Image-based quality monitoring system of limestone ore grades

Computers in Industry 61 (2010) 391–408

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Computers in Industry journal homepage: www.elsevier.com/locate/compind

Image-based quality monitoring system of limestone ore grades Snehamoy Chatterjee a,*, Ashis Bhattacherjee b,1, Biswajit Samanta b,2, Samir Kumar Pal b,3 a b

Department of Mining and Materials Engineering, McGill University, Montreal, Canada Department of Mining Engineering, Indian Institute of Technology Kharagpur, Kharagour 721302, India

A R T I C L E I N F O

A B S T R A C T

Article history: Received 15 March 2008 Received in revised form 29 September 2009 Accepted 26 October 2009 Available online 24 November 2009

In this study, an image analysis-based ore quality monitoring system was developed. The study was conducted at a limestone mine located in India. The samples were collected based on a stratified random sampling method, and images of these samples were taken in a simulated environment in a laboratory. The image preprocessing and segmentation were performed using different segmentation methods to extract morphological, colour and textural features. A total of 189 features was extracted during this study. Principal components analysis was conducted to reduce the feature vector for modeling purposes. Five principal components, which were extracted from the feature vectors, captured 95% of the total feature variance. A neural network model was used as a mapping function for ore grade prediction. The five principal components were used as input, and four grade attributes of limestone (CaO, Al2O3, Fe2O3 and SiO2) were used as output. The developed model was then used for day to day quality monitoring at 3 different face locations of the mine. Results revealed that this technique can be successfully used for ore grade monitoring at the mine level in a controlled environment. ß 2009 Elsevier B.V. All rights reserved.

Keywords: Image analysis Ore grade prediction Principal component analysis Neural network Off-line monitoring

1. Introduction Quality is the key to survival in global competition. An effective quality assurance program can result in increased market penetration, higher productivity, lower manufacturing and service costs, and improved consumer satisfaction. Adequate quality monitoring and control systems are the two critical components in achieving such quality assurance. The quality of ore plays a major role in deciding the economic viability of a mine. Sales revenue generated from a mine primarily depends upon the consistent supply of ore grade in accordance with a desired specification. An ore body and its immediate surroundings contain the factors given by natural factors which determine the ore quality. However, the quality of ore varies widely over the entire range of a deposit. In a heterogeneous deposit, the ore material extracted from one part of a mine might differ markedly in quality compared to the other parts. In such situations, stringent quality control programs have to be adopted to ensure consistent and timely supply of ore grade. In general, several grade

* Corresponding author at: Department of Mining and Materials Engineering, McGill University, Montreal, H3A2A7, Canada. E-mail addresses: [email protected] (S. Chatterjee), [email protected] (A. Bhattacherjee), [email protected] (B. Samanta), [email protected] (S.K. Pal). 1 +91 3222 283704. 2 +91 3222 283752. 3 +91 3222 283714. 0166-3615/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.compind.2009.10.003

control measures are practiced at the mine level itself, which might include: (i) accurate grade control planning, (ii) selection of the proper extracting method and equipment to minimize ore dilution, (iii) blending of different grades of ore, and (iv) processing of ore to improve the grade. Even though all possible measures are taken to control the grade of ore, the final ore grade projected from a quality control system, as a whole, might not comply with the requirements. This might be because of the occasional presence of some inherent flaws in the quality control system, which might go unnoticed by the quality control practitioners. As a result, the quality of ore may deteriorate over time. To present a safeguard to the above, a suitable quality monitoring and control system must be adopted at the mine level. One of the most important elements for a successful quality monitoring and control system in a mine is the use of fast, reliable and inexpensive online sensors, which will continuously monitor the ore grade. However, in most cases, it is nearly impossible to measure all the critical variables simultaneously. Even if, in some situations, it is possible to measure all the variables, it still might be prohibitively expensive. In these situations, a strategy often practiced is the measurement of some of the variables using a sensor, while other variables can be estimated from the measured variables through an appropriate model [1,2]. Furthermore, the mineral industry altogether experienced much less success in implementing a suitable monitoring scheme because of the nonavailability of online sensors. Even though the sensors are available, the reliability of measuring output from the sensors often becomes questionable. In the Indian scenario, the situation

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appears to be bleaker. Only a handful of examples were documented where some attempts were made to apply online sensors. In most cases, the ore grades are periodically determined by manually collecting samples from ore material and then analyzing them chemically in a laboratory. The sample collection, preparation and subsequent chemical analysis are tedious and time-consuming operations, which can span several hours to a few days. Therefore, it is usually impossible to adopt an online quality monitoring scheme, and even a simple quality control system cannot be implemented. In this situation, an inferential sensor derived from an image-based system might be an attractive technology for online quality monitoring. By taking images of the raw material, the samples remain untouched and the sampling rate can be very high. The ore grade can then be predicted online in realtime from the image data. The idea of implementing online grade monitoring schemes using image-based systems is beneficial for several reasons, such as: (i) image-based systems have great success in quality monitoring for mineral industry [3] as well as for other industries [4], and (ii) the grade control of ore particularly ‘ore sorting’ at the mine level is usually carried out by human experts. For example, during loading time, shovel operators segregate ore and waste at mine faces and make judgments about the ore grade based on their visual observations—a crude human approach. These examples show that it is possible to determine ore quality visually, which leads us to draw an analogy with an image-based system. Vision-based systems have great success in the mineral industry [4]. A study conducted by Oestreich [5] demonstrated the use of an online sensor for mineral composition determination. Petruck and Lastra [6] reported a study that was connected with the determination of mineral grade values on a microscopic scale. Shafarenko et al. [7] used an image-based technique to inspect the quality of granite rock. Casali et al. [8] proposed a vision-based model for ore grindability analysis. Ore textural analysis using the

