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Bubble size estimation for flotation processes
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Minerals Engineering 21 (2008) 539–548 This article is also available online at: www.elsevier.com/locate/mineng
Bubble size estimation for flotation processes Bao Lin a,*, Bodil Recke b, Jørgen K.H. Knudsen b, Sten Bay Jørgensen a a
Department of Chemical Engineering, Technical University of Denmark, Lyngby 2800, Denmark b FLSmidth Automation, Valby 2500, Denmark Received 29 March 2007; accepted 7 November 2007 Available online 2 January 2008
Abstract This paper presents a real-time image analysis system that was installed at a phosphorus oxide flotation process. The focus of the image analysis system is to effectively estimate bubble size. Flotation is one of the most challenging processes for modelling and control in mineral processing industry due to the inherently chaotic nature of the underlying microscopic phenomena and the lack of sufficiently accurate process measurements. Digital image processing is a promising technology for obtaining process related information that can potentially be used to improve the control of flotation processes. Traditional bubble size estimation techniques based on morphological operators and the concept of texture spectrum perform unsatisfactorily on froth images from the phosphorus oxide flotation process. A modified texture spectrum approach and a method based on binary images are proposed and implemented. The reliability of the proposed bubble size estimation approach is demonstrated on phosphorus oxide flotation processes. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Flotation bubbles; Sizing; On-line analysis
1. Introduction Froth flotation is a selective separation process that is widely used in mining industry to extract valuable minerals. Modelling and effective control of flotation processes are challenging tasks, due to the complicated dynamics and chaotic nature of the underlying microscopic phenomena. The lack of sufficiently accurate and reliable process measurements poses additional difficulties. Experiences have shown that process conditions are highly correlated to the appearance of the flotation froth (Moolman et al., 1996a; Aldrich et al., 1997). Advances in digital image processing techniques enable the quantification of froth properties, which is a prerequisite step for automatic control of flotation processes. There are several conventional process measurements on flotation processes, including the flow-rate of feed and *
Corresponding author. Present address: FLSmidth Automation, Bethlehem, PA 18017, United States. Tel.: +1 610 2646529. E-mail address: bao.lin@flsmidth.com (B. Lin). 0892-6875/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2007.11.004
chemical additives, pH, fluid level in the flotation machine, etc. But, ‘‘measurements” related to the type and movement of the flotation froth are based on human visual inspection in most plants. In fact, many flotation processes are manually controlled by operators looking at the appearance of the froth (Moolman et al., 1996b). The performance thus depends on the operator’s experience and is limited by the absence of physical, quantitative methods for measurement and characterization of the froth. Vision-based methods have been developed recently for observation and analysis of froth images. Applications include the classification of froth and the extraction of physical features, such as color, average bubble size and size distribution. Statistical techniques (Nguyen and Thornton, 1995), neural network (Moolman et al., 1995) and fuzzy logic (Chuk et al., 2005) are also integrated to enhance the performance of image analysis systems. Duchesne et al. (2003) report the investigation of flotation froth images analysis using the multivariate image analysis (MIA) concept. The MIA approach is based on multivariate statistical analysis approaches, such as Principal
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components analysis (PCA) and partial least squares (PLS) regression. The most relevant information of the highly correlated data is efficiently extracted through the projection of the original image data onto a reduced dimensional space. The applicability of the MIA approach to flotation systems is described with several industrial case studies. Bartolacci et al. (2006) present applications of image analysis systems to control flotation processes. Several image analysis approaches are described, including MIA, grey-level cooccurrence matrix (GLCM) and wavelet transform analysis (WTA) methods. A feedback control strategy based on a froth structure indicator is described and implemented on an industrial zinc flotation circuit. A hybrid control scheme using a froth/concentrate grade is also proposed to stabilize the froth structure. Several image analysis systems have been developed during recent years, including FrothMasterTM (Outokumpu), VisioFrothTM (Metso), PlantVisionTM (KnowledgeScape), WipFrothTM (Wipware). COREM (Bartolacci et al., 2006) develops the iFrothTM system that predicts the froth grade concentrate. This paper reports an image analysis system for flotation processes that was developed using the image analysis toolbox of MATLAB. This paper investigates the issue of bubble size estimation using images collected from a chamber and a column of a phosphorus oxide flotation process. Initial results demonstrate that the reported approaches are infeasible for the specific process. A modified texture spectrum approach and a method based on binary images are proposed and described in detail. Case studies reveal the reliability of these methodologies. The next section describes the mechanism of the flotation process, as well as the introduction of two types of flotation equipment: the chamber and the column. Section 3 reviews reported approaches of characterizing the flotation froth. The infeasibility of these approaches is illustrated with case studies. Based on preliminary results, two novel approaches are described in Section 4. Section 5 presents the hardware and software of image analysis system that was installed on-site, followed by the conclusions and a list of future research activities. 2. Flotation process Flotation process is commonly used in mineral industry for concentrating valuable minerals from raw ore, such as gold, silver, zinc and phosphor. Ground ore powder, mixed with water, frothing reagents and collecting reagents, is fed into the flotation machine, where air is continuously injected into the pulp through a sparger at the bottom of the container, forming a large number of air bubbles (see Fig. 1). Chemical reagents are added to modify the surface hydrophobicity of the solid particles. The valuable mineral particles are made to be hydrophobic in order to attach easily to bubbles. Air bubbles float to the top and form the froth layer on the surface; while gangue materials are hydrophilic and settle to the bottom. Thus, the concen-
Fig. 1. Scheme of a flotation process.
