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Real-Time Measurement of the Size Distribution of Rocks on a Conveyor Belt
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REAL-TIME MEASUREMENT OF THE SIZE DISTRIBUTION OF ROCKS ON A CONVEYOR BELT T. B. Lange C II/II/I'i/ .1"1' ,\l i Il ITII/ Tn/llw /(Jgy , /' 1'/. '1111' /i llg SJ / 1!5, NIIIII//Jl II }! 21 2'), SIIIIIII ,4/l'il'll
Abstr a ct . An on-line, real-time instrument is currently under d eve l opment for the measurement of the size distribution of rocks on a conveyor b e lt . The system captures images of rocks from conveyor bel ts, and proc esses t hese images to a state from which chord-length distributions a r e measured. These chord-length distributions are then transformed to equivalent s ieve si zes. Experiments have shown that the system can differentiate b e twe e n g r o u ps of rocks of different sizes and size distributions. Owing to diffi c ulties i n sampling! the accuracy and precision of the measurements is not satisfa c t o r y , and statl.stical and stereological aspects must be considered careful l y i f th e resul ts are to be accurate and easily understood. Techniques suc h as mathematical morphology are shown to be more useful than ' c l a ssi ca l' i mage processing in the preparation of the images for the measureme nt of c h o r d length distributions. In addition, the architec ture a nd p owe r of th e h ardware mus t be considered in conjunc tion with th e software and a lgor ithms employed . Only in this way can a practi c al instrume nt b e r ealized , and the spec if i c a tions for the instrument b e sat isf ied . Keywo rds. Autogenous milling; instrume ntation; rock- s iz e dist ribu ti on; image processing; morphology; chord lengths; stereology.
INTRODUCTION In the mining and mineral-processing industry, it is necessary to measure the size distribution of rocks on conveyor belts on1 i ne and in real-time. This measurement has b ecome particularly important in the goldmining industry where new control systems are b e ing applied to the milling stages of mi n e ral-recovery plants. Aut o genous milling is a grinding process in whi c h the ore itself is used as the grinding med ium. This is in contrast to other types of mil l ing such as baIlor rod milling, where stee l rods or balls are introduced into the mill as the grinding me dium. Run-of-mine milling is a process in which mined rock as large 0, 5m, is fed via conveyor belts directly into autogenous mills, and ground into smaller particles. Autogenous mills are becoming more widely used in South Africa, particularly on new plants in the gOld-mining sector and as a result of narrowing profit margins, lower yields , increasing energy costs and other problems, efficient control of these mills, and the optimization of this control is becoming increasingly important. Exactly how the size of the input ore affects the operation of an autogenous mill is not fully understood. However, it is hypothesized that if the size of the ore input to a mill , could be measured, the understanding of autogenous-milling processes would improve, and the measurement could be used as a feedforward input to the control system on the mill.
The i nitial spec ifi ca tion for on-line meas ur e ment of the feed size is the provision of a t least a single-point measurement ind i ca ting the percentage of material sma l le r than 75 or 10 0mm. Obviousl y a more accurate mul tipoint measurement would be mo r e de sirable. Th is paper discusses the feasibility, desig n, and development of a computer-vision sys t em for the measurement of the size dis t r ibution of rocks on a conveyor belt. Some preliminary results are presented, and some fundamental areas where serious p ro bl e ms have arisen and must be solved are d isc u s sed. These problems cover many asp e c ts of engineering and s c ience, and are th e r e f o re only briefly highlighted. Existing Instruments va r io us instruments of which the MSD 95 from Au t ometrics (Vignos and co - workers 1979) is th e best known, have been designed for the online measurement of the size distribution of r o cks and other material on a conveyor bel t. Th e MSD 95 uses photo-detectors to detect the sh a dows between the rocks along a probe line in the centre of the conveyor belt. These s h a dow data are then converted to size me a surements. Other instruments operate on similar principles, except that two- dimensional scenes of rocks are captured by a video camera and then processed by a computer to produce a size measurement. (Grannes, 1986, Yacher and co-workers, 1985) . Another sizing instrument (Eriksen 1978) uses the time during which
T. B. LlIlgc free-falling rocks intercept a laser beam to measure chord lengths. The Council for Mineral Technology was approached by various parties in the mineralprocessing industry to investigate and solve problems experienced with the measurement of the size distribution of rocks. It was fel t that the measurement from the MSD 95 was seriously biased because the instrument ignores the rock material on either side of the probe line, and is sensitive to changes in the levels of ambient light. It was also pointed out that all the methods for the measurement of rock size that use visuallight techniques are very biased because the sensors ( light detectors, video camera) can see only the top layer of the rocks. This, and other aspects such as poor accuracy and correlation with sieve Slzes, led to a request for an in-depth investigation of rock-size measurement.
