Determining the fragmented rock size distribution using textural feature extraction of images

Accepted Manuscript Determining the fragmented rock size distribution using textural feature extraction of images

Hadi Yaghoobi, Hamid Mansouri, Mohammad Ali Ebrahimi Farsangi, Hossein Nezamabadi-Pour PII: DOI: Reference:

S0032-5910(18)30836-2 doi:10.1016/j.powtec.2018.10.006 PTEC 13780

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

8 April 2018 28 September 2018 1 October 2018

Please cite this article as: Hadi Yaghoobi, Hamid Mansouri, Mohammad Ali Ebrahimi Farsangi, Hossein Nezamabadi-Pour , Determining the fragmented rock size distribution using textural feature extraction of images. Ptec (2018), doi:10.1016/j.powtec.2018.10.006

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ACCEPTED MANUSCRIPT Determining the fragmented rock size distribution using textural feature extraction of images Hadi Yaghoobi1 , Hamid Mansouri2,* [email protected], Mohammad Ali Ebrahimi Farsangi3 4

[email protected] , Hossein Nezamabadi-Pour [email protected]

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PhD Student of Mining Engineering, Mining Engineering Department, Shahid Bahonar University of Kerman, Iran Associate Professor of Mining Engineering, Department of Mining Engineering, Shahid Baho nar University of

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Associate Professor of Mining Engineering, Department of Mining Engineering, Shahid Baho nar University of

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Kerman, Iran 4

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Kerman, Iran

Professor of Electrical Engineering, Department of Electrical Engineering, Shahid Bahonar University of Kerman,

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Iran *

Corresponding author.

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Abstract

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Fragmented rock size distribution is one of the most important parameters in open pit blasting that can affect the mining and the mineral processing efficiency. For evaluating fragmentation by blasting, digital

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image analysis is a fast and reliable indirect technique. In this study, based on the neural network and features extraction methods, an algorithm was proposed to determine the size distribution of fragmented

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rocks. For this purpose, 226 images of fragmented rocks from various blasts, carried out at Gole-Gohar

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iron ore mine, Iran were used to prepare a dataset. To extract visual features of these images, Fourier transforms, Gabor, wavelet methods and their combinations were used and features extracted considered as the input vectors of neural network. Also, for these images, using the manual mode of Split-Desktop software, F10 to F100 were determined (as the target data of neural network). Then, the results of features extraction methods for 26 test images were compared with the results of auto mode of Split-Desktop. The results obtained showed improvements in the estimation of fragmented rock size distribution using Fourier transform, Gabor and Fourier–wavelet methods with the value of 67%, 57%, and 48 %, respectively. Also, the estimation of fragmented rock size distribution has higher MRE in fine to medium

ACCEPTED MANUSCRIPT particles (F10 -F50 ). Moreover, for F10 -F50 the most improvements with the values of 52%, 40%, and 32 %, are corresponding to Fourier transform, Gabor and Fourier-Gabor methods, respectively. Also, all of the suggested features extraction methods for estimating uniformity coefficient give better results than auto mode of Split-Desktop.

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Key words: Rock fragmentation, Size distribution, Image processing, Visual feature extraction

1. Introduction

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In open pit mining, rock fragmentation by blasting can affect different stages of the production cycle

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[1,2]. Optimal fragmentation can contribute to control and minimize the loading, hauling, crushing, grinding, and processing costs in the mining industry [3-5]. Therefore, it is an important to minimize the

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costs of production [6].

Extensive studies were carried out on the methods of determining the rock fragmentation by blasting.

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These methods include direct (sieving) [1] and indirect methods (counting large particles, consumption of

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explosives in secondary blasting, efficiency of loading machine, delays caused by bridging in the crusher, visual analysis, photogrammetry, and image processing methods) [7-9]. Among these methods, sieving is

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the most accurate one, but it is costly and time consuming that can also disturb the production cycle [8, 9]. One of the common methods in determining the size distribution of fragmented rocks is digital image

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processing technique [7-9]. The results of this indirect method are closer to the reality than the other

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methods [10]. In this method, images are captured from the surface of the muck-pile and then manually or by computer, distribution of fragmented rocks is determined. The main advantage of this method is that it can be used in a wide range without disturbing the production cycle [11]. Image processing, as a technique of measuring fragmented rock size, has been developed by Maerz since 1987 [12]. The earliest image processing system is introduced by Gallagher [13]. In this research work the size distribution of the fragmented particles is determined using a system set up on a conveyor belt. The size distribution of the fragments then evaluates by delineating the particles' edges using a chord sizing method. Nyberg [14] presents an image system scan ning chord size on an edge of the fragmented rock

ACCEPTED MANUSCRIPT image in a muck-pile. Lin et al. [15] use edge detection methods for identification of particles and find an estimate of the sieve size distribution of measured chord lengths taken across the particle. Kemeny [16] applies elliptical approximation to images of rock fragments after using edge detection. Koizumi et al. [17] investigate the problem of partially obscured particles where spherical polymer particles were delineated and circular approximations were fitted on the two-dimensional projections of the detected

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particles' edges. Yen et al. [18] develop a method based on a watershed segmentation algorithm. The

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segmentation result was not that very satisfactory even to well sorted particles with a good background. Since 1997, image processing of fragmented rock particles has become a hot topic of research and a

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number of algorithms have been developed for measuring the size of rock fragments in different applications such as gravitational flows, conveyor, muck-pile and laboratory. Crida and Jager [19]

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develop a machine vision system for rock fragmentation in which the image processing was based on the human visual system (HVS). HVS has a pre-attentive stage and incorporates an attention focus stage. In

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spite of the highly insightful results, computation time was approximately 10 minutes. Wang et al. study

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the split of touched rock particles [20,21]. This algorithm firstly tries to find a pair of cut points (start and end points) on the boundaries of fragmented rock particles and then identifies a desired cutting path or a

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split path using a cost function. Al-Thyabat and Miles [22] use images of separated rock particles to

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evaluate the efficiency of measuring two different dimensions of the particles, resulting in particle size distribution. Also, in order to separate touched particles in images, the watershed algorithm was utilized.