trated product is readily collected from the top. The bottom flow is recycled for further treatment. There are two main types of flotation machines: the chamber and the column. Flotation chambers are shallow tanks (usually 3–4 m in depth), which concentrate minerals that are easily separated. The columns are long vertical vessels (might be more than 10 m high) that are now used worldwide. The objective of flotation process control is to achieve the target mineral grade recovered from the feed of varying compositions. The separation efficiency of flotation processes depends significantly on the chemical and hydrodynamic conditions. In many plants, chemical reagents that are used to increase the efficiency of flotation are controlled by human operators, who determine adjustments to the addition rates based on empirical analysis of visual appearance of the froth. Consequently, the operation of flotation processes depends essentially on the experience of operators. Therefore, a reliable and consistent approach to quantify the froth characteristics is essential for automatic monitoring and control of flotation processes. 3. Reported bubble size estimation approaches The fast development of digital image processing renders the possibility to automatically acquire and interpret images of the froth in real-time, resembling the more or less heuristic features used by the operators. It is widely accepted that mineral concentrations and process status are closely related to the color and morphological features of the froth (Moolman et al., 1996b). Color indicates the type and concentration of mineral carried by the froth. The operational status of the flotation process can be characterized from the features of froth bubbles, especially the size, which determines the froth load, collision and attachment efficiency. The investigations of the relationship between bubble size and the separation efficiency have received considerable attention. A number of methods were reported for determining the size of bubbles, including
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segmentation (Sadr-kazemi and Cilliers, 1997; Bonifazi et al., 2001), texture spectrum (Nguyen and Thornton, 1995) and wavelet (Liu et al., 2005) approaches. Texture spectrum, segmentation and edge detection based approaches are briefly reviewed and evaluated using images collected from an industrial flotation process. 3.1. Texture spectrum The concept of texture spectrum was proposed by He and Wang (1990), i.e., an image can be characterized by statistical features of small units, termed texture units. The feature of the texture unit is calculated from the information of a given pixel and its neighbourhoods. As shown in Fig. 2, the texture unit is a 3 3 pixels square, which is denoted by a set of nine elements: V ¼ fV 0 ; V 1 ; . . . ; V 8 g, where V0 represents the intensity value of the central pixel and V i ; i ¼ 1; 2; . . . ; 8 is the intensity value of the neighboring pixel i. The feature of the texture unit is defined by eight elements, fE1 ; E2 ; . . . ; E8 g: 8 > < 0 if V 0 < V i ð1Þ Ei ¼ 1 if V 0 ¼ V i > : 2 if V 0 > V i
E1
E2
E8
E7
E3
E4
E6
E5
Fig. 2. Texture unit with clockwise successive ordering elements.
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The texture unit is indexed by the following formula: N TU ¼
8 X
Ei 3i1
ð2Þ
i¼1
where NTU represents the index of the texture unit. Therefore, the index of a texture unit ranges between 0 and 6560 (38 1). The texture unit describes the local features of a given pixel, specifically the relative grey level relationships between the central pixel and its neighbours. The statistics of all texture units characterizes the whole image. Therefore, texture spectrum is defined as the histogram of all texture units: the distribution of all the texture units. Nguyen and Thornton (1995) reported the application of texture spectrum to the classification of flotation froth. Due to the reflection of light, pixels in the center of froth bubbles normally have larger intensity values than surrounding pixels. According to Eq. (1), the index of a texture unit is probably large. Therefore, an intuitive value for bubble size, BS, can be calculated as vffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 6560 uX BS ¼ t ð3Þ hi i¼3281
where hi is the number of texture units whose value equal to i. Eq. (3) is applied to the following two pictures in Fig. 3, where white circles are used to denote the bubbles. BS equals to 128.91 and 100.77, respectively. The texture spectrum approach is applied to several images collected from the flotation chamber of a phosphorus oxide process (see Fig. 4). As shown in Fig. 5, the texture spectrum approach is able to detect that the averaged bubble size of the 2nd picture is the smallest among the first 3 images. However, it fails to obtain the correct size estimation for the bubbles in the 4th picture. Therefore, improvements are necessary to obtain reliable bubble size estimation.
Fig. 3. Pictures used for bubble size estimation with the texture spectrum approach.
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Fig. 4. Images collected from a flotation chamber.
Fig. 5. Bubble size estimated with the original texture spectrum approach.
3.2. Watershed segmentation Another commonly used approach to determine bubble size is based on the concept of segmentation. Image segmentation is a process that partitions an image into constituent regions or objects. For this study, individual bubbles have to be segmented from the froth image. Then, parameter and the statistical distribution of bubbles can be calculated. Among reported image segmentation methodologies, watershed segmentation is a particularly attractive method (Sadr-kazemi and Cilliers, 1997; Bonifazi et al., 2001). The main idea of watershed segmentation is based on the concept of simulating water flows in a topographic representation of image intensity (Vincent and Soille, 1991). As shown in Fig. 6, the intensity of an image is represented by a topographic landscape, where local minima are the bottom of valleys. Assume water fills from the bottom up, watershed lines can be identified when two lakes meet. Consequently, local maxima will progressively disappear as
Fig. 6. Schematic watershed segmentation in one dimension.
the level of lakes increases. The flooding process continues until the complete landscape is flooded. Therefore, watershed transformation maps the original image to a partitioned one, where all points in the same valley are uniquely labeled. Watershed transformation tends to over-segment the image since a basin is created for every local minimum. A similarity-based approach replaces the original local optima with a marker, which is defined as a region surrounded by pixels of higher altitude. Other improvements such as the hierarchical watershed scheme, combining it with a neural network, as well as the smoothing and thresholding background values before segmentation, are also reported to address the issue of over-segmentation. These approaches work well in handling noisy images (Huang and Chen, 2004). However, over-segmentation can still be a problem when applying the watershed transformation to highly detailed images, especially the images collected from phosphorus oxide flotation processes as shown in
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Fig. 7. Froth images of reported applications.
Fig. 4. In addition, these complicated algorithms have not been reported for on-line real-time applications. The image analysis system is developed for flotation processes that are used to purify phosphorus oxide. Fig. 7 compares froth images from the flotation chamber and column with those of previously reported applications, such as Cu–Pb flotation (Bonifazi et al., 2001) and the flotation processes to concentrate zinc (Hyotyniemi and Ylinen, 2000; Liu et al., 2005). Images of this study are significantly different from those reported in literature, where bubbles are clustered on top of froth surface. In addition, the large number of small-size bubbles poses a challenging segmentation task. The MATLAB function ‘‘watershed”, an implementation of the immersion simulations based algorithm (Vin-
cent and Soille, 1991), is applied to the 1st image in Fig. 4. Poor performance is obtained even with carefully selected parameters (see Fig. 8). Preprocessing of images, such as contrast enhancement, is normally utilized to improve the performance of watershed segmentation. However, the preprocessing is too computationally intensive to be integrated with realtime control system. 3.3. Edge detection–based approach Cipriano et al. (1998) reported a visual system (ACEFLOT), which estimated bubble size based on the edge detection technique. The center and edge of each bubble were detected through the high/low intensity gradient.
