearest non-object pixel by a distance function. The interior of a closed boundary is considered as object pixels and exterior as non-object pixels [13,14]. Because of its rotation invariance property, the Euclidean distance function is used. The distance d(p, q) between a pixel p(x, y) in a pore region A and a pixel q(u, v) in the non-pore region Ac is defined by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðp; qÞ ¼ ðx uÞ2 þ ðy vÞ2 ; pðx; yÞ 2 A and qðu; vÞ 2 Ac , (8) where (x, y) and (u, v) are coordinates of pixels p and q, respectively, and Ac is the complement of A. The distance transform assigns a value DT(x, y) to the pixel p(x, y): DTðx; yÞ ¼ minðu;vÞ fdðp; qÞg; qðu; vÞ 2 Ac ,
pðx; yÞ 2 A
and ð9Þ
where DT(x, y) is the minimum distance from the pixel p(x, y) to non-pore pixels in Ac. By repeating the above procedure to all pixels in the pore region, a distance transformed matrix is formed. From this matrix, a local maximum value can be found by searching throughout the pore region A: DTðxc ; yc Þ ¼ maxfDTðx; yÞg;
pðx; yÞ 2 A.
(10)
The coordinates (xc, yc) of this maximum represent the center of the virtual circle in terms of definition in previous
Deff ¼ 2Rv .
(12)
This means that the particles with a diameter equal to or less than Deff can pass through this pore. An example of pore blob extracted from Fig. 3(g) is displayed in Fig. 4a, where the pore region shown in gray color for better viewing, has a pixel value of 1 while the pixels in non-pore region (i.e., the membrane walls) have a value of 0. The distance transformed image matrix of the pore in Fig. 4a is displayed in Fig. 4b. The center of the largest virtual circle and its radius are marked in a black box and an arrow in Fig. 4b, respectively. 3.2.3. Calibrations Normally, calibration bars or scale markers are present and clearly visible on all SEM photomicrographs. In the sample image shown in Fig. 3a, calibration bars, which are the little lines, are located in the lower right corner of the image. The distance between the first bar and the last one, which represents 10.0 mm, is measured as 252 pixels. By referencing this calibration rate, the program automatically calibrated the measurements, which were obtained in the previous section, into microns. 4. Results and discussion From the experiments described in Section 3.1, it can be seen that the image pre-processing can be automatically performed and is robust to extract the pore regions without human interaction (Fig. 3b–h). From this membrane image, 437 pore blobs are found. In Section 3.2.1, a set of parameters, including effective diameter, area, perimeter, equivalent diameter based on the same area as each pore blob, pore shape factor, solidity, extent and porosity, are computed to characterize the pore morphologies of the membrane. Their statistical values are listed in Table 1 and distributions are shown in Fig. 5. These parameters, being used together, will give more information about the pore morphologies than when used alone. Some parameters can hardly be extracted by using other methods, such as effective diameter, shape factor, solidity and extent, while some others are very costly to obtain. Especially, we computed the effective diameter of pores (Deff) and its distribution as a new parameter. By using EDT, this algorithm performs a comprehensive search for the largest virtual circle and its diameter throughout each
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
432
Fig. 4. An example of distance transform: (a) an example of pore blob in the binary image of the membrane shown in Fig. 3g; (b) the distance transformed image of (a): the pixel with the highest value marked in the dark black box is the center of the virtual circle, the radius of the virtual circle (shown as a dashed circle) is shown by a black arrow, which represents the distance between the center to its closest edge point.
pore region. Consequently, the effective pore diameters and their distribution in the porous membrane are computed by using Eqs. (8)–(12). The effective pore diameter obtained has a very clear mathematical definition and it simply represents the diameter of the largest particles which can pass through the pore. For the example shown in Fig. 4a, there are 29 pixels belonging to this pore, then the equivalent diameter based on the same area (DEq Area ) is equal to 6.07 pixels by using Eqs. (2) and (4). Comparatively, from the corresponding distance transformed image of Fig. 4a, the pixel with the highest value of 3.00 is found and marked in the dark black box in Fig. 4b. While the pixel is the location of the center of the largest virtual circle (shown as a dashed circle in Fig. 4b) for this pore region, the radius of the circle is 2.5 pixels by using Eq. (11). Therefore, the effective diameter of this pore (Deff) is equal to 5.00 pixels, which means that the particles with a diameter equal to or less than 5.00 pixels can pass through the pore (i.e., can be encompassed by the pore region). However, the particles with the equivalent diameter DEq Area (i.e., 6.07 pixels) cannot pass through the pore (i.e., cannot be encompassed by the pore region). Deff is less than DEq Area . This trend is increased to a great extent when the shape of pore is far away from a circle. When pores are perfect circles, Deff is equal to DEq Area . Our experiment results have shown the trend in Table 1, Fig. 5a and d. From the results obtained above, the effective pore diameter will provide more objective and accurate information about the particle permeability. The membrane performance in both filtration and separation and, specially, particle permeation performance can be better understood and predicted by measuring this parameter and its distribution. Furthermore, the EDT used in this study has rotation invariance property as shown in Eq. (9). With this quality, membrane samples can be imaged at any rotation angle, which makes sampling more convenient. The time spent on both image pre-processing and measurement of all those parameters and their distributions for the membrane is 15.58 s. This indicates the image analysis method is very efficient in characterizing membrane morphologies. The calibration can be done by comparing the measurements in the unit of pixels with the length (in pixels) of the calibration bars. Furthermore, unlike other traditional methods, all of these parameters in Table 1 can be easily measured with this image analysis approach.