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Thurley [23] employs a morphological edge detection strategy to draw the boundary of limestone particles on a conveyor belt using 3D data. Obara et al. [24] apply mathematical morphology in order to segmentation of micro-cracks. Zelin et al. [25] apply a series of pre-analyzing steps on the images to solve the overlapping problem for coal particles on the conveyor belt. In the first step, the primary image was enhanced using Otsu method. Also, exponential high pass filter and Fourier transform were used in order to improve the images; and then the edges of particles in image were detected by morphological edge detection. Chimi et al. [26] use a method based on a watershed segmentation method in order to detect clods in the soil; that is also applicable for remote sensing. In 2006, Al-Thyabt et al. [27] focus on

ACCEPTED MANUSCRIPT the difficulties occurred in analyzing the images of coal particles on a moving conveyor belt, such as, camera location, overlapping of particles, image blurring, conveyor belt speed, dust generation, and the treatment. After image analysis and using a Gaussian filter for the image enhancement, the coal particles’ boundary was determined manually. Sereshki et al. [7] propose an algorithm for automated determination of the rock particles’ boundary using a Sobel filter and mathematical morphology.

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The aforementioned studies were based on edge detection of particles to determine the size distribution of

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fragmented rocks.

Another approach is based on neural network and pattern recognition (machine learning) [28]. The major

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obstacle in applying neural networks for pattern recognition is the excessive number of inputs [29]. Luerkens [30] and Plansky et al. [31] reduce the number of inputs to the neural network by taking the

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Bessel Fourier transform of digitized images. Bootlenger et al. proposed the problem of rotational invariance by averaging the concentric "rings" of two-dimensional Fourier transformation. Averaged

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Fourier coefficients were used as inputs to a neural network to determine the size distribution of particles

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of digitized images. Hand- sorting and sizing of fragmented rocks gave the training sets [32]. Barron et al. propose a simulated neural network to recognize fragmented rock size classes from muck-piles images in

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a large open pit mine. Features were extracted from the digitized image using two dimensional Fast

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Fourier transformation coefficients. A back propagation algorithm was used to train the neural network. Inputs and outputs of neural networks were ring cut profiles of Fourier transforms and class size

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distribution, respectively [29]. Jones and Maxwell [33] investigate the use of neural networks to predict the size distribution of rock fragments. In this case, profiles of fragments were processed and reduced to a feature vector using fractal geometry information. Parkin and Calkin [34] use a laser system to map edge features of particles as they fall behind a sensor plane in order to determine the particle shape and to estimate size distributions. In order to determine shape descriptions, geometric and fractal features of the digitized edge profile were used as input to a neuro-fuzzy classifier. While this investigation improved overall particle characterization, the system requires particles to be sorted into controllable sizes, typically less than 75 mm. Petersen et al. [35] use a textural approach based on the use of the variance and range

ACCEPTED MANUSCRIPT operators to estimate the average particle size and identify ore type on industrial ore feed systems. Tessier et al. [36] present an online automatic ore composition estimator mounted on a conveyor belt in a laboratory. Color and texture features based on wavelets and principal component analysis (PCA) was used for training three different support vector machines (SVM) to classify five rock types into three different classes. Murtagh and Starck use up to fourth order moments of wavelet transforms to classify

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images of mixture aggregate [37]. Goncalves et al. [38] present a study for classification of macroscopic

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rock texture based on a hierarchical neuro-fuzzy model.

Chatterjee et al. select a segmentation algorithm from several tests and then applied morphological,

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textural, and color feature extraction. PCA was applied to reduce the feature vector and a neural network was used for classification [39,40]. Singh et al. develop an application of image processing on

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classification of basalt rock samples where parameters are inputs to a neural network for classification [41]. Also, estimation of muck-pile size distribution is investigated by [11,22,35,42].

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Perez et al. propose a method to improve rock classification using digital image analysis and feature

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selection based on mutual information and a voting process to take into account boundary information. Their proposed method includes feature selection and texture and rock color feature extraction and uses

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SVM for classification. The original image was divided into sub-images that are assigned to one class

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based on the selected color and texture features using a set of classifiers in cascade. Post-processing step included rock segmentation based on the watershed algorithm; and a voting process based on this

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information that enhanced rock classification [43]. A neural network based soft sensor using image analysis was proposed by Ko et al. [44]. Based on the captured surface images of muck-piles, the uniformity was characterized and the neural network models for particle sizes were generated using the uniformity and an initial estimate of particle size from software WipFrag. A nonlinear model was built to provide improved accuracy in particle size estimation. The neural network was trained using the Levenberg Marquardt (LM) algorithm. Hamzeloo et al. [45] extract a number of the most frequently used size features from the segmented images to estimate the particle size distribution on an industrial conveyor belt in crushing circuit of a copper concentrator using PCA and neural network techniques. An

ACCEPTED MANUSCRIPT investigation for remote rock lithological classification is proposed by Perez et al. [46]. The proposed method was based on dividing the image into sub-images and Gabor feature extraction using five different spatial scales with eight orientations applied to each sub-image. Then, each sub-image was classified using an SVM classifier. Each rock was classified using contour information making all subimages that fall within the contour vote for the rock class.