Fig. 8. Watershed segmentation of a froth image.
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Morphological operators, such as opening and closing, were also utilized to combine with the edge detection approach in order to identify the bubbles from the froth image background. However, the edge-detection based approach still did not perform well for this application due to the following reasons. First, the bubbles are quite small under nominal operating conditions. Second, froth bubbles of phosphorus oxide flotation processes do not usually cluster together, especially in the flotation chamber. The areas among bubbles are difficult to be handled by the edge detection approach. Third, images collected from the flotation machines do not have sufficiently high contrast between bubbles and the background, which adds extra difficulty in applying edge detection based approach. 4. New approaches for bubble size estimation Applications of reported bubble size estimation approaches, including the texture spectrum, the watershed segmentation and edge detection based methodologies, to the froth images collected at phosphorus oxide flotation processes revealed unsatisfactory performance. Two novel approaches are proposed in sequel: an improved texture spectrum approach and a method based on binary images. 4.1. Improved texture spectrum approach As shown in Fig. 5, the original texture spectrum approach is not able to provide reliable estimation of bubble size. The observation is attributed to the following two reasons. Firstly, Eq. (1) does not take into the account the relationship between the intensity of the central pixel and the average value of the image. Secondly, the number of bubbles should also be taken into account. Given a texture unit consists of 9 pixels with the same intensity, the value of the texture unit is 3280 according to Eq. (2), no matter this unit is at the center of the bubble (with high intensity) or in the background (with low intensity). Therefore, Eq. (2) is modified as 8 8 P > > > Ei 3i1 if I C 6 I < i¼1 N TU ¼ ð4Þ 8 > P > i1 > 6581 þ Ei 3 if I C > I :
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 6560 uX Na hi ð1 B Þ BS ¼ t NN i¼3281
ð5Þ
where a is a polynomial factor and NN is a scaling factor. In this study, a = 0.25 and NN = 100 are obtained through empirical analysis of images collected from the flotation process. It should be noted that the parameters depend on the setting of the camera and the type of flotation processes. The summation of Eq. (5) calculates the index based on 6560 bins. Thus, the bins of 3281–6560 correspond to the actual index values of 6561–13161. Fig. 9 shows the estimated bubble size of froth images (in Fig. 4) with the modified texture spectrum approach. The second image has the smallest bubbles, while images (1), (3) and (4) have similar average bubble size. Compare with the results in Fig. 5, the modified texture spectrum approach correctly identifies the change of bubble size when applied to froth images. Although the modified texture spectrum approach improves the calculation of bubble size, it is not straightforward to obtain the distribution of bubble size. 4.2. Methods based on binary images Binary (black and white) is the simplest form to represent an image, which has been widely used in medical applications due to the advantages of easiness to obtain and low storage requirement. A binary image can be straightforwardly obtained by thresholding the intensity component of a gray-scale image, such that pixels above the threshold are white and those below are black (see Fig. 10). In this study, the threshold is experimentally determined as 0.8 by analyzing an extensive collection of images over a period of several months. The statistics of the bubble can then be obtained from the binary image, including the number of bubbles, the average size as well as the distribution of bubble size. Bubble size of froth images (in Fig. 4) is estimated with the approach based on binary image. As shown in Fig. 11, image (1) has the largest number of bubbles while the second has the smallest number. Comparing to image (3), image (4) has smaller number of small bubbles (of size 1) but larger number of bubbles of size 3.
i¼1
where IC is the intensity of the center pixel and I is the average intensity of the image. The new range for the value of texture unit is between 0 and 13161. Moreover, the texture units on top of bubbles have larger value than those from the background. The size of bubbles can thus be estimated more reliably. The original formula for bubble size estimation, Eq. (3), tends to denote ‘‘big” bubbles when the number of bubble is large. Therefore, the number of bubbles, NB, should be taken into account for bubble size estimation with the texture spectrum approach. The modified equation is: Fig. 9. Bubble size estimation with improved texture spectrum approach.
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Fig. 10. Color and binary images of froth bubbles.
Fig. 11. Number of bubbles estimated with binary image-based approach.
Therefore, average bubble size of image (4) is larger than that of image (3). The x-axis of Fig. 11 denotes the number of pixels of a bubble. Given that most bubbles are indicated with one pixel and the normal diameter of bubbles is about 2 cm, the corresponding diameter of bubbles during normal operations is between 2 and 4 cm. The averaged bubble size is shown in Fig. 12, which is consistent with the modified texture spectrum approach (see Fig. 9). In summary, the binary image based approach estimates the features of froth bubbles reasonably well. Fig. 13 summarizes results from a flotation column at varied operational conditions. The horizontal and vertical
Fig. 12. Average bubble size estimation with binary image.
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axes of the rightmost graphs represent the number of pixels of each bubble and the total number of bubbles detected of
such size on the froth image. The diameter of bubbles indicated with one pixel is about 1 cm.
Fig. 13. Bubble size estimation of flotation column using the approach of binary image.
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In Case 1, there are hardly visible bubbles except two small ones around the left bottom corner. Case 2 and 3 show a transition period that the number of bubbles starts increasing. In Case 2, bubbles are not visible in the left upper corner, but in the right bottom area. Case 3 reveals that relatively large bubbles appear in the right bottom of the image while small ones resident mostly on the left upper area. Both the number and the size of froth bubbles increase from the Case 3 to Case 4, as the process is approaching the nominal condition. Case 5 shows a scenario that the bubbles are ‘‘watery” due to little amount of minerals in the column. The binary image-based approach detects the significant increase of the number and the size of bubbles. It should be noted that the bubbles are ‘‘thin” (as marked by the circles). Although larger bubbles are detected, the detected size is smaller than the actual bubble. However, this observation does not pose a significant influence on the implemented system, since Case 5 only represents an infrequent and abnormal operating mode.