the true rock scene; i. e. the light eflected off the rocks is a function not only of the height of the rocks above the belt, but also of each rocks I geometric and reflective properties such as shape, as well as its interaction with other rocks (occlusion).
Probe line
It was decided to address this measurement problem using machine vision and image processing after a number of other techniques, some of which utilize lasers and ultrasound, had been examined. A discussion of those techniques, most of which were rejected because they were too expensive or subj ect to technical problems, is beyond the scope of this paper.
b
Advantages of Two-Dimensional Machine Vision 20
Two-dimensional imaging allows the full width of the belt to be sampled, whereas the MSD 95 provides one set of one- dimensional data from a line along the belt. simulation of the MSD 95 on real images led to the conclusion that too many errors occur in the detection of the edges of the rocks when only one line of information is used because only a small part of the rock is available for interpretation. Further simulation indicated that, although the use of a number of probe lines working in parallel on different parts of the belt decreased the sampl ing bias, serious errors still occurred far too often due to incorrect ideJlltification of the rock edges.
1) •
One of the assumptions inherent in the use of many sizing intruments using machine vision is that the grey levels of the image represent the height of the rocks above the belt. This is true within limits. However, there are many features in these images where the grey levels do not correspond to the topology of
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Pixel position
Fig. 1. Example of a profile taken from an from an image. a. Image; b.Profi1e MEASUREMENT OF ROCK SIZE The process for the measurement of rock-size distribution by use of this image system consists of the following main sequential stages: the transformation of the raw image to a form where a parameter related to size can be measured,
(i)
These types of errors can be caused by the shadow cast by the ridges on a single rock, which causes the instrument to sense two chords instead of one. In addi tion, I spot I or impulse noise causes the MSD 95 to sense many short chords. It was hypothesized that twodimensional images, providing a larger amount of information, would improve the detection of valid edges, and eliminate these ambiguities. Sizing systems such as the MSD 95 work well under certain conditions, with certain types of image scenes. However, the output from these instruments often cannot be used since the light-intensity patterns reflected off autogenous rock material,particularly when it .is wet, renders inval id the assumptions on which such instruments are based. (see Fig.
40
(ii) the measurement of this parameter (or parameters) from the transformed image; and (iii)the transformation of the measured parameter to the required measurement output: It = (/)(I o )
m = u.(I t
s
}
= f (m)
where Io It
(/) u. m f
s
is the the the the the the the
original image, transformed image, image transformation, measurement process, measurement parameter, transformation to size and, size measurement.
( 1) (2 ) (3 )
'27 The objective of the design process was the development of suitable transformations, ~,u,f, and the choice of the correct parameter m. In addition, it had to be borne in mind that the transformations should be implemented on hardware of relatively low cost, and that they should operate in realtime (Fig 2).
The most important characteristics of these rock scenes can be summarized as follows. (a)
The rocks overlap (occlude)and hide portions of one another.
(b)
occasionally a large rock Looks like a group of small rocks, and groups of small rocks look like large single rocks.
(c)
The surfaces of these rocks range from very smooth to very rough. The rocks can be described generally as having convex surfaces, but they may have many ridges, indentations, and other features on their surfaces.
(d)
Although not apparent in the images presented, the colour and intensities of these rocks also vary greatly, not only from rock to rock, but within a single rock.
The Rock Scenes to be Analysed
(e)
Figures J and 4 show typical rock scenes from conveyor belts.
The rocks are 'randomly' orientated, but there are packing patterns.