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In many cases, an extracted feature alone cannot have acceptable performance. Therefore, another

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approach is based on Feature fusion techniques. Feature fusion is the process of combining the specific extracted feature vectors to obtain a single feature vector, which is more discriminative than any of the

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input feature vectors [47]. Sudha et al. [48] study feature extraction using 2-D fast Fourier transform, DWT, the Local Binary Pattern (LBP) and features fusion techniques for Iris. A design-based texture

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feature fusion using Gabor filters and co-occurrence probabilities is proposed by Clausi and Deng [49]. An investigation on data fusion, feature extraction, feature selection and neural network classification for

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multi-source remote sensing and geographical data is proposed by Ulfarsson et al. [50]. The considered

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feature extraction method is based on the discrete wavelet transformation (DWT) [50].

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A summary of these studies are presented in Table 1.

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Based on the above studies, the advantages and disadvantages of edge detection and machine learning based methods are summarized in Table 2.

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In this research, based on Feature fusion techniques and neural networks, a new algorithm is developed to determine fragmented rock size distribution. 2. The fragmented rock size distribution software packages Digital image processing algorithms and software packages have been developed to determine the size distribution of rock particles since 1990 and have actually found a world acceptance in the mining and mineral processing industries. In rock engineering, many computer software packages have been developed based on image processing, which make a rapid blast fragmentation distribution assessment [7,9,51]. Some of these 2D image

ACCEPTED MANUSCRIPT processing software packages are IPACS, TUCIPS, FragScan, CIAS, GoldSize, WipFrag, Split-Desktop, PowerSieve and Fragalyst [7-9]. Split-Desktop, WipFrag, FragScan, and GoldSize are the most popular software packages for performing the size distribution analysis of the rock particles [7,9,52].

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2.1 Split-Desktop software

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Split-Desktop is the most commonly used software in determining fragmented rock size distribution and

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is based on the 2D image processing. It uses images captured with two objects that are used as scale. After the scaling process, the software delineates grayscale images automatically with an image filter; and

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then size distribution of fragmented rock is determined [7,16,53]. Girdner describe steps of fragmented

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rock image analyses as equalizing the gray levels, Sobel edge detection, binary conversion using threshold, the distance transform on the edge of the binary image, and modifying the watershed

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segmentation [54,55]. Split-Desktop creates the best-fitted elliptical on the detected area and calculates the size of each particle. Then, small and large elliptical diameters are considered as an input to a

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correction function [53]. In this software, delineation of images can be done manually or automatically.

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However, both modes have the same algorithm. In manual mode, the boundary between rock particles is determined by the user; while in automatic mode, due to the contrast in the image, the boundary is

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automatically [9] recognized by software. In the automatic mode, the processing speed is higher while in

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the manual mode, the precision is greater [7].

3. The proposed algorithm The proposed algorithm is based on pattern recognition and machine learning techniques. The main purpose is the extraction of appropriate and discriminator features and then applying neural networks to determine the fragmented rock size distribution. The structure of the proposed algorithm is shown in Fig.1. In this algorithm, the steps of sampling, image acquisition, preprocessing and image enhancement, extraction of scales, elimination of perspective and normalization are similar to classical image analysis algorithms.

ACCEPTED MANUSCRIPT 3.1 Visual features extraction When the input data to an algorithm is too large to be processed and it is suspected to be redundant, then it can be transformed into a reduced set of features (also named a feature vector) [56,57]. For example, an image with dimensions of 800 × 900 pixels is considered; If all pixels to be included in the calculations, 720000 pixels must be processed, but by extracting representative features, it can be presented by a vector

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1 × n, where n is usually a number less than 100 and subsequent calculations are carried out on this

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vector.

In this section, features of muck-pile images are extracted and feature vectors are obtained by various

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methods. The more discriminant extracted feature is preferred.

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3.1.1 Fourier transform

The discrete Fourier transform of a function (image) f (x, y) of size M×N and its inverse is given as

 j2π (  ) 1 M 1 N 1 M N F(u, v)  f(x, y)e  MN x  0 y  0

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follows [48, 58]:

 j2π (  ) 1 M 1 N 1 M N F(u, v)e  MN u  0 v  0

(2)

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, u, x=0, 1, 2… M-1 and v, y=0, 1, 2… N-1.

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Where j=√

(1)

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ux vy

f(x, y) 

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ux vy

To extract the feature vector of fragmented rocks image in frequency domain using Fourier transform, at the first, the image is resized to equal size (800×800), then the Fourier amplitude is extracted and image is divided into 20 rings, using concentric circles. Then the mean and standard deviation are calculated in each ring [30,31]. The FV feature vector with 40 members for each image is extracted as follows: FV = [μ 1 , …, μ 20 , σ1 , …, σ 20 ]

(3)

ACCEPTED MANUSCRIPT Where μ i and σi are mean and standard deviations of the Fourier coefficients amplitude in ring i. If the obtained feature is more unique, the ability to recognize images is more. The feature vectors of all images in dataset (200 images) were extracted. An example of the concentric rings on the Fourier transformed image is shown in Fig.2. The logarithm of the mean of each concentric ring in Fourier transformed image

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is shown in Fig.3.