5. Image analysis system configuration The structure of the real-time image analysis system is shown in Fig. 14. The system resides on the same computer as the process control system, ECS/ProcessExpertÒ by FLSmidth Automation that enables data exchange with MATLAB. An Axis 2120 network camera is installed approximately 1 m above the surface of the flotation froth. The camera is triggered by a Programmable Logic Controller (PLC) signal. Considering the time constant of the flotation process and the network load, the camera is triggered once every 15 min. Then, a high pulse of 3 s is initialized. During this period, around 12 images are collected and uploaded to PC through a ftp server. PXP (ProcessExpert) units (imple-
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mented in MATLAB) extract image features and send them to the data log system. The resolution and quality of images used in this study are determined by the following factors: I. Velocity measurement is also part of the system, which requires the processing of a sequence of images that are obtained within a short time interval. II. The network band of the plant is limited. In-office test shows that 13 images can be uploaded each second for the designed system. However, only four images per second can be uploaded in the plant. III. The camera is installed approximately 1 m above the surface in order to cover sufficiently large area for velocity calculation. IV. Plant personnel clean the working area using pressurized water. Water might be splashed on the lenses cover that causes problems, i.e., blurred images, if the camera is not installed sufficiently high (see Fig. 15). V. Images of high resolution are definitely useful to obtain a better estimation of bubble size. However, the image analysis system resides on the same computer performing the process control activities. The CPU load has to be limited for the specific application, in order not to completely occupy the CPU and cause data communication problems with lower level PLC. Taking all factors into consideration, the current resolution of images is 352 by 240. The described image analysis systems have been installed on a flotation chamber and a column at a client company in Brazil. Preliminary results over the past several months revealed that reasonable estimation of the bubble size and distribution were obtained without overloading the process control computer.
PC FTP Server reading & analyzing images
uploading images
Camera
ProcessExpert®
external trigger
ECS
PLC
Process
Fig. 14. Real-time image analysis system for flotation processes.
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Fig. 15. Blurred images due to the splashed water on the cover of the camera.
6. Conclusions An industrial application of image analysis systems for flotation processes is reported in this paper, focusing on the estimation of bubble size that is believed to be the most important indication of the operating conditions. The system is applied to an industrial flotation process for purifying phosphorus oxide. Since the visual appearance of the froth is significantly different from those of previously reported flotation processes, the application of traditional edge-detection, watershed segmentation and texture spectrum approaches reveals unsatisfactory performance. A modified texture spectrum method and the novel approach based on binary image are presented. Preliminary results show consistent performance using froth images collected from phosphorus oxide flotation processes. The result can be improved by using high resolution cameras; however, the computational intensity needs to be taken into consideration for real-time implementation. Currently, a constant threshold is used in obtaining the binary images. Although high intensity lamps are installed on site, the light condition still varies slightly. Therefore, an adaptive threshold is an interesting task to be investigated in the future. The final objective of the project is to derive data-driven models from process measurements and image features such that effective flotation process control can be achieved. References Aldrich, C., Moolman, D.W., Gouws, F.S., Schmitz, G.P.J., 1997. Machine learning strategies for control of flotation plants. Control Engineering Practice 5 (2), 263–269. Bartolacci, G., Pelletier, P., Tessier, J., Duchesne, C., Bosse´, P.-A., Fournier, J., 2006. Application of numerical image analysis to process
diagnosis and physical parameter measurement in mineral processes – Part I: Flotation control based on froth textural characteristics. Minerals Engineering 19 (6–8), 734–747. Bonifazi, G., Serranti, S., Volpe, F., Zuco, R., 2001. Characterisation of flotation froth colour and structure by machine vision. Computers & Geosciences 27 (9), 1111–1117. Chuk, O.D., Ciribeni, V., Gutierrez, L.V., 2005. Froth collapse in column flotation: a prevention method using froth density estimation and fuzzy expert systems. Minerals Engineering 18 (5), 495–504. Cipriano, A., Guarini, M., Vidal, R., Soto, A., Sepulveda, C., Mery, D., Briseno, H., 1998. A real time visual sensor for supervision of flotation cells. Minerals Engineering 11 (6), 489–499. Duchesne, C., Bouajila, A., Bartolacci, G., Pelletier, P., Breau, Y., Fournier, J., Girard, D., 2003. Application of multivariate image analysis (MIA) to predict concentrate grade in froth flotation processes. In: Proceedings of the 35th Annual Meeting of the Canadian Mineral Processors, Ottawa, Ontario. He, D.C., Wang, L., 1990. Texture feature extraction from texture spectrum. IEEE Transactions on Geosciences and Remote Sensing 28 (4), 509–512. Huang, Y.-L., Chen, D.-R., 2004. Watershed segmentation for breast tumor in 2-D sonography. Ultrasound in Medicine and Biology 30 (5), 625–632. Hyotyniemi, H., Ylinen, R., 2000. Modeling of visual flotation froth data. Control Engineering Practice 8 (3), 313–318. KnowledgeScape Plantvision. hhttp://www.kscape.com/downloads/ PlantVision%20for%20Flotation.pdfi. Liu, J.J., MacGREGOR, J.F., Duchesne, C., Bartolacci, G., 2005. Flotation froth monitoring using multiresolutional multivariate image analysis. Minerals Engineering 18, 65–76. Metso Visiofroth, hhttp://www.metsominerals.com/inetMinerals/mm_home.nsf/FR?ReadForm&ATL/inetMinerals/mm_proc.nsf/WebWID/ WTB-041208-2256F-8CDAAi. Moolman, D.W., Aldrich, C., Van Deventer, J.S.J., Bradshaw, D.J., 1995. The interpretation of flotation froth surfaces by using digital image analysis and neural networks. Chemical Engineering Science 50 (22), 3501–3523. Moolman, D.W., Aldrich, C., Schmitz, G.P.J., van Deventer, J.S.J., 1996a. The interrelationship between surface froth characteristics and industrial flotation performance. Minerals Engineering 9 (8), 837–854. Moolman, D.W., Eksteen, J.J., Aldrich, C., van Deventer, J.S.J., 1996b. The significance of flotation froth appearance for machine vision control. International Journal of Mineral Processing 48 (3–4), 135– 158. Nguyen, K.K., Thornton, A.J., 1995. The application of texture-based image analysis techniques in froth flotation. In: Conference Proceedings DICTA-95. Digital Image Computing: Techniques and Applications, Australian Pattern Recognition Society. Outokumpu FrothmasterTM 2, hhttp://www.outotec.com/pages/ Page____9561.aspxi. Sadr-kazemi, N., Cilliers, J., 1997. An image processing algorithm for measurement of flotation froth bubble size and shape distributions. Minerals Engineering 10 (10), 1075–1083. Vincent, L., Soille, P., 1991. Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence 13 (6), 583–598. Wipware Wipfroth., hhttp://www.wipware.com/wipfroth.phpi.