Table 1 The parameters computed to characterize membrane pore morphologies
Mean Minimum Maximum Standard deviation
r
Deff (mm)
Ap (mm2)
lp (mm)
DEq Area (mm)
fs
S
E
0.31
0.32 0.14 1.35 0.19
0.26 0.02 2.95 0.39
2.26 0.48 15.36 1.99
0.48 0.16 1.94 0.31
1.89 0.88 8.48 0.91
0.93 0.57 1.00 0.07
0.60 0.34 0.81 0.08
ARTICLE IN PRESS F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
433
Fig. 5. The distributions of the parameters of pore morphologies: (a) effective pore diameter, (b) area, (c) perimeter, (d) equivalent diameter based on the same area as pore region, (e) shape factor, (f) solidity, and (g) extent.
5. Conclusions In this work, we employed advanced image analysis techniques to characterize pore morphologies of porous filtration membrane, focusing on measuring the effective pore diameter and its distribution of PVDF porous membrane together with other parameters. The image analysis approach developed in this work allows data-intensive and comprehensive analysis of membrane pore morphologies by computing many parameters including effective pore diameters. It is the effective pore diameters that are actually responsible for the
membrane performance in both filtration and separation, specially, particle permeation performance. It was found that the proposed method is very efficient, fast and accurate and the calibration is simple and straightforward. Acknowledgments Financial support provided for F.H. She to visit Chung Yuan University and work on this project by Australian Academy of Science and National Science Council, ROC, under Scientific Visits to Taiwan Scheme is gratefully acknowledged.
ARTICLE IN PRESS 434
F.H. She et al. / Robotics and Computer-Integrated Manufacturing 24 (2008) 427–434
References [1] Nakao S. Determination of pore size and pore size distribution. 3: filtration membranes. J Membr Sci 1994;96(1–2):131–65. [2] Gijsbertsen-Abrahamse AJ, Van der Padt A, Boom RM. Influence of membrane morphology on pore activation in membrane emulsification. J Membr Sci 2003;217(1–2):141–50. [3] Zeman L, Denault L. Characterization of microfiltration membranes by image analysis of electron micrographs. Part I. Method development. J Membr Sci 1992;71(3):221–31. [4] Mietton-Peuchot M, Condat C, Courtois T. Use of gas–liquid porometry measurements for selection of microfiltration membranes. J Membr Sci 1997;133(1):73–82. [5] Cuperus FP, Bargeman D, Smolders CA. Permporometry: the determination of the size distribution of active pores in UF membranes. J Membr Sci 1992;71(1–2):57–67. [6] Mey-Marom A, Katz MG. Measurement of active pore size distribution of microporous membranes—a new approach. J Membr Sci 1986;27(2):119–30.
[7] Hemmler R, Bose G, Wagner R, Peters R. Nanopore unitary permeability measured by electrochemical and optical single transporter recording. Biophys J 2005;88(6):4000–7. [8] Mulherkar P, Van Reis R. Flex test: a fluorescent dextran test for UF membrane characterization. J Membr Sci 2004;236(1):171–82. [9] Hilal N, Al-Zoubi H, Darwish NA, Mohammad AW. Characterization of nanofiltration membranes using atomic force microscopy. Desalination 2005;177(1–3):187–99. [10] MathWorks. MatLab: the language of technical computing. Natick: The MathWorks Inc.; 2004. [11] Russ JC. The image processing handbook. 3rd ed., vol. 1. Raleigh: CRC Press LLC; 1999. p. 771. [12] Alhichri HS, Kamel M. Virtual circles: a new set of features for fast image registration. Pattern Recognit Lett 2003;24(9–10):1181–90. [13] Vincent L. Exact Euclidean distance function by chain propagations. IEEE Comp Vis Pattern Recog 1991. [14] Shih FY, Wu Y-T. Fast Euclidean distance transformation in two scans using a 3 3 neighborhood. Comput Vis Image Und 2004;93(2):195–205.