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3.1.2 Wavelet transform

Wavelet is a wavelike with limited time and zero mean and an unusual and asymmetric waveform. In the

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wavelet analysis, the desired signal decomposes to shift and scaled signals of main wavelet signal. Changing the scale means the press or stretch the signal. To describe changes in scale, a coefficient called

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scale factor is used. Smaller scale factor, causes more compaction of wavelet signal. Shifting signal also can be expressed by the delay or acceleration of signal. For the larger scale factor, wavelet signal is

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longer, changes of details are slow and frequency is low and vice versa. In most signals, low frequencies

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have often an important part of signal information and this part of the signal, in fact, is the identity of the signal. The high frequencies, also, express the detailed information and minor changes of signal. The

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wavelet analysis includes approximation and details. The approximation is included in large-scale and

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low -frequency signal components and details are included in small-scale and high-frequency signal components. In the initial stage of filtering, the original signal passes through two complementary filters,

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being decomposed into two signals. Decomposition can be done in the form of consecutive stages [48, 58]. This process is shown in Fig.4. The result will be as a tree, named wavelet decomposition tree. Theoretically, consecutive stages of decomposition can be infinitely done, but in reality the decomposition continues until obtaining specific details of the signal; and the number of steps is determined based on the nature of the signal and the criteria such as entropy.

ACCEPTED MANUSCRIPT Extensive works have been carried out on wavelet analysis and various forms of wavelet were proposed through studies such as Haar, Daubechies, Biorthogonal, Coiflets, Symlet, Morlet, Mexican Hat, and Meyer [58].

Discrete wavelet transform of a signal f (t) can be derived from a continuous wavelet transform. The

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scales and positions are discretized based on powers of two while the signal is also discretized. The

(5)

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a, b  ; a  0

(4)

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1 t  b ψ a  a 

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 n  kb a j   1 ψ  0 o DWT (j, k)   f(n)ψ   f j j a a n     0 0 ψab (t) 

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resulting expression is shown in the Eqs. (4) and (5) [58].

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dilation (a) and translation (b).

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Where j, k, nZ and a0 > 1 and  is the mother wavelet with two characteristic parameters, namely,

In this study, considering previous works carried out in the field of wavelet analysis of rock images, Haar

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wavelet type was used and decomposition was performed up to the fifth level. Then, using wavelet

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analysis, the mean and standard deviation of horizontal, vertical, and diagonal details and the mean and standard deviation of the entire image were calculated as a feature vector with 32 members. The components of details and approximations of wavelet decomposition in five levels and histogram plots of original image, details and approximations, for a fragmented rock image are shown in Fig.5.

3.1.3 Gabor filters

In image processing, a Gabor filter, named after Dennis Gabor, is a linear filter used for texture analysis. It means that it basically analyses whether there are any specific frequency content in the image in

ACCEPTED MANUSCRIPT specific directions in a localized region around the point or region of analysis. Frequency and orientation representations of Gabor filters are claimed by many contemporary vision scientists to be similar to those of the human visual system. It has been found that this filter is particularly appropriate for texture representation and discrimination. In the spatial domain, a 2D Gabor filter is a Gaussian kernel function modulated by a sinusoidal plane wave. A set of Gabor filters with different frequencies and orientations

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may be helpful for extracting useful features from an image [48, 58].

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The two-dimensional (2D) Gabor function and its Fourier transform are calculated as follows 58 :

1 1 x 2 y2 )exp(- ( 2 + 2 )cos(2πu0 x) 2πsxs y 2 sx sy

F(u,  ) =

2  2     (u - u ) 2   (u  u ) 2  1  exp 1  2 0   2    exp 1  2 0   2   2 s   s    2  s u  2  s u

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s 

1 2s y

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1 , 2sx

(7)

(8)

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su 

(6)

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f(x, y) = (

Where u0 is the central frequency of sinusoidal wavelet in x direction, s x and sy are the standard deviation

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of Gaussian function in x and y directions and s u and sν are the standard deviation of Gaussian function in u and ν directions. Gabor filters are obtained by expansion (scale) and rotation (direction) of the main

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wavelet (f (x, y)), as below [58]:

a > 1 , m, n = integer

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fmn (x, y) = a - mf(x, y),

(9)

x  = a - m (xcos q + ysin q)

(10)

y  = a - m (-xsin q + ycos q)

(11)

q

n k

n  0,1,..., k  1

m  0,1,...s  1

(12)

Where fmn, is scaled and rotated f(x, y), a, is scale coefficient, k, is number of rotations, s, is number of scales and x´ and y´ are scaled and rotated coordinates.. A 2D Gabor function is shown in Fig.6.

ACCEPTED MANUSCRIPT Gabor wavelets created by 4 expansion and 6 rotation of the main wavelet are shown in Fig.7.

In this research, the images are resized to 800 × 800 pixels, then filters of Gabor filter bank that already has been made, applied to images. In this filter bank, to create a two-dimensional Gabor filter with 800 × 800, five scales (0.4, 0.2, 0.1, .05 and 0.025) and six directions (0, 30, 60, 90, 120 and 150) are used and

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a, su and sν are 0.5, 0.65 and 0.35. Therefore, an array with 6 ×5 elements is created. By applying any of

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the Gabor filters (with 4 × 4 down sampling factor in the rows and columns) on images, the filtered image

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was obtained [59]. For each of the filtered images, mean and standard deviation were calculated and with the mean and standard deviation of the entire image, a feature vector with 62×1 members was extracted

  f

mn

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mn

(x, y) dxdy

(13)

mn



2  ( | f mn (x, y) | μ mn ) dxdy

(14)

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σ

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μ

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from the image as follows:

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3.1.4 Features combination

Data fusion technology is one of the emerging technologies of data processing. The three levels of information fusion are pixel level (low-level fusion), feature level (intermediate-level fusion), and decision level (high-level fusion) [60]. The advantage of the feature level fusion is obvious. Different feature vectors extracted from the same pattern always reflects the different characteristic of patterns. By optimizing and combining these different features, it not only keeps the effective discriminant information of multi-feature, but also

ACCEPTED MANUSCRIPT eliminates the redundant information to certain degree. This is especially important to classification and recognition [60-63]. In this research the combination of before mentioned extracted features was used. In Table 3, extracted feature vectors (single and combination of features) are presented, which were used as inputs to the neural network.