Minerals Engineering 21 (2008) 539–548 This article is also available online at: www.elsevier.com/locate/mineng
Bubble size estimation for flotation processes Bao Lin a,*, Bodil Recke b, Jørgen K.H. Knudsen b, Sten Bay Jørgensen a a
Department of Chemical Engineering, Technical University of Denmark, Lyngby 2800, Denmark b FLSmidth Automation, Valby 2500, Denmark Received 29 March 2007; accepted 7 November 2007 Available online 2 January 2008
Abstract This paper presents a real-time image analysis system that was installed at a phosphorus oxide flotation process. The focus of the image analysis system is to effectively estimate bubble size. Flotation is one of the most challenging processes for modelling and control in mineral processing industry due to the inherently chaotic nature of the underlying microscopic phenomena and the lack of sufficiently accurate process measurements. Digital image processing is a promising technology for obtaining process related information that can potentially be used to improve the control of flotation processes. Traditional bubble size estimation techniques based on morphological operators and the concept of texture spectrum perform unsatisfactorily on froth images from the phosphorus oxide flotation process. A modified texture spectrum approach and a method based on binary images are proposed and implemented. The reliability of the proposed bubble size estimation approach is demonstrated on phosphorus oxide flotation processes. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Flotation bubbles; Sizing; On-line analysis
1. Introduction Froth flotation is a selective separation process that is widely used in mining industry to extract valuable minerals. Modelling and effective control of flotation processes are challenging tasks, due to the complicated dynamics and chaotic nature of the underlying microscopic phenomena. The lack of sufficiently accurate and reliable process measurements poses additional difficulties. Experiences have shown that process conditions are highly correlated to the appearance of the flotation froth (Moolman et al., 1996a; Aldrich et al., 1997). Advances in digital image processing techniques enable the quantification of froth properties, which is a prerequisite step for automatic control of flotation processes. There are several conventional process measurements on flotation processes, including the flow-rate of feed and *
Corresponding author. Present address: FLSmidth Automation, Bethlehem, PA 18017, United States. Tel.: +1 610 2646529. E-mail address: bao.lin@flsmidth.com (B. Lin). 0892-6875/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2007.11.004
chemical additives, pH, fluid level in the flotation machine, etc. But, ‘‘measurements” related to the type and movement of the flotation froth are based on human visual inspection in most plants. In fact, many flotation processes are manually controlled by operators looking at the appearance of the froth (Moolman et al., 1996b). The performance thus depends on the operator’s experience and is limited by the absence of physical, quantitative methods for measurement and characterization of the froth. Vision-based methods have been developed recently for observation and analysis of froth images. Applications include the classification of froth and the extraction of physical features, such as color, average bubble size and size distribution. Statistical techniques (Nguyen and Thornton, 1995), neural network (Moolman et al., 1995) and fuzzy logic (Chuk et al., 2005) are also integrated to enhance the performance of image analysis systems. Duchesne et al. (2003) report the investigation of flotation froth images analysis using the multivariate image analysis (MIA) concept. The MIA approach is based on multivariate statistical analysis approaches, such as Principal
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components analysis (PCA) and partial least squares (PLS) regression. The most relevant information of the highly correlated data is efficiently extracted through the projection of the original image data onto a reduced dimensional space. The applicability of the MIA approach to flotation systems is described with several industrial case studies. Bartolacci et al. (2006) present applications of image analysis systems to control flotation processes. Several image analysis approaches are described, including MIA, grey-level cooccurrence matrix (GLCM) and wavelet transform analysis (WTA) methods. A feedback control strategy based on a froth structure indicator is described and implemented on an industrial zinc flotation circuit. A hybrid control scheme using a froth/concentrate grade is also proposed to stabilize the froth structure. Several image analysis systems have been developed during recent years, including FrothMasterTM (Outokumpu), VisioFrothTM (Metso), PlantVisionTM (KnowledgeScape), WipFrothTM (Wipware). COREM (Bartolacci et al., 2006) develops the iFrothTM system that predicts the froth grade concentrate. This paper reports an image analysis system for flotation processes that was developed using the image analysis toolbox of MATLAB. This paper investigates the issue of bubble size estimation using images collected from a chamber and a column of a phosphorus oxide flotation process. Initial results demonstrate that the reported approaches are infeasible for the specific process. A modified texture spectrum approach and a method based on binary images are proposed and described in detail. Case studies reveal the reliability of these methodologies. The next section describes the mechanism of the flotation process, as well as the introduction of two types of flotation equipment: the chamber and the column. Section 3 reviews reported approaches of characterizing the flotation froth. The infeasibility of these approaches is illustrated with case studies. Based on preliminary results, two novel approaches are described in Section 4. Section 5 presents the hardware and software of image analysis system that was installed on-site, followed by the conclusions and a list of future research activities. 2. Flotation process Flotation process is commonly used in mineral industry for concentrating valuable minerals from raw ore, such as gold, silver, zinc and phosphor. Ground ore powder, mixed with water, frothing reagents and collecting reagents, is fed into the flotation machine, where air is continuously injected into the pulp through a sparger at the bottom of the container, forming a large number of air bubbles (see Fig. 1). Chemical reagents are added to modify the surface hydrophobicity of the solid particles. The valuable mineral particles are made to be hydrophobic in order to attach easily to bubbles. Air bubbles float to the top and form the froth layer on the surface; while gangue materials are hydrophilic and settle to the bottom. Thus, the concen-
Fig. 1. Scheme of a flotation process.