image processing techniques was addressed by several investigators [9–11]. The main focus of their studies was on the estimation of average particle size, and distinguishing various ore types in industrial ore feeding systems. Lin et al. [12] also worked on the development of an online particle size analyzer. However, there is no such literature available on ore grade prediction using a visionbased model. In this paper, a vision-based model was developed for the prediction of ore quality at the face level of a mine. Rock samples were collected from different locations of a limestone mine and images were taken in the controlled environment of a laboratory. An attempt was made to find out the inherent relationship between the image-extracted features with grades using neural network techniques. The paper is organised as follows. Section 2 presents a brief overview of the steps involved in the methodology. A case study with a limestone deposit is presented in Section 3. Section 4 presents the ore grade monitoring at the mine level using the proposed method. Section 5 draws conclusions and summarizes the results. 2. Brief overview of proposed methodology A schematic diagram of the methodology applied in this study is presented in Fig. 1. The figure shows the step by step procedures for evaluating the grades of ores from the images of ore samples. Main components of the methodology are described in the following subsections. 2.1. Image acquisition One of the critical components in image processing tasks is the appropriate acquisition of images. The images should be taken in a controlled and identical environment so that influences of

Fig. 1. Image processing based quality monitoring method.

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nated as: (i) Technique A, (ii) Technique B, (iii) Technique C, and (iv) Technique D. Fig. 1 also shows the different steps involved in each segmentation technique. The basic philosophy and the operational principle of these techniques are well established in the image processing literature. The theoretical discussion of these techniques is outside the purview of the paper. Interested readers are requested to consult the following text books [13,16]. 2.4. Object identification

Fig. 2. Schematic diagram of image acquisition experimental setup.

extraneous factors can be eliminated with earnest care. With this aim, a laboratory set is developed for image acquisition. This acquisition system is a replica of a mine’s real life image acquisition system through which ores can be passed and images can be taken and analyzed. The image acquisition system consists of a wooden box, an illumination system, a digital camera and a personal computer. The box is made of wood with dimensions of 25 cm  30 cm  30 cm. The top of the box is cylindrically arched and bowl shaped with an approximate diameter of 40 cm. Since the lighting type, the location and the colour quality are crucial for clear images, uniform diffuse lighting was used. Four fluorescent tubes (150 mm diameter, 23 W circular tubes) are fitted at the four sides on the bowl with an angle of 458 to the horizontal so that it would produce minimal shadowing. The box top has an opening for camera placement for the capturing of images. A schematic diagram of the image acquisition setup is presented in Fig. 2. A digital camera with an aspect ratio of 4:3 has been used to take the images.

After a particular segmentation technique is applied, the different image regions containing the rock samples should be traced out. However, a particular segmented region might contain more than one rock sample. Thus, individual rock samples should be identified with labels from the segmented image. For object identification, a region labeling algorithm has been used [18]. Typically, a region labeling algorithm examines each pixel in a mapping, and compares its value to those of its neighbours. If the pixel value is close enough to its neighbouring values, then it is assumed to be in the same region as those of the neighbour. For the use of a regional leveling algorithm, a binary image is scanned from the top left to the bottom right. The first object pixel (i, j) encountered in the image is assigned a unique label (e.g., a value of 100). This label value is propagated and the region is grown to those pixels, which possess the same pixel value as that of the (i, j) pixel using the 8-neighbour connectivity method [16]. In the next step, the eight neighbours of those previously labeled pixels are examined and those that have the same pixel value are labeled. After the regional labeling, the original gray values of the labeled objects are then superimposed on the segmented images so that each object has its original gray value with the background value set to zero [19].

2.2. Image preprocessing 2.5. Feature extraction Several preprocessing algorithms are available for removing unwanted noise and other artifacts that are introduced in images during image acquisition. The average and the median filters are popular for noise reduction in images [13]. A major advantage of the median filter over average filter is that the median filter can eliminate the effect of input noise values with extremely large magnitudes. Therefore, if any unwanted high magnitude noise is introduced in an image, the median filter can successfully eliminate that noise. In this study, a median filter has been applied, which sorts the pixels in an n x n region and replaces the central pixel with the median value. It is assumed that the same experimental setup, camera and lighting arrangement will be used for all the images. Hence, no attempt has been made to calibrate the image and the camera. 2.3. Image segmentation Segmentation is a technique whereby an image is subdivided into its constituent regions or objects. The level to which the subdivision is carried out depends upon the goal of carrying out such segmentation process [13–15]. In our work, the objective is to identify discrete regions, representing rock samples, in an image by applying an image segmentation technique. The manual digitization technique is one of the easiest image segmentation techniques, but it is time consuming. Several automatic and semiautomatic segmentation techniques are available in the literature [13,16]. However, Graham et al. [17] suggested that no single image segmentation technique is perfect for segmenting the grain samples from their neighbours. In this study, four different hybrid image segmentation techniques have been tested for automatic detection of rock samples present in an image. Fig. 1 presents these four segmentation techniques, which are desig-

Each of the objects identified in the image represents a rock sample. Depending on the properties of a rock sample, the object properties in the image vary considerably, and are represented by various features. Therefore, the next step of the image processing phase is the extraction of different features from the rock images. The features are characterized by three categories: colour, morphology and texture. One of the most important properties for distinguishing limestone is that of colour [20]. The colour feature is characterized by the intensity levels of its seven components, namely r, g, b, H, S, I, and gray. The texture and morphology features of limestone rocks also vary with the depositional variability and weathering of the limestone beds [20]. Key morphological features include area, perimeter, areaperimeter ratio, minimum and maximum radius, convex hull, and some other derived features. These parameters vary according to the rock types. For example, for the limestone mine under investigation, it has been observed that the pink limestone rock acquires an elongated shape after blasting; whereas, the weathered rock becomes somewhat spherical in shape after blasting. It is very likely that, if these morphological features are extracted and mapped with proper modeling, then these features might have some relationships with their individual rock types as well as their grades. The type of textural features include statistical feature, cooccurrence matrix [21,22], and run length feature [23]. 2.6. Feature value calculation of an image Assume that from an image I, it is possible to identify n number of distinct rock objects and that the numbers of features extracted per rock object is M. Then, the feature value Xi for the image I is