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After extracting the visual features of images and obtaining the feature vectors, the images dataset is

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prepared. 3.2 Dataset of images

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226 images of fragmented rocks from various blasts, carried out at Gole-Gohar iron ore mine, Iran were

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used to prepare a dataset. The rock type and number of images for each type are presented in Table 4.

For these images, using different types of feature extraction methods, the feature vectors were extracted

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and considered as inputs of the supervised neural network. Also, for these images, using the manual mode of Split-Desktop software, F10 to F100 were determined (as target data of neural network). Basic

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descriptive statistics of F10 to F100 are given in Table 5. Also, the lognormal histogram plot of fine factors

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(percentage of fine particles) of F10 to F100 of images is shown in Fig. 8. This graph shows the frequency of occurrence of fine particles in images and represents the combination of images in terms of fine and

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large particles. Lognormal distribution has been widely used in many fields. It is suitable to describe the

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distributions with skewed curves (also called skew distribution) [64].

An example of an image of fragmented rocks and delineated image by manual mode of Split-Desktop software are shown in Fig. 9. Also, the corresponding distribution curve is presented in Fig. 10.

3.3 MLP neural network to determine fragmented rock size distribution In this study, feed forward neural network (supervised) with back propagation learning algorithm was used to determine fragmented rock size distribution. LM learning function, using 200 image dataset for which features extracted by different methods were used as inputs and F 10 -F100 as outputs, was applied to

ACCEPTED MANUSCRIPT train the network. To achieve the best possible results, neural network was formed and tested with a number of different neurons for input, hidden and output layers, and different number of hidden layers. The number of hidden layers and neurons in the hidden layers change according to the problem to be solved. The number of input and output neurons is the same as the number of input and output variables. In this research, multi-layer network architecture with two hidden layers between input and output units

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was applied. In order to train, validate, and test the neural network, the data portions are 70%, 15%, and

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15%, respectively. To reach an appropriate architecture, MLP networks were examined for all of the suggested features extraction methods and optimum model for each method was determined. The

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structure of MLP network is shown in Fig. 11.

To determine the optimum network, RMSE was calculated for various models as follows [58]:

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1 N  (Ti  Oi )2 N 1

(15)

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RMSE =

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Where Ti , Oi and N represent the target, the predicted output and the number of output data respectively.

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Examples of the networks examined are shown in Table 6.

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After establishing and implementing the neural network, out of 226 image datasets, 26 images were used as test data and the results were evaluated. An example of cumulative size distribution curves of

Fig. 12.

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fragmented rocks, using different methods of visual feature extraction for an image of dataset, is shown in

4. Evaluation of results

Mean relative error (MRE) (Eq. 16) was used to compare the results of different methods of visual feature extraction with the results obtained, using the manual mode of Split-Desktop MRE = (

100 A -F n ) t 1 ( t t ) n At

ACCEPTED MANUSCRIPT software [65].

(16)

Where, At is the actual value (F10 to F100 in the manual mode of Split-Desktop), Ft is the obtained value

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(F10 to F100 in the proposed features extraction methods and auto mode of Split-Desktop) and n is number

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of sizes (here n=10). The MRE for 26 test images for different features extraction methods and auto mode

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of Split-Desktop are shown in Table 7.

S M  100 S

was used.

(17)

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M

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IM=

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To compare the results of suggested methods with the results of Auto mode of Split-Desktop, the Eq.(17)

Where, IM is improvement in the results (%), S and M are the average value of MRE of Split-Desktop

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auto mode and the suggested methods respectively.

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As it can be seen in Table 7, the most improvements in the estimation of fragmented rock size distribution are achieved for the Fourier transform, Gabor and Fourier–wavelet methods with the value of 67%, 57%,

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and 48 %, respectively.

Also, the MRE for F10 to F100 of test images were compared as shown in Fig. 13.

As it can be observed from Fig. 13, the estimated fragmented rock size distributions have higher MRE in fine to medium particles (F10 -F50 ). Also, the improvements in the estimation of fragmented rock size distribution using different features extraction methods relative to auto mode of Split-Desktop for F10 -F100 are given in Table 8. As it can be seen, for F10 -F50 the most improvements of estimations are achieved for

ACCEPTED MANUSCRIPT the Fourier transform, Gabor, and Fourier-Gabor methods with the value of 52%, 40%, and 32 %, respectively.

Also,

using

suggested

model

by

Chung

and

Katsabanis

(CK

model)

[66,67]

(Eq.

(18)), uniformity coefficient (n) for different feature extraction methods and auto mode of Split-Desktop

(18)

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0.842 Ln F80 - Ln F50

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n=

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was calculated and compared with the manual mode of Split-Desktop values.

Where, F50 and F80 are the sizes at which the passing percent is 50% and 80%, respectively.

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The average MRE of uniformity coefficient estimations for different feature extraction methods and auto

M

mode of Split-Desktop are given in Table 9.

ED

As it can be seen in Table 10, all of the suggested features extraction methods for estimating n, give better

PT

results than auto mode of Split-Desktop.