trated product is readily collected from the top. The bottom flow is recycled for further treatment. There are two main types of flotation machines: the chamber and the column. Flotation chambers are shallow tanks (usually 3–4 m in depth), which concentrate minerals that are easily separated. The columns are long vertical vessels (might be more than 10 m high) that are now used worldwide. The objective of flotation process control is to achieve the target mineral grade recovered from the feed of varying compositions. The separation efficiency of flotation processes depends significantly on the chemical and hydrodynamic conditions. In many plants, chemical reagents that are used to increase the efficiency of flotation are controlled by human operators, who determine adjustments to the addition rates based on empirical analysis of visual appearance of the froth. Consequently, the operation of flotation processes depends essentially on the experience of operators. Therefore, a reliable and consistent approach to quantify the froth characteristics is essential for automatic monitoring and control of flotation processes. 3. Reported bubble size estimation approaches The fast development of digital image processing renders the possibility to automatically acquire and interpret images of the froth in real-time, resembling the more or less heuristic features used by the operators. It is widely accepted that mineral concentrations and process status are closely related to the color and morphological features of the froth (Moolman et al., 1996b). Color indicates the type and concentration of mineral carried by the froth. The operational status of the flotation process can be characterized from the features of froth bubbles, especially the size, which determines the froth load, collision and attachment efficiency. The investigations of the relationship between bubble size and the separation efficiency have received considerable attention. A number of methods were reported for determining the size of bubbles, including
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segmentation (Sadr-kazemi and Cilliers, 1997; Bonifazi et al., 2001), texture spectrum (Nguyen and Thornton, 1995) and wavelet (Liu et al., 2005) approaches. Texture spectrum, segmentation and edge detection based approaches are briefly reviewed and evaluated using images collected from an industrial flotation process. 3.1. Texture spectrum The concept of texture spectrum was proposed by He and Wang (1990), i.e., an image can be characterized by statistical features of small units, termed texture units. The feature of the texture unit is calculated from the information of a given pixel and its neighbourhoods. As shown in Fig. 2, the texture unit is a 3 3 pixels square, which is denoted by a set of nine elements: V ¼ fV 0 ; V 1 ; . . . ; V 8 g, where V0 represents the intensity value of the central pixel and V i ; i ¼ 1; 2; . . . ; 8 is the intensity value of the neighboring pixel i. The feature of the texture unit is defined by eight elements, fE1 ; E2 ; . . . ; E8 g: 8 > < 0 if V 0 < V i ð1Þ Ei ¼ 1 if V 0 ¼ V i > : 2 if V 0 > V i
E1
E2
E8
E7
E3
E4
E6
E5
Fig. 2. Texture unit with clockwise successive ordering elements.
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The texture unit is indexed by the following formula: N TU ¼
8 X
Ei 3i1
ð2Þ
i¼1
where NTU represents the index of the texture unit. Therefore, the index of a texture unit ranges between 0 and 6560 (38 1). The texture unit describes the local features of a given pixel, specifically the relative grey level relationships between the central pixel and its neighbours. The statistics of all texture units characterizes the whole image. Therefore, texture spectrum is defined as the histogram of all texture units: the distribution of all the texture units. Nguyen and Thornton (1995) reported the application of texture spectrum to the classification of flotation froth. Due to the reflection of light, pixels in the center of froth bubbles normally have larger intensity values than surrounding pixels. According to Eq. (1), the index of a texture unit is probably large. Therefore, an intuitive value for bubble size, BS, can be calculated as vffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 6560 uX BS ¼ t ð3Þ hi i¼3281
where hi is the number of texture units whose value equal to i. Eq. (3) is applied to the following two pictures in Fig. 3, where white circles are used to denote the bubbles. BS equals to 128.91 and 100.77, respectively. The texture spectrum approach is applied to several images collected from the flotation chamber of a phosphorus oxide process (see Fig. 4). As shown in Fig. 5, the texture spectrum approach is able to detect that the averaged bubble size of the 2nd picture is the smallest among the first 3 images. However, it fails to obtain the correct size estimation for the bubbles in the 4th picture. Therefore, improvements are necessary to obtain reliable bubble size estimation.
Fig. 3. Pictures used for bubble size estimation with the texture spectrum approach.
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Fig. 4. Images collected from a flotation chamber.
Fig. 5. Bubble size estimated with the original texture spectrum approach.
3.2. Watershed segmentation Another commonly used approach to determine bubble size is based on the concept of segmentation. Image segmentation is a process that partitions an image into constituent regions or objects. For this study, individual bubbles have to be segmented from the froth image. Then, parameter and the statistical distribution of bubbles can be calculated. Among reported image segmentation methodologies, watershed segmentation is a particularly attractive method (Sadr-kazemi and Cilliers, 1997; Bonifazi et al., 2001). The main idea of watershed segmentation is based on the concept of simulating water flows in a topographic representation of image intensity (Vincent and Soille, 1991). As shown in Fig. 6, the intensity of an image is represented by a topographic landscape, where local minima are the bottom of valleys. Assume water fills from the bottom up, watershed lines can be identified when two lakes meet. Consequently, local maxima will progressively disappear as
Fig. 6. Schematic watershed segmentation in one dimension.
the level of lakes increases. The flooding process continues until the complete landscape is flooded. Therefore, watershed transformation maps the original image to a partitioned one, where all points in the same valley are uniquely labeled. Watershed transformation tends to over-segment the image since a basin is created for every local minimum. A similarity-based approach replaces the original local optima with a marker, which is defined as a region surrounded by pixels of higher altitude. Other improvements such as the hierarchical watershed scheme, combining it with a neural network, as well as the smoothing and thresholding background values before segmentation, are also reported to address the issue of over-segmentation. These approaches work well in handling noisy images (Huang and Chen, 2004). However, over-segmentation can still be a problem when applying the watershed transformation to highly detailed images, especially the images collected from phosphorus oxide flotation processes as shown in
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Fig. 7. Froth images of reported applications.
Fig. 4. In addition, these complicated algorithms have not been reported for on-line real-time applications. The image analysis system is developed for flotation processes that are used to purify phosphorus oxide. Fig. 7 compares froth images from the flotation chamber and column with those of previously reported applications, such as Cu–Pb flotation (Bonifazi et al., 2001) and the flotation processes to concentrate zinc (Hyotyniemi and Ylinen, 2000; Liu et al., 2005). Images of this study are significantly different from those reported in literature, where bubbles are clustered on top of froth surface. In addition, the large number of small-size bubbles poses a challenging segmentation task. The MATLAB function ‘‘watershed”, an implementation of the immersion simulations based algorithm (Vin-
cent and Soille, 1991), is applied to the 1st image in Fig. 4. Poor performance is obtained even with carefully selected parameters (see Fig. 8). Preprocessing of images, such as contrast enhancement, is normally utilized to improve the performance of watershed segmentation. However, the preprocessing is too computationally intensive to be integrated with realtime control system. 3.3. Edge detection–based approach Cipriano et al. (1998) reported a visual system (ACEFLOT), which estimated bubble size based on the edge detection technique. The center and edge of each bubble were detected through the high/low intensity gradient.
Fig. 8. Watershed segmentation of a froth image.