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Fig. 3. Schematic diagram for calculation of image features from rock features.

calculated from the individual rock object features present in the image by Xi ¼

n X w j xi j

(1)

j¼1

where j = 1, 2, . . ., n; i = 1, 2, . . ., M, xij is the ith feature of jth rock object from a given image. aj and w j ¼ Pn ; j¼1 a j aj = number of pixels in the rock object j. Fig. 3 illustrates the procedure for calculating the image feature from the rock feature of the image. In this image, there are seven distinct rock objects having pixel numbers: a1, a2, a3, . . ., a7. A feature such as uniformity, which indicates the uniform gray level in a region [32], is measured for the individual rock objects with values b1, b2, b3, . . ., b7. Then, the average uniformity value for the image can be calculated by a1 B ¼ P7

ai a5

i¼1

þ P7

i¼1

a2 b1 þ P7

ai a6

i¼1

ai

b5 þ P7

i¼1

a3 b2 þ P7

ai a7

i¼1

ai

b6 þ P7

i¼1

a4 b3 þ P7

i¼1

ai

ai

b4

b7

where B is average uniformity of this image and of all numbers of pixels in the seven rocks.

(2) P7

i¼1

Hence, an attempt has been made in this paper to find out the inherent relationship between various image-based rock parameters with the grades using neural network techniques. Prediction of ore grades is achieved by feeding the feature vectors (after dimensionality reduction) as inputs to a neural network model that captures the relationship between ore grades and feature vectors. Artificial Neural Networks (ANN) is a modeling tool with the ability to learn the complex inter-relationship between the input and the output variables of multi-dimensional data [26,27]. The multi-layer perceptron neural network (MLP) model is a popular model that has been used in this study. The network consists of three layers: namely the input, the output and a single hidden layer. The input layer is connected to the hidden layer and the hidden layer is connected to output layer. Each connection is associated with a connection weight. During the learning phase, the network is presented with a set of known image features and grade values. Using an optimal learning algorithm, the weights are modified iteratively. After some iteration, they become adjusted in such a way that when the input image features are presented, the network produces grade outputs, which are close to their actual output values. Detailed descriptions of neural networks are beyond the scope of this paper. The reader is referred to [26,28]. The gradient descent learning algorithm was used for error minimization. The learning basically starts with an untrained network, presents a training pattern (here PCs of image features) to the input layer, passes the signals through the network, and determines the output (grade attributes) at the output layer. These outputs are compared to the target values and any observed differences between these two correspond to an error. The error value is a function of the weights and is minimized when the network outputs match the desired output. The weights are thus adjusted to reduce this measure of error. The error on a pattern is given by EðwÞ 

a1 is the sum

2.7. Feature vector reduction The large number of features obtained during feature extraction results in a high-dimensional feature vector, whose processing is prohibitively expensive [24]. Moreover, some of these features might be co-related causing them to be redundant in subsequent analysis. These redundant features can be safely discarded without losing much information by the use of dimensionality-reduction techniques on the feature vector. The dimensionality-reduction technique employed in this study is the Principal Component Analysis (PCA) [25]. Principal Component Analysis is one of the most widely used methods for reducing the dimensionality of a multivariate data set. It transforms a set of correlated features into the principal components (PCs) via the application of a linear transformation. These orthogonal PCs are capable of successfully extracting a major portion of the total data variance represented by the original feature vector. It is possible to extract as many PCs as the number of features in the feature vector. However, successive PCs are arranged in descending order by variance. The variances of the last few PCs do not have a significant contribution to the total data variance, and thus, can be eliminated. In this way, PCA becomes an effective means for reducing the dimensionality of feature vectors. 2.8. Neural networks for ore grade modeling The feature sets extracted from the rock images are key characteristics that can help in predicting the ore grade quality.

c 1X 1 ðt  zk Þ2 ¼ jt  zj2 2 k¼1 k 2

(3)

In the above expression, t and z are the actual grades and the network output grades. c is number of grade attributes, and w represent the weights in the network. The weights are initialized with random values, and are then changed in a direction that will reduce the error. This method is known as a back-propagation gradient decent with momentum [27]:

@EðmÞ þ m Dwðm  1Þ @w where, h is the learning rate and m is momentum. DwðmÞ ¼ h

(4)

The iterative algorithm requires taking a weight vector at iteration m and updating it as wðm þ 1Þ ¼ wðmÞ þ DwðmÞ

(5)

From the chain rule, it shows that the weight change is:

@E @E @netk @netk ¼ ¼  dk @wk j @netk @wk j @wk j where net j ¼ f

P

M i¼1

(6)

 P  M xi wi j þ w j0 ¼ f i¼0 xi wi j . The index i

indicates variables in the input layer (that is M number of principal components in this case), j in the hidden layer, wij denotes the input to hidden layer weights at the hidden unit j, and f is the activation for hidden j. In this study, logistic activation function has been used [27], which is expressed by following equation: ! M X 1 f xi wi j ¼ (7) M X i¼0 xi wi j