CE

5. Conclusions

In this study, based on the neural network and features extraction methods, an algorithm was proposed to

AC

determine the size distribution of fragmented rocks. The results obtained showed that the most improvements in the estimation of fragmented rock size distribution were achieved, using Fourier transform, Gabor, and Fourier-wavelet methods with the value of 67%, 57%, and 48 %, respectively. Also, the estimation of fragmented rock size distributions has higher MRE in fine to medium particles (F10 -F50 ). Furthermore, for fine to medium particles F10 -F50 , Fourier transforms, Gabor, and Fourier Gabor methods with the values of 52%, 40%, and 32 %, respectively, have the most improvements in the

ACCEPTED MANUSCRIPT estimation of the fragmented rock size distribution. Also, all of the suggested features extraction methods for estimating uniformity coefficient give better results than auto mode of Split-Desktop.

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ACCEPTED MANUSCRIPT Table 1 A summary of the presented studies in the field of fragmented rock size distribution, lithological classification, and

M aterial

Application

Location

Gallag her

1976

Fragmented rock

Size distribution

Conveyor belt

1982

Fragmented rock

Size distribution

M uck-pile

1986

Fragmented rock

Size distribution

M uck-pile

1988

Fragmented rock

Size distribution

M uck-pile

Bootli nger

1992

Fragmented rock

Size distribution

Lin et al.

1993

Fragmented rock

Barro n et al.

1994

Fragmented rock

Keme ny

1994

Yen et al.

Peters en

M

ED

PT

M uck-pile

Size distribution

M uck-pile

Size distribution

Open pit mining

Fragmented rock

Size distribution

M uck-pile

1998

Fragmented rock

Size distribution

M uck-pile

1998

AluminaSilicate Geopolymer, Gold

Ore type characterizati on and particle size estimation

Industrial conveyor belts

CE

Luerk ens Norbe rt et al.

AC

Nyber g

M ethod

M ain results and comments

Delineating the particles' edges using a chord sizing method

Not reported

US

Year

Instead of segmenting, this method used to simplify the analysis to meet speed and memory limitations Reduced the number of inputs to the neural network by taking the Bessel Fourier transform Particles were segmented, then used a number of reconstruction techniques to further delineate particles, which are only partly outlined during the first step Rotational invariance Computational advantages in by averaging the solution speed. Neural concentric "rings" of networks were trained and two-dimensional accuracy was 98% Fourier transformation The chord lengths are Edge detection methods statistically related to and measuring chord stereological probabilities, lengths taken across the which yield dimensional particle results Takes two dimensional FFT, takes "ring" cuts The neural network was able as input nodes or to generalize and identify the pattern recognition size classification with 97% features, trains the of accuracy neural networks Size estimation of partially Elliptical approximation obscured particles shows was applied to images good agreement with size of rock fragments after measured by the sieve using edge detection analysis The segmentation result was A method based on not that satisfactory even to watershed segmentation well sorted particles with a algorithm good background An image system scanned chord-length on edge of fragmented rock

AN

Refere nce

CR

IP

T

ore grade estimation.

A textural approach (the use of variance and range operators) was investigated

Average error of 7.1% in the estimation of mean particle size

ACCEPTED MANUSCRIPT

Fragmented rock

On the conveyor belt

Natural rock images

Rock classification

-

2006

Ferruginous Indian manganese ores

Rock classification

M uck-pile

Linek

2007

Basalt, lapilli tuff and breccia

Rock classification

Kaarti nen and Tolon en

2008

Pyhäsalmi mine in Finland

Non-invasive particle size analyses

M urta gh and Starck

Fragmented rock

Gonca lves

2009

Gneiss, basalt, diabase, and rhyolite

Singh

2010

Thin sections of different basalt

1

AC

CE

2008

Thurle y

2011

Limestone particles

M

Borehole wall images

ED

Singh and Rao

AN

2005

PT

Lepist o

Lithological classification

Aggregate mixture grading

Classification of macroscopic rock texture Classification of rock textures Coarse particle size distribution

For the testing set, the resulting error is smaller than 3%

T

2001

Error of 10% in splitting and identifying touched rock particles

IP

Casali

Conveyor belt

CR

1998

Split and identify touched rock particles

US

Wang

Turmaline Breccia, Porphyritic Dykes Dacitic Diatreme Granodiorites Andesite

Polygonal approximation; classifies concave points; split large clusters into simple clusters; finds the candidates of start and end points; use a supplementary cost function Segmentation, feature extraction, feature selection by genetic algorithms, neural network classificatory Applies Gabor filtering to different color spaces for the classification of natural rock images that are used in bed rock investigations Histogram analysis in the RGB color space, combined with textural analysis, based on the gray level cooccurrence matrix and edge detection

Standard conveyor belt

In the laboratory

In the laboratory In the laboratory

On a conveyor belt

Improvement of the classification of natural rock texture images by combining the color information to the texture description

Not reported

Combined Haralick features and wavelet analysis based on resistivity patterns

The combined classification based on Haralick features and WTA improved classification up to a level of 98%.

Based on a combination of a belt weighed and a 3D laser scanner

The average error is around 3%.

Up to fourth order moments of wavelet transforms was used

NFHB-class1

27 extracted numerical parameters are inputs to a neural network A morphological edge detection strategy was employed to draw the boundary of limestone particles on a conveyor belt using 3D data

Neuro-fuzzy hierarchical class model based on binary space partitioning (NFHB-class)

Taking the second, third, and fourth moments as features, at multiple resolution scales, may enhance the discrimination between images For all rock classes, the NFHB-class method achieved a percentage of correct hits over 73% 92.22% accuracy of automatically identification Overestimates the amount of <40mm size class in the 40– 70 mm products by about 10%, and underestimates the cumulative amount in the 20– 40mm product by about 25%

ACCEPTED MANUSCRIPT

Particle size distribution

Randomly distributed over a flat tray

2012

Gravel and cobble, size varies from 2 to 20 cm

3D size distribution and shape of coarse particles

Non-touch particles

2014

Copper concentration

Size distribution

Industrial conveyor belt in crushing

Perez et al.