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Morphological operators, such as opening and closing, were also utilized to combine with the edge detection approach in order to identify the bubbles from the froth image background. However, the edge-detection based approach still did not perform well for this application due to the following reasons. First, the bubbles are quite small under nominal operating conditions. Second, froth bubbles of phosphorus oxide flotation processes do not usually cluster together, especially in the flotation chamber. The areas among bubbles are difficult to be handled by the edge detection approach. Third, images collected from the flotation machines do not have sufficiently high contrast between bubbles and the background, which adds extra difficulty in applying edge detection based approach. 4. New approaches for bubble size estimation Applications of reported bubble size estimation approaches, including the texture spectrum, the watershed segmentation and edge detection based methodologies, to the froth images collected at phosphorus oxide flotation processes revealed unsatisfactory performance. Two novel approaches are proposed in sequel: an improved texture spectrum approach and a method based on binary images. 4.1. Improved texture spectrum approach As shown in Fig. 5, the original texture spectrum approach is not able to provide reliable estimation of bubble size. The observation is attributed to the following two reasons. Firstly, Eq. (1) does not take into the account the relationship between the intensity of the central pixel and the average value of the image. Secondly, the number of bubbles should also be taken into account. Given a texture unit consists of 9 pixels with the same intensity, the value of the texture unit is 3280 according to Eq. (2), no matter this unit is at the center of the bubble (with high intensity) or in the background (with low intensity). Therefore, Eq. (2) is modified as 8 8 P > > > Ei 3i1 if I C 6 I < i¼1 N TU ¼ ð4Þ 8 > P > i1 > 6581 þ Ei 3 if I C > I :
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 6560 uX Na hi ð1 B Þ BS ¼ t NN i¼3281
ð5Þ
where a is a polynomial factor and NN is a scaling factor. In this study, a = 0.25 and NN = 100 are obtained through empirical analysis of images collected from the flotation process. It should be noted that the parameters depend on the setting of the camera and the type of flotation processes. The summation of Eq. (5) calculates the index based on 6560 bins. Thus, the bins of 3281–6560 correspond to the actual index values of 6561–13161. Fig. 9 shows the estimated bubble size of froth images (in Fig. 4) with the modified texture spectrum approach. The second image has the smallest bubbles, while images (1), (3) and (4) have similar average bubble size. Compare with the results in Fig. 5, the modified texture spectrum approach correctly identifies the change of bubble size when applied to froth images. Although the modified texture spectrum approach improves the calculation of bubble size, it is not straightforward to obtain the distribution of bubble size. 4.2. Methods based on binary images Binary (black and white) is the simplest form to represent an image, which has been widely used in medical applications due to the advantages of easiness to obtain and low storage requirement. A binary image can be straightforwardly obtained by thresholding the intensity component of a gray-scale image, such that pixels above the threshold are white and those below are black (see Fig. 10). In this study, the threshold is experimentally determined as 0.8 by analyzing an extensive collection of images over a period of several months. The statistics of the bubble can then be obtained from the binary image, including the number of bubbles, the average size as well as the distribution of bubble size. Bubble size of froth images (in Fig. 4) is estimated with the approach based on binary image. As shown in Fig. 11, image (1) has the largest number of bubbles while the second has the smallest number. Comparing to image (3), image (4) has smaller number of small bubbles (of size 1) but larger number of bubbles of size 3.
i¼1
where IC is the intensity of the center pixel and I is the average intensity of the image. The new range for the value of texture unit is between 0 and 13161. Moreover, the texture units on top of bubbles have larger value than those from the background. The size of bubbles can thus be estimated more reliably. The original formula for bubble size estimation, Eq. (3), tends to denote ‘‘big” bubbles when the number of bubble is large. Therefore, the number of bubbles, NB, should be taken into account for bubble size estimation with the texture spectrum approach. The modified equation is: Fig. 9. Bubble size estimation with improved texture spectrum approach.
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Fig. 10. Color and binary images of froth bubbles.
Fig. 11. Number of bubbles estimated with binary image-based approach.
Therefore, average bubble size of image (4) is larger than that of image (3). The x-axis of Fig. 11 denotes the number of pixels of a bubble. Given that most bubbles are indicated with one pixel and the normal diameter of bubbles is about 2 cm, the corresponding diameter of bubbles during normal operations is between 2 and 4 cm. The averaged bubble size is shown in Fig. 12, which is consistent with the modified texture spectrum approach (see Fig. 9). In summary, the binary image based approach estimates the features of froth bubbles reasonably well. Fig. 13 summarizes results from a flotation column at varied operational conditions. The horizontal and vertical
Fig. 12. Average bubble size estimation with binary image.
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axes of the rightmost graphs represent the number of pixels of each bubble and the total number of bubbles detected of
such size on the froth image. The diameter of bubbles indicated with one pixel is about 1 cm.
Fig. 13. Bubble size estimation of flotation column using the approach of binary image.
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In Case 1, there are hardly visible bubbles except two small ones around the left bottom corner. Case 2 and 3 show a transition period that the number of bubbles starts increasing. In Case 2, bubbles are not visible in the left upper corner, but in the right bottom area. Case 3 reveals that relatively large bubbles appear in the right bottom of the image while small ones resident mostly on the left upper area. Both the number and the size of froth bubbles increase from the Case 3 to Case 4, as the process is approaching the nominal condition. Case 5 shows a scenario that the bubbles are ‘‘watery” due to little amount of minerals in the column. The binary image-based approach detects the significant increase of the number and the size of bubbles. It should be noted that the bubbles are ‘‘thin” (as marked by the circles). Although larger bubbles are detected, the detected size is smaller than the actual bubble. However, this observation does not pose a significant influence on the implemented system, since Case 5 only represents an infrequent and abnormal operating mode.