1þe

i¼0

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The adjusted weights are then used to calculate the error term for the next iteration. The process is repeated in the same fashion and stopped when the error reaches a threshold value. After completion of the training, the model can be used for prediction purposes. One of critical aspects in neural network modeling is the development of a generalized model. The generalization entails the applicability of a model beyond the data set by which the model is trained. The neural network model is very flexible and, therefore, powerful enough to capture any complex relationship between the input and the output variables [27]. However, too much flexibility can be a curse by overfitting the model to noise. A neural network modeler always strives to build up a generalized model with a given data set. A model calibration exercise is a good practice to obtain generalized model [27]. 3. Case study 3.1. Data collection The study was carried out in a limestone mine situated in the western part of India. The mine is located 18 km southwest of the district headquarters. The area covered by the mine is more than 6 km2. The terrain is more or less flat with gentle undulation and the ground level rises by about 10 m towards the northern and the southern end of the area as compared to the central part. Most of the area is covered by soil except for outcrops of limestone. The mine has nine different litho-types: namely pink limestone, greenish gray limestone, dark gray limestone, light gray limestone, weathered limestone, upper gray limestone, shale, clay, and overburden soil [29]. Most of the high grade limestone is associated with pink, greenish and upper gray limestone. The representative samples were collected from the blasted muck of the case study mine while maintaining the proper sampling strategy. The stratified random sampling method was adopted for this study. In this scheme, the samples were collected

395

from different strata, which were classified according to the lithotypes present in the deposit. The rock samples from each stratum were collected randomly. It was also decided to capture an equal number of samples from each stratum. As the mine under investigation was in its initial stage of production, none of the lithological units were exposed at the time of sampling. Therefore, the samples were gathered from five lithological units exposed to the working faces. Altogether 120 samples, 24 from each lithology, were collected from the case study mine. The samples weighed approximately 5 kg, and the size range varied from 2 to 8 cm. A pictorial diagram of the sampling strategy is presented in Fig. 4. 3.2. Image analysis of the samples Samples collected from the mine were then placed in the laboratory setup for the image acquisition. Ten successive images for each sample were taken by changing the placement and the orientation of the rock samples. The changing of position and orientation of the rock samples was done for two basic reasons. Firstly, if images are taken from one side of the rocks, features extracted may not be the true representative of the rock samples. So by taking the images from changing positions and of varying rock orientations, the generalization capability of image-extracted rock features is improved. Secondly, the colour of a rock may vary on different sides due to its exposure to the environment or due to its interaction with other rocks. Thus, changing its orientation during image capture may help to highlight these differences, ultimately facilitating robust model development. In total, 1200 images were generated collectively from the rock samples. After the image acquisition, a 33 median filter was used to remove as much noise as possible. The image segmentation techniques were then applied on the filtered images. As discussed earlier, four segmentation techniques were examined [30,31]. Figs. 5–8 present the image outputs of the individual segmentation techniques at various stages for a sample image. A validation exercise was then carried out to

Fig. 4. Pictorial diagram sampling technique.

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Fig. 5. Sample images of different stage involved in segmentation Technique A: (a) gray image; (b) bottom hat transformation; (c) top hat transformation; (d) image subtract (image add (top hat, gray), bottom hat); (e) image complement; (f) extended minima; (g) imposed minima; (h) watershed segmentation.

select the best segmentation technique for subsequent image processing operations. For this purpose, 520 randomly chosen rock objects from the image data set were manually segmented. The manual segmentation was performed by digitizing the periphery of the rocks present in the image. For validation purposes, the dimensions of manually segmented rock samples are referred to as actual measurements. The same rock objects were then segmented using four segmenta-

tion techniques. The major axis length and the minor axis length of the tested rock samples were used as the metric for determining the optimal performance of the segmentation techniques, as these two parameters are used as the prime parameters of defining the shape of a segmented object [32]. The major and minor axes lengths on a segmented rock are presented in Fig. 9, along with other morphological features. It can be noted that an imprecise estimate of major and minor axes lengths might not properly

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Fig. 6. Sample images of different stage involved in Technique B: (a) gray image; (b) threshold image; (c) complement image; (d) distance transformation; (e) watershed segmentation; (f) over segmented image.

represent the true shape of a segmented rock. As an example, in Fig. 9, if the major axis length is under-estimated and minor axis length is over-estimated, then the segmented rock will take a somewhat circular shape instead of its original spherical shape. The values of major and minor axes lengths of segmented images of rock samples obtained from four segmentation techniques were compared with the corresponding values obtained from manual segmentation techniques for all 520 rock images. The mean error, the mean absolute error, the mean squared error (MSE) and the R2 values were used as the performance statistics and were calculated using 520 actual (manually segmented) values, with the values obtained using four segmentation techniques (referred to as

estimated). Table 1 shows the error statistics of the major and minor axis lengths for all four segmentation techniques. For the major axis length, the mean error values for the techniques A, B, C, and D are 0.21, 0.32, 0.05, and 0.48 pixels, respectively. The corresponding mean absolute error values for the four techniques are 10.1, 11.42, 12.89, and 14.44 pixels, respectively. The mean squared error of Technique D is the highest (508.3 pixels2) as compared to the other three techniques. The error variance of the Technique A is the lowest followed by the techniques B, C, and D, respectively. The R2 value of the Technique A is the highest as compared to the other three techniques. For the variable minor axis length, the mean error values are 0.315, 0.51, 0.19, 0.86

Table 1 Error statistics of four segmentation techniques. Segmentation technique

A B C D

Mean error

Mean absolute error

R2

Error variance

Mean squared error

Major length (pixel)

Minor length (pixel)

Major length (pixel)

Minor length (pixel)

Major length (pixel2)

Minor length (pixel2)

Major length

Minor length

Major length (pixel2)

Minor length (pixel2)

0.21 0.32 0.15 0.48

0.315 0.51 0.19 0.86

10.1 11.42 12.89 14.44

13.42 17.2 21.2 22.7

106.95 240.1 296.8 499.1

72.93 127.8 193.4 292

0.96 .91 .887 .81

0.952 0.93 0.894 0.84

111.16 246.8 303.1 508.31

74.16 131.8 201.3 299.6

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Fig. 7. Sample images of different stages involved in segmentation Technique C: (a) gray image; (b) median filtered image; (c) canny edge detection; (d) morphological dilation; (e) skeleton of previous image; (f) operation of gray image and complement of previous image.