2015

Dry and wet rock (nickel and copper)

Rock lithological classification

Seresh ki et al.

2016

Fragmented rock

Tafess e

PT

ED

M

Hamz eloo

In the laboratory

Not reported

There were substantial differences between size distributions obtained from various size measured

Improvements in classification accuracy, between 8.3% and 26%, relative to previously published results Error of 30% in estimation D80

AC

CE

Size distribution

On a conveyor belt

R2 of the model prediction for D50 is 79.59%, lower than those for D 75 and D90

T

2011

Ore particles from nickel mine

Koand Shang

The RM SE2 on rock composition classification decreased 8.8% by using voting method with the automatic segmentation with respect to direct sub-image classification. The RM SE decreased 29.5% using a mixture of dry and wet rocks

IP

Conveyor belt

CR

Ore grade estimation

US

Nickel mine contain five ore types

AN

2011

Perez

Extract and select features based on rock color and texture, and using rock boundary information to improve classification performance by a subimage voting scheme and use of SVM The uniformity of particles was characterized and the neural network models were generated (using the uniformity and an initial estimate of particle size from WipFrag©) The size and shape of the particles were processed using GID 3 program. This image analysis program produced different kinds of output images Extraction a number of the most frequently used size features from the segmented images using PCA and neural network Gabor filters were used to extract features from each sub-image. Each sub-image was classified into a lithological class using SVM Sobel filter and mathematical morphology

Table 2 Advantages and disadvantages of edge detection and machine learning based methods. Method Advantages Disadvantages Based on Often these methods deal with some problems such as shadow, No need for comprehensive edge dust, overlapping of particles, and the level of light reflected in training sets detection particles of rock fragments

2

Root mean square error Glow in the dark (GID)

3

ACCEPTED MANUSCRIPT

Neural networks can be quickly trained to recognize size distribution

IP

AN

Highly accurate results if used with comprehensive training set

Need to sort and determine the boundary of fragmented rock particles to provide training sets There are no specific rules or instructions for network design for an optional use With regard to modeling issues, it is simply not possible to understand the physics by using the neural network Network training may be difficult or even impossible It is simply not possible to predict the future function of the network (generalization)

CR

Reducing the number of inputs to the neural network will lead to a large increase in the computational speed

Limitation of the number of inputs to the neural network

US

Based on machine learning

T

The potential of developing image processors based on neural networks that recognize the size distribution in real-time

In most cases, the segmentation results are not that satisfactory due to the fact that the edge particles are not closed curves and therefore wrong edges are formed Common algorithms cannot be used to separate the rock particles that are being touched with each other A neural network can only detect the size distribution of rock particles in images, based on the closest distribution of size used in the training sets The accuracy of the results depends on the size of the comprehensive training sets, which includes all the distributions of probable dimensions that may be observed on the field

M

Table 3 Extracted feature vectors (single and combination of features) as inputs to the neural network. Feature extraction

Number of features

M ean and standard deviation of each ring

40

Wavelet

M ean and standard deviation of horizontal, vertical, and diagonal details and the

30+2

Gabor

mean and standard deviation the entire image M ean and standard deviation of 30 filters (fiveofscales and six directions), and the

ED

Data type

Fourier - Gabor

60+2

mean and standard deviation of the entire image 72 Combine two features

102 94

AC

Wavelet- Gabor

CE

Fourier - Wavelet

PT

method Fourier transform

Table 4 Type of fragmented rocks and number of images for each type. Number of Images 75 4 56 13 52 18

Rock Type Hematite Hematite and magnetite Magnetite Amphibole Quartz schist Gneiss

ACCEPTED MANUSCRIPT 8

Sand and gravel

19.7 m32.3 (in) 58.1 65.6 71.7 77.2 82.4 87.7 93.0 103.6

2.0 (in) 4.2 6.1 8.0 9.8 11.7 13.6 15.9 18.9 24.5

Media

Skewnes

7.1 (in) 26.6 53.8 76.6 101.1 131.1 164.7 206.3 261.8 350.6

132.5 (in) 123.9 120.4 109.8 103.0 98.2 94.2 90.3 85.6 76.5

1.2 n 2.3 3.7 (in) 5.3 7.0 8.7 10.3 11.8 14.2 19.1

3.4 s 3.2 3.6 (in) 3.2 2.9 2.7 2.5 2.4 2.3 2.1

2.674 Dev 5.2 7.3 (in) 8.8 10.1 11.5 12.8 14.4 16.2 18.7

Table 6 Examples of the networks examined. Transfer function (hidden layer1,2, Output layer)

1

TANSIG- TANSIG- TANSIG

2

LOGSIG- TANSIG- TANSIG

US

No

T

0.01 m0.01 (in) 0.01 0.02 0.01 0.03 0.2 0.9 2.5 5.1

C-variation

IP

F10 (%) F20 F30 F40 F50 F60 F70 F80 F90 F100

Variance

CR

Table 5 Basic descriptive statistics of F10 to F100 of dataset. Passing Minimu Maximu Mean St-

M odel

RM SE

40-15-10-10

1.628

40-15-10-10

2.27

LOGSIG- LOGSIG- TANSIG

40-15-10-10

2.65

4

TANSIG- LOGSIG- TANSIG

40-15-10-10

2.54

5

TANSIG- TANSIG- PURELIN

40-15-10-10

3.13

AN

3

LOGSIG- LOGSIG- LOGSIG

40-15-10-10

5.51

PURELIN- TANSIG- PURELIN

40-15-10-10

7.56

8

TANSIG – TANSIG- TANSIG

40-10-10-10

2.504

9

LOGSIG- TANSIG- TANSIG

40-10-10-10

2.72

10

LOGSIG- LOGSIG- LOGSIG

40-10-10-10

6.32

11 12

TANSIG- TANSIG TANSIG- TANSIG

40-10-10 40-15-10

3.61 3.36

CE

PT

ED

M

6 7

Table 7 The MRE for test images for different features extraction methods and auto mode of Split-Desktop.