5. Image analysis system configuration The structure of the real-time image analysis system is shown in Fig. 14. The system resides on the same computer as the process control system, ECS/ProcessExpertÒ by FLSmidth Automation that enables data exchange with MATLAB. An Axis 2120 network camera is installed approximately 1 m above the surface of the flotation froth. The camera is triggered by a Programmable Logic Controller (PLC) signal. Considering the time constant of the flotation process and the network load, the camera is triggered once every 15 min. Then, a high pulse of 3 s is initialized. During this period, around 12 images are collected and uploaded to PC through a ftp server. PXP (ProcessExpert) units (imple-
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mented in MATLAB) extract image features and send them to the data log system. The resolution and quality of images used in this study are determined by the following factors: I. Velocity measurement is also part of the system, which requires the processing of a sequence of images that are obtained within a short time interval. II. The network band of the plant is limited. In-office test shows that 13 images can be uploaded each second for the designed system. However, only four images per second can be uploaded in the plant. III. The camera is installed approximately 1 m above the surface in order to cover sufficiently large area for velocity calculation. IV. Plant personnel clean the working area using pressurized water. Water might be splashed on the lenses cover that causes problems, i.e., blurred images, if the camera is not installed sufficiently high (see Fig. 15). V. Images of high resolution are definitely useful to obtain a better estimation of bubble size. However, the image analysis system resides on the same computer performing the process control activities. The CPU load has to be limited for the specific application, in order not to completely occupy the CPU and cause data communication problems with lower level PLC. Taking all factors into consideration, the current resolution of images is 352 by 240. The described image analysis systems have been installed on a flotation chamber and a column at a client company in Brazil. Preliminary results over the past several months revealed that reasonable estimation of the bubble size and distribution were obtained without overloading the process control computer.
PC FTP Server reading & analyzing images
uploading images
Camera
ProcessExpert®
external trigger
ECS
PLC
Process
Fig. 14. Real-time image analysis system for flotation processes.
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Fig. 15. Blurred images due to the splashed water on the cover of the camera.
6. Conclusions An industrial application of image analysis systems for flotation processes is reported in this paper, focusing on the estimation of bubble size that is believed to be the most important indication of the operating conditions. The system is applied to an industrial flotation process for purifying phosphorus oxide. Since the visual appearance of the froth is significantly different from those of previously reported flotation processes, the application of traditional edge-detection, watershed segmentation and texture spectrum approaches reveals unsatisfactory performance. A modified texture spectrum method and the novel approach based on binary image are presented. Preliminary results show consistent performance using froth images collected from phosphorus oxide flotation processes. The result can be improved by using high resolution cameras; however, the computational intensity needs to be taken into consideration for real-time implementation. Currently, a constant threshold is used in obtaining the binary images. Although high intensity lamps are installed on site, the light condition still varies slightly. Therefore, an adaptive threshold is an interesting task to be investigated in the future. The final objective of the project is to derive data-driven models from process measurements and image features such that effective flotation process control can be achieved. References Aldrich, C., Moolman, D.W., Gouws, F.S., Schmitz, G.P.J., 1997. Machine learning strategies for control of flotation plants. Control Engineering Practice 5 (2), 263–269. Bartolacci, G., Pelletier, P., Tessier, J., Duchesne, C., Bosse´, P.-A., Fournier, J., 2006. Application of numerical image analysis to process
diagnosis and physical parameter measurement in mineral processes – Part I: Flotation control based on froth textural characteristics. Minerals Engineering 19 (6–8), 734–747. Bonifazi, G., Serranti, S., Volpe, F., Zuco, R., 2001. Characterisation of flotation froth colour and structure by machine vision. Computers & Geosciences 27 (9), 1111–1117. Chuk, O.D., Ciribeni, V., Gutierrez, L.V., 2005. Froth collapse in column flotation: a prevention method using froth density estimation and fuzzy expert systems. Minerals Engineering 18 (5), 495–504. Cipriano, A., Guarini, M., Vidal, R., Soto, A., Sepulveda, C., Mery, D., Briseno, H., 1998. A real time visual sensor for supervision of flotation cells. Minerals Engineering 11 (6), 489–499. Duchesne, C., Bouajila, A., Bartolacci, G., Pelletier, P., Breau, Y., Fournier, J., Girard, D., 2003. Application of multivariate image analysis (MIA) to predict concentrate grade in froth flotation processes. In: Proceedings of the 35th Annual Meeting of the Canadian Mineral Processors, Ottawa, Ontario. He, D.C., Wang, L., 1990. Texture feature extraction from texture spectrum. IEEE Transactions on Geosciences and Remote Sensing 28 (4), 509–512. Huang, Y.-L., Chen, D.-R., 2004. Watershed segmentation for breast tumor in 2-D sonography. Ultrasound in Medicine and Biology 30 (5), 625–632. Hyotyniemi, H., Ylinen, R., 2000. Modeling of visual flotation froth data. Control Engineering Practice 8 (3), 313–318. KnowledgeScape Plantvision. hhttp://www.kscape.com/downloads/ PlantVision%20for%20Flotation.pdfi. Liu, J.J., MacGREGOR, J.F., Duchesne, C., Bartolacci, G., 2005. Flotation froth monitoring using multiresolutional multivariate image analysis. Minerals Engineering 18, 65–76. Metso Visiofroth, hhttp://www.metsominerals.com/inetMinerals/mm_home.nsf/FR?ReadForm&ATL/inetMinerals/mm_proc.nsf/WebWID/ WTB-041208-2256F-8CDAAi. Moolman, D.W., Aldrich, C., Van Deventer, J.S.J., Bradshaw, D.J., 1995. The interpretation of flotation froth surfaces by using digital image analysis and neural networks. Chemical Engineering Science 50 (22), 3501–3523. Moolman, D.W., Aldrich, C., Schmitz, G.P.J., van Deventer, J.S.J., 1996a. The interrelationship between surface froth characteristics and industrial flotation performance. Minerals Engineering 9 (8), 837–854. Moolman, D.W., Eksteen, J.J., Aldrich, C., van Deventer, J.S.J., 1996b. The significance of flotation froth appearance for machine vision control. International Journal of Mineral Processing 48 (3–4), 135– 158. Nguyen, K.K., Thornton, A.J., 1995. The application of texture-based image analysis techniques in froth flotation. In: Conference Proceedings DICTA-95. Digital Image Computing: Techniques and Applications, Australian Pattern Recognition Society. Outokumpu FrothmasterTM 2, hhttp://www.outotec.com/pages/ Page____9561.aspxi. Sadr-kazemi, N., Cilliers, J., 1997. An image processing algorithm for measurement of flotation froth bubble size and shape distributions. Minerals Engineering 10 (10), 1075–1083. Vincent, L., Soille, P., 1991. Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence 13 (6), 583–598. Wipware Wipfroth., hhttp://www.wipware.com/wipfroth.phpi.