pixels, respectively. The mean absolute errors, as well as the mean squared errors, are higher for the techniques B, C, and D as compared to the Technique A. The mean absolute errors of the techniques A, B, C, and D are 13.42, 17.2, 21.2, and 22.7 pixels, respectively, and the corresponding mean squared errors are

74.16, 131.8, 201.3, and 299.6 (pixels)2, respectively. It is revealed from the results that Technique A has a higher R2 value compared to the other techniques. Thus, it can be inferred that Technique A produces the least error in measuring the major and minor axis lengths compared to the other techniques. Fig. 10(a) and (b) shows

Table 2 Paired sample t-test between manual segmentation vs. automatic segmentation techniques for major axis length and minor axis length. Segmentation technique

Paired samples test (paired differences) Mean (pixel)

Std. deviation (pixel)

Std. error mean

95% confidence interval of the difference

t

df

Sig. (2-tailed)

Lower

Upper

Technique A

Major axis length Minor axis length

Observed vs. estimated value Observed vs. estimated value

0.21 0.315

10.34 8.54

0.45 0.37

1.07 0.39

0.654 1.02

0.466 0.851

519 519

0.64 0.395

Technique B

Major axis length Minor axis length

Observed vs. estimated value Observed vs. estimated value

0.32 0.51

15.49 11.3

0.68 0.49

1.62 0.43

0.98 1.45

0.470 1.041

519 519

0.63 0.29

Technique C

Major axis length Minor axis length

Observed vs. estimated value Observed vs. estimated value

0.15 0.19

17.23 13.9

0.756 0.61

1.3 1.36

1.6 0.98

0.2 0.31

519 519

0.84 0.75

Technique D

Major axis length Minor axis length

Observed vs. estimated value Observed vs. estimated value

0.48 0.86

22.34 17.09

0.98 0.75

2.36 0.58

1.4 2.3

0.49 1.15

519 519

0.62 0.25

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Fig. 8. Sample images of different stage involved in Technique D: (a) gray image; (b) gradient magnitude image; (c) opening of gradient magnitude image; (d) closing of previous image; (e) watershed image; (f) over segmented watershed image.

the scatter plots of the actual values vs. the estimated values of the major and the minor axes length, respectively, using Technique A. The statistical similarities between the actual values and the estimated values for the major and minor axes length were also

Fig. 9. Major and minor axis length with other morphological feature in a segmented image.

tested for all the segmentation techniques. The t-statistics were performed for this purpose and the results are presented in Table 2. The t-statistics and their level of significance values, however, indicate that the mean values of the actual and estimated major and minor axes length are not significantly different. In view of above performance measures, it was decided that the segmentation Technique A would be used for subsequent processing of all the rock images. The segmented images were then processed for identifying and labeling the individual rock objects present in the segmented parts using the regional labeling algorithm. The MATLAB software was used for this purpose. After a careful examination of all the images, 5276 distinct rock objects were identified. The features were then extracted from each of the individual rock objects. Altogether, 189 features, including 28 morphological features, 112 colour features, and 49 textural features, were extracted. A list of extracted features is presented in Table 3. After the extraction of features from each distinct rock object, the feature values for each of the 1200 images were calculated as per the methodology described in Section 2.6. However, 189 features imposed a huge computational burden in subsequent neural network modeling for ore grade estimation using these image-extracted features. Therefore, PCA technique

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Fig. 11. Percentage of data variance captured by five principal components.

Fig. 10. Scatter plot of (a) major and (b) minor axis length of manually vs. semiautomatic segmentation using Technique A.

Table 3 Feature extracted from segmented rock sample. Type of feature

Number of feature

Colour feature Measure of location Measure of spread Measure of shape Gray level moment

112 21 35 14 42

Morphological feature Area Perimeter Major and minor axis length Convex hull and convex area Minimum and maximum radius Derived feature Binary moment

28 1 1 2 2 2 14 6

Textural feature Statistical feature Co-occurrence matrix Run length matrix

49 4 30 15

Fig. 12. Scatter plots matrix of five principal components.

was used to reduce the dimensionality of these image-extracted features. From the PCA analysis, it was noticed that total data variance could be explained by 189 features, of which 95% of the data variance could be conveniently explained by the first five principal components (PCs). Hence, it was decided that the first five principal components captured from the image-extracted features would be retained. Table 4 shows the amount of data variance, percentage of data variance and cumulative percentage of data variance shared by the five principal components. Fig. 11 shows the percentage of variance captured by first five principal components. Another important consideration dealing with the PCs is that they are statistically independent and hence mutually orthogonal. Therefore, each PC bears independent information. The statistical independencies of the PCs can very well be observed from the scatter plots presented in Fig. 12. Fig. 13(a)–(e) presents

Table 4 Amount of data variance, percentage of data variance, and cumulative percentage of data variance captured by first five principal components. Principal component

PC 1

PC 2

PC 3

PC 4

PC5

Data variance captured Percentage of data variance captured (%) Cumulative percentage of data variance captured (%)

2.56e+132 63.1 63.1

8.68e+131 21.35 84.45

2.62e+131 6.45 90.9

1.28e+131 3.16 94.06

3.82e+130 0.94 95

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Fig. 13. Factor loading of 25 major features on five principal components: (a) principal component 1; (b) principal component 2; (c) principal component 3; (d) principal component 4; (e) principal component 5.