1 2 3 4 5 6 7 8 9 10 11 12 4

Fourier transform

Gabor

Fourier Wavelet

Wavelet

Auto SplitDesktop

GaborWavelet

Fourier Gabor

0.5 0.5 0.6 0.5 0.7 0.7 0.3 1.2 0.6 0.3 0.5 0.4

0.47 0.3 0.68 0.29 0.15 0.63 0.27 4.31 0.12 0.22 0.26 0.28

0.3 0.4 0.3 0.3 0.3 1.3 0.3 4.2 0.2 0.4 0.7 1.3

0.41 0.19 3 0.23 0.24 0.24 0.62 8.07 0.13 0.32 1.99 0.63

0.213 0.444 0.184 0.447 0.745 0.525 0.859 7.117 0.151 0.813 4.852 0.383

0.5 0.4 2.8 0.3 1.5 2 1.3 0.9 0.3 0.5 2.6 0.3

0.5 0.6 1.5 0.6 0.6 0.2 1.2 3.9 0.4 0.4 0.6 0.2

AC

Image No.

Standard deviation

ACCEPTED MANUSCRIPT 0.45 0.44 6.81 0.21 0.35 0.71 0.18 0.7 1.19 0.21 0.1 0.18 0.24 0.31 1.08

St-Dev

0.29

0.93

1.23

1.98

IM (%)

67

57

48

28

2.066 0.628 12.32 0.226 1.069 0.47 0.099 1.273 2.04 0.481 0.234 0.526 0.418 0.455 1.50

0.8 0.4 3 0.1 0.4 1.5 0.4 0.6 0.3 0.1 0.5 0.2 0.5 0.6 0.87

0.4 0.5 3.1 0.4 0.3 1.8 0.8 0.6 1.5 0.2 1 0.2 0.1 0.5 0.84

2.71

0.85

0.9

-

42

44

T

0.5 0.4 5.4 0.1 0.2 0.2 0.3 0.9 0.5 0.6 0.4 0.2 0.3 0.5 0.79

IP

0.64 0.61 2.96 0.04 0.19 0.74 0.34 0.68 0.4 0.82 0.32 0.14 0.31 0.75 0.65

CR

0.1 0.7 1.2 0.1 0.5 0.5 0.2 0.6 0.3 0.7 0.7 0.1 0.2 0.2 0.50

AN

US

13 14 15 16 17 18 19 20 21 22 23 24 25 26 M ean

Table 8 The improvements in the estimation of fragmented rock size distribution using different features

F10 88 76 39 71 83 64

F20 76 65 27 58 52 70

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Results improvement (%) F30 57 41 18 26 27 47

F40 34 18 19 0 0 9

F50 3 1 0 0 0 0

Mean 52 40 20 25 11 32

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Fourier transform Gabor Wavelet Wavelet- Fourier Gabor -Wavelet Fourier- Gabor

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Method

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extraction methods for F10 to F50.

Desktop.

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Table 9 The average MRE of uniformity coefficient estimations for different methods and auto mode of Split-

M ethod

Average M RE of n

IM (%)

Fourier Transform Gabor Wavelet Fourier - Gabor Fourier -Wavelet Gabor-Wavelet Auto Split- Desktop

0.29 0.26 0.4 0.31 0.23 0.37 0.6

51 56 34 48 61 39 -

Fig. 1. The structure of the proposed algorithm to determine the fragmented rock particles' size distribution.

ACCEPTED MANUSCRIPT Fig. 2. An example of the concentric rings on the Fourier transformed image. Fig. 3.The logarithm of the mean of each concentric ring in Fourier transformed image. Fig. 4. Wavelet decomposition tree [Error! Reference source not found.]. Fig. 5.a. The components of details and approximations of wavelet decomposition in five levels, for a fragmented rock image, b. Histogram plots of original image, details and approximations

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Fig. 6. Two-dimensional Gabor function [Error! Reference source not found.].

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Fig. 7. Gabor wavelets created by expansion and rotation of the main wavelet [Error! Reference source not found.].

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Fig. 8. Histogram plot of fines of all dataset images.

Fig. 9.a. An image of fragmented rock, b. Delineated image by manual mode of Split-Desktop software.

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Fig. 10. The corresponding distribution curve of image in Fig. 9.a. Fig. 11. The structure of MLP network.

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Fig. 12. Size distribution curves of fragmented rock, using different methods of visual features extraction.

M

Fig. 13. Comparing the MRE of different features extraction methods with auto mode of Split -Desktop for F10 to F100.

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Graphical abstract

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An algorithm to determine the size distribution of fragmented rocks is proposed. This algorithm is based on neural network and visual feature extractions methods. The features extraction methods are Fourier, Gabor, wavelet, and their combinations. The input and target are features and F 10 to F100 (manual mode of Split-Desktop). The suggested methods, give better results than auto mode of Split-Desktop.

AC

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Highlights

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