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Fig. 13. (Continued ).

only the first 25 major contributory features and their factor loadings to each of the five PCs. 3.3. Neural network model for grade prediction The multi-layer perceptron neural network (MLP) model was used for predicting the grades of the mineral from image-extracted features. A three layered neural network model was used for this purpose. The five principal components, as obtained from the PCA analysis of image-extracted features, were used as the input parameters and the grade attributes (CaO, Al2O3, SiO2, and Fe2O3) were used as the output parameters of the neural network model. It can be noted that the grade values of these four grade attributes, CaO, Al2O3, Fe2O3, and SiO2, were determined by chemical analysis of all the rock samples following the ASTM standard [33]. Fig. 14 presents the architecture of the neural network model. The network consisted of an input layer containing five input nodes (principal components), an output layer consisting of four output nodes corresponding to four grade attributes, and a single hidden layer. The logistic activation was used both in the hidden and the output layers. In order to create a generalized neural network model in this study, the model was calibrated using the early-stop training method [26]. Early-stop training method used two data sets: (i) the training, and (ii) the calibration. The model was trained using the

Fig. 14. Architecture of neural network model for ore grade prediction.

training data set and was calibrated using the calibration data set. However, the generalization capability of the model was tested using the testing data set. To prepare these three data sets, all of the data available to the neural network modeling was divided into the three data sets. For this purpose, images were randomly picked up and put into any of the three data sets in the proportion of 2:1:1 for training, calibration and testing sets. Thus, 600 images were chosen for the training, 300 images for the calibration, and the remaining 300 images for the testing. The parameter values, e.g. five PCs and four grade attributes, were then ascertained for these images. The quality of this random data division was judged by checking the statistical similarity among the three data subsets across all the input and the output parameters. To this end, the ANOVA F-test was performed to check the statistical similarities in mean values of the parameters for all the three data sets. The ANOVA test results are presented in Table 5. The values of the F test indicate that there is no significant difference between the mean values of all the input and the output parameters for the three data sets. The Levene statistics were also performed for the test of homogeneity of the variance [34]. The results of the test statistics are presented in Table 6. The Levene statistics and their significance level values show that the variance values of the parameters for the three data sets are not significantly different from each other. The gradient descent with momentum algorithm was used to train the network using the training data set. Performance of the network was observed on the calibration data set. It was noted that, at the beginning, the errors on the training and the calibration data were gradually decreased; however, after certain iterations, calibration error ceased to decrease while the training error continued to decrease as shown in Fig. 15. As per the early-stop criterion, the training was stopped at the point where the lowest error of value, 0.41, was observed on the calibration data. The Neural Network toolbox of the MATLAB software was used for this part of neural network modeling. Another important decision pertaining to neural network modeling was the selection of the number of hidden nodes and the learning parameters, e.g. learning rate (a) and momentum parameter (m). The optimal number of hidden nodes was manually determined by observing the mean squared errors of the model vs. the number of hidden nodes, as presented in Fig. 16. The result shows that eight nodes in the hidden layer produce the minimum mean squared error in the training data set. The grid pattern search method was implemented to discover the best learning parameters of a and m for the model. In the grid search algorithm, the a value was kept within the range of 0.05–0.8 with an increment of 0.05, and the m was kept within the range of 0.1–0.8 with an increment of 0.1. The initial weight value of the

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403

Table 5 ANOVA test results of training, calibration and testing data sets. ANOVA df

Mean Square

F

Sig.

PC 1

Between data sets Within data set Total

Sum of squares 304.691 96616.248 96920.938

2 1197 1199

152.345 69.160

2.203

.111

PC 2

Between data sets Within data set Total

5.707 39028.263 39033.970

2 1197 1199

2.853 27.937

.102

.903

PC 3

Between data sets Within data set Total

38.917 26659.118 26698.036

2 1197 1199

19.459 19.083

1.020

.361

PC 4

Between data sets Within data set Total

12.712 20910.342 20923.054

2 1197 1199

6.356 14.968

.425

.654

PC 5

Between data sets Within data set Total

54.251 17029.068 17083.319

2 1197 1199

27.126 12.190

2.225

.108

SiO2

Between data sets Within data set Total

159.004 561973.900 562132.903

2 1197 1199

79.502 402.272

.198

.821

Al2O3

Between data sets Within data set Total

12.955 26318.827 26331.783

2 1197 1199

6.478 18.840

.344

.709

Fe2O3

Between data sets Within data set Total

7.859 29373.915 29381.774

2 1197 1199

3.929 21.026

.187

.830

CaO

Between data sets Within data set Total

58.775 378887.758 378946.533

2 1197 1199

29.388 271.215

.108

.897

Table 6 Homogeneity test of variance of training, validation and testing data sets. Test of homogeneity of variances

PC 1 PC 2 PC 3 PC 4 PC 5 SiO2 Al2O3 Fe2O3 CaO

Levene statistic

df1

df2

Sig.

1.946 0.971 2.436 0.113 2.424 1.359 1.844 0.707 0.973

2 2 2 2 2 2 2 2 2

1197 1197 1197 1197 1197 1197 1197 1197 1197

.143 0.379 0.088 0.893 0.089 0.257 0.159 0.493 0.378

Fig. 15. Training, calibration and testing error during neural network learning.

NEURAL NETWORK was chosen as 0.3 for the entire exercise. Fig. 17 shows the surface and contour plots of the training errors at the grid points across the two parameters. The optimum values for the parameters’ learning rates and momentums were determined by the grid search algorithm as being 0.65 and 0.5, respectively. The network was trained with these optimal parameter values until the convergence. After the model was developed, the generalization capability, as well as the performance of the model, was examined using the testing data set. The error statistics of the observed values and the model predicted values for the testing data set are presented in Table 7. The mean squared error values are 22.20, 3. 17, 1.02 and 48.60, and the R2 values are 0.89, 0.78, 0.85 and 0.87 for the grade attributes CaO, Al2O3, Fe2O3, and SiO2, respectively. The magnitude of the coefficient of determination (R2) indicates the proportion of actual data variance of a predictor variable (here grade attribute), which can be explained by the model. High R2 values for the neural

Fig. 16. Error of training data with different hidden node size.

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Table 7 Error statistics of neural network model run for testing data. Statistics

CaO

Al2O3

Fe2O3

SiO2

Mean error (%) Error variance (%2) Mean absolute error (%) R2 Mean squared error (%2)

0.18 22.247 3.10 0.89 22.206

0.043 3.185 1.15 0.785 3.176

0.378 0.888 0.703 0.85 1.028

0.31 48.64 4.97 0.87 48.58

network models for the grade attributes (close to 0.8) illustrate that 80% of the grade attributes’ data variances are explained by the model. The t-statistics were also performed to check the statistical similarities between the observed values and the model predicted values. The t-statistics along with the significance level for the means of observed values and the model predicted values

for the test data set are presented in Table 8. It is observed from the table that there is no significant difference in means for the attributes CaO, Al2O3 and SiO2, whereas the mean values for the observed and the model predicted values are significantly different for the attribute Fe2O3. This result indicates that the model produces a biased estimate for the attribute Fe2O3. Therefore, it can be inferred that the model can satisfactorily predict the ore grades of the limestone for the CaO, Al2O3 and SiO2, whereas, it is not particularly reliable for Fe2O3. Fig. 18(a)–(d) shows the scatter plots of the observed vs. model predicted values for all the four attributes. Regression lines were fitted for the observed vs. predicted values using the least square method, as can be seen in the figures. The error statistics of these regression lines are shown in histogram plots, as presented in Fig. 19(a)–(d). As per the regression model assumption [35], it can be seen that the errors are more or less normally distributed and their mean values come near to zero.

Fig. 17. Error surface plots of neural network model with different combination of learning rate and momentum.

Fig. 18. Scatter plot of observed vs. predicted value of four attributes using neural regression: (a) CaO; (b) Al2O3; (c) Fe2O3; (d) SiO2.

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Table 8 Paired sample t-test between observed vs. estimated value of testing data set of neural network model. Paired samples test (paired differences)

CaO Al2O3 Fe2O3 SiO2

Observed Observed Observed Observed

vs. vs. vs. vs.

estimated estimated estimated estimated

value value value value

Mean (%)

Std. deviation (%)2

Std. error mean

95% confidence interval of the difference Lower

Upper

0.18 0.043 0.378 0.31

4.717 1.78 0.942 6.974

0.272 0.103 0.054 0.403

0.716 0.16 0.484 0.484

0.356 0.246 0.272 1.1

4. Ore grade monitoring at face level The image-based method developed for ore grade prediction was applied for ore grade monitoring at mine faces to demonstrate the usefulness of the proposed method in a real life scenario. To this extent, three different face locations were chosen in the mine. Blasted rock samples were collected from each individual face at 2h intervals over a 1-week period. This resulted in the collection of 35 rock samples from each of the faces. The ore grades of these rock samples were determined by chemical analysis following the ASTM standard. The images of the rock samples were then taken and the features were extracted. The image-extracted features were reduced to five principal components, and these PCs were fed to a neural network model to determine the ore grades. The time required for analyzing one image was less than a minute. These grades values were compared with the grades values obtained from the chemical analysis. Fig. 20(a)–(c) shows the comparison between the image-based grade values and the chemical analysisbased grade values for CaO for all three faces considered. One can

t

df

Sig. (2-tailed)

0.661 0.417 6.95 0.77

299 299 299 299

0.51 0.677 0.0 0.44

see from these figures that the grade values obtained from the image-based model are in good agreement with the chemical analysis. It is also noticed that, out of the three faces, the imagebased model relatively produces better prediction in Faces 1 and 2 in comparison to Face 3. This anomaly may be attributed to the presence of a number of overlapping geological structures in that face, resulting in a complex zone. The predictions obtained for the other three grade attributes are also presented in Figs. 21–23. The paired sample t-test was carried out to check the statistical similarities between the image-based values with the values of chemical analysis for all the four grade attributes. The results are presented in Table 9. It can be seen that there is no significant difference in mean values for the image-based values and the values of chemical analysis for the attributes CaO and SiO2. On the contrary, there is a significant difference in mean values of the two methods for the grade attribute Fe2O3 at Faces 2 and 3 and for the grade attribute of Al2O3 at Face 3. This indicates that the imagebased model is unable to produce a reliable estimate for the Fe2O3, as was observed during the model testing phase. However, possible

Fig. 19. Histogram plot of error value of all the four variables: (a) CaO; (b) Al2O3; (c) Fe2O3; (d) SiO2.

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Table 9 Paired sample t-test between chemical analysis and image analysis-based values at 3 different face locations. Paired samples test Mean (%)

Std. deviation (%2)

Std. error mean

95% confidence interval of the difference

t

df

Sig. (2-tailed)

Lower

Upper

Face 1

CaO Al2O3 Fe2O3 SiO2

0.33714 0.02457 0.88750 0.98000

2.087 0.25354 1.632 2.99

0.35288 0.04286 0.27207 0.50687

0.37999 0.11167 1.43983 0.05007

1.05428 0.06252 0.33517 2.01007

0.955 0.573 3.26 1.933

34 34 34 34

0.346 0.570 0.002 0.062

Face 2

CaO Al2O3 Fe2O3 SiO2

1.04286 0.13714 0.14028 0.60571

3.183 0.33477 0.27636 20.754

0.53807 0.05659 0.04606 0.46561

0.05063 0.25214 0.23378 0.34051

2.13634 0.02215 0.04677 1.55194

1.938 2.42 3.05 1.301

34 34 34 34

0.061 0.021 0.004 0.202

Face 3

CaO Al2O3 Fe2O3 SiO2

0.20857 0.10686 0.00029 0.52286

1.81778 0.41961 0.42577 3.185

0.30726 0.07093 0.07197 0.53841

0.41586 0.25100 0.14597 1.61704

0.83300 0.03728 0.14654 0.57132

0.679 1.51 0.004 0.971

34 34 34 34

0.502 0.141 0.997 0.338

failure of the model for the Al2O3 at Face 3 could merely be a fluke, as Face 3 presents a disturbed zone with multiple rock types crosscutting each other. Overall, the image-based model shows encouraging outcomes and can reasonably be applied for ore grade

prediction on a regular basis for the three attributes, CaO, Al2O3 and SiO2. However, for Fe2O3, further study is required to draw any meaningful conclusion for the performance of the image-based model.

Fig. 20. Off-line monitoring of CaO at 3 faces from the limestone case study mine: (a) Face 1; (b) Face 2; (c) Face 3.

Fig. 21. Off-line monitoring of Al2O3 at three benches: (a) Face 1; (b) Face 2; (c) Face 3.

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Fig. 22. Off-line monitoring of Fe2O3 at three benches: (a) Face 1; (b) Face 2; (c) Face 3.

5. Summary and conclusions This study was conducted to enhance the present quality monitoring and control practices in the mineral industry. An image-based grade evaluation system was developed by mapping the image features of individual samples with their respective grades. The images were captured, segmented, and features were extracted from the segmented images. Four hybrid image segmentation techniques were investigated and their performances were compared. Finally, the most suitable segmentation technique was used for subsequent processing of the images. A total number of 189 features were extracted from the segmented rock images. Principal component analysis was carried out for the dimensional reduction of these 189 image-extracted features. Ultimately, five principal components, which captured 95% of the data variance, were used for the grades’ determination from the images using the neural network technique. The effectiveness of the above image-based grade control strategy was tested using a testing data set at the model development stage. The testing results showed that the model was a good predictor for three grade attributes: CaO, Al2O3 and

407

Fig. 23. Off-line monitoring of SiO2 at three benches: (a) Face 1; (b) Face 2; (c) Face 3.

SiO2, However, it did not produce reliable prediction for another grade attribute, Fe2O3. The developed image-based grade evaluation strategy was then applied in a real life application for grade monitoring at three different face locations for a period of 1 week. The grade monitoring studies at the face locations showed that the output generated from the images was in good agreement with the grade values obtained from chemical analysis at Faces 2 and 4, whereas there is no such result obtained at Face 3. This study was conducted on a laboratory scale after collecting data from the case study mine. It is presumed that the same type of image acquisition setup could be developed for actual field implementation. Samples from the faces could be collected and images could be taken in a controlled environment of the proposed image acquisition system. Apart from that, the proposed model is case specific because it was developed by using mine case study sample. Although the developed model might not be applicable to other minerals directly, the methodology is still valid for other mineral deposits as well. Before applying the model to other deposits, the neural network model is required to train with rock sample images of known grade values.

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[31] L. Shafarenko, M. Petrou, J. Kittler, Automatic watershed segmentation of randomly textured color images, IEEE Transaction on Image Processing 6 (11) (1997) 1530–1543. [32] P. Soille, Morphological Image Analysis: Principles and Applications, SpringerVerlag, Berlin, 2003, p. 316. [33] ASTM C25-99: Standard Test Methods for Chemical Analysis of Limestone, Quicklime, and Hydrated Lime, ASTM International, http://www.astm.org/ Standards/C25.htm, 36 pp. [34] I. Olkin, S.G. Ghurye, W. Hoeffding, W.G. Madow, H.B. Mann, Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, Stanford University Press, 1960,, p. 520. [35] S. Mazumdar, A.E. Begley, P.R. Houck, Y. Yang, C.F. Reynolds, D.J. Kupfer, Residual analysis in random regressions using SAS and S-PLUS, Computer Methods and Programs in Biomedicine 58 (3) (1999) 281–282. Snehamoy Chatterjee is a Research Associate in the Department of Mining and Materials Engineering, McGill University. He did his Bachelor and Masters in Mining Engineering in 2000 and 2002, respectively from Bengal Engineering College, India. He completed his PhD in 2007 from Indian Institute of Technology Kharagpur, India. He was a post-doctoral Fellow at the University of Alaska, Fairbanks, USA from 2006–2008. Prior to join in McGill, he was working as a Lecturer in NIT Rourkela, India. His research areas include multipoint and multi-scale geostatistics, vision-based quality monitoring, machine learning algorithm, mine planning and design. Ashis Bhattacherjee is a Professor of the Department of Mining Engineering, IIT Kharagpur, India. He did his BTech in Mining Engineering from ISM Dhanbad, India. He was awarded the MS in Operations Research from Florida Institute of Technology, USA. He received his PhD in Mining and Operation Research from Pennsylvania State University in 1991. He was a Postdoctoral Fellow at the same University for two years. In 1992, he joined the IIT Kharagpur, and was appointed as the Head of the Department during 2003–2006. His current research interests include injury epidemiology, quality control, geostatistics, and computer applications in mining. Biswajit Samanta is currently working as an Assistant Professor in the Department of Mining Engineering, IIT, Kharagpur. He completed his Bachelor in Mining Engineering from Bengal Engineering College. He did his Master and PhD from Indian Institute of Technology, Kharagpur. He worked as a post-doctoral research associate at Oregon health and Science University as well as at university of Alaska, Fairbanks, USA. He was a recipient of DST young scientist award. He is currently serving as an associate editor of SME Transactions, and Journal of Mining Engineering. His research areas include geostatistics, mine planning, and AI applications in mineral industry. Samir Kumar Pal, BTech, MTech, PhD, has been teaching in IIT, Kharagpur, since 1981. He has authored many papers published in Indian and International journals as well as presented papers in conferences held in India and abroad. He received the MGMI Gold Medal for the best paper and the ‘Certificate of Merit’ for a paper published in Journal of Institution of Engineers (India). His areas of specialisation are Geomatics, Rock Mechanics & ground control, and Mine Mechanisation. He has undertaken many projects and received the Sukumar Rakshit Award for outstanding contribution in Mine Stowing and Rock Mechanics.