(f)
Some form of classification occurs on the conveyor belts. Small rocks may fall to the bottom of the rocks may be sorted across the width of the belt during loading from the hopper.
Transformation
Image
Parameter
processing
measurement
R'w'--_ _ _---' image
to size ' - - - - - - - - - - ' Size
Edge
Parameter
pattern
distribution
di str ibution
(cnords)
Fig. 2. Block diagram of the main parts of the rock-size instrument
The points above highlight the ambiguity associated with the recognition of individual rocks in the images captured from conveyor bel ts. The examples and images shown in Fig. J and 4 are not exceptions, but typical of the scenes to be analysed.
a
Keller and co-workers (1987) used fractals to analyse natural scenes, and commented, 'many objects in images of natural scenes are so complex, that describing them by the familiar models of classicial geometry is inadequate'. Perhaps new techniques such as those based on fractals may ultimately hold the answer to the analysis of scenes such as those described above. What is Rock Size?
b
Before it can be decided how these raw images of autogenous rock material must be tran sfo rmed, a parameter of the objects (rocks) in the images must be chosen for measurement, e.g. projected area, volume. F i g. J . Images of sieved rock piles a . - J8+25mm; b. - 15+12mm
a
b
Fig. 4. Images of mixed rock piles a. N=2.0; b. N=O.5
However, the following questions arise.
*
What is rock size and how can it be measured?
*
Are there standards for the measurement of rock size that can be used for evaluation of the accuracy of the measurement?
The size of rocks or naturally occurring objects, appears to be an almost subjective observation, and each class of objects appears to have its own standard for size measurement. Luerkens and colleagues (1987) comment, 'there is a major uncertainty in particle characterization which is due to the lack of precision in the definition of the terms which are claimed to be measured'. They continue by stating that the nature of the uncertainty in the measurement of properties (e.g. size) ,as related to their definitions, is fuzzy.
28
T. B. Lallgc
Despi te this uncertainty, Sresty and Venkateswar (1980) provide the following fairly succinct definition of particle size: 'Particle size can be defined as the characteristic dimension of the material that can best represent the state of subdivision of its constituting particles' . Characteristic particle dimensions used in size measurement are generally related to the diameters of spheres. This is because the diameter of a regularly shaped homogeneous particle such as a sphere uniquely defines its size irrespective of whether diameter, area, or volume is being considered. The same holds good for a cube, since the length along one edge defines its size. with other regularly shaped particles it may be necessary to specify more than one dimension, e. g. for acyl inder, length and diameter must be defined (AlIen, 1981). It has been stated (Luerkens and co-workers, 1987) that, although an instrument may measure the size of spheres perfectly from a characteristic dimension, perfect spheres rarely occur in nature, and the instrument still leaves one in doubt as to the worth of its readings for irregularly shaped particles. The characteristic particle dimension chosen to represent the material also depends largely on the technique of measurement and the purpose of measurement. For example, Stokes' diameter is used for particles moving in a fluid, proj ected area is used for particles used in the paint industry, and mass or volume-mean diameter is used in the mineral- processing industry. The size of an object is also dependent on shape and other factors irrespective of the method used and, for a class of objects, a number of different sizing instruments often give different measurements. For example, laser scattering, sieving, and ultrasound attentuation produce different measurements for small particles. This is because different parameters or properties are being sensed, and the different instruments produce different errors. To quote Sresty and Venkateswar (1980) again: 'Due to these factors, a quoted average particle size can be meaningful only if it is substantiated by other pertinent information such as method and calculating procedure employed'. The above points are important and must be borne in mind when the results produced by this imaging system are being evaluated. As will be shown later, the imaging system as developed has produced measurements that are not the same as those from sieving, but do correlate with sieving. However, because no absolute standard exists, it would be difficult to justify the rejection of this method out of hand. Sieving as a Standard In general, sieve sizing is the most widely accepted standard for the measurement of coarse particle size, and it was decided to compare sieve size as an independent standard, with the output of the image system. No realistic alternative for rocksize measurement exists in any case. It should be noted that there are factors in sieving that may also introduce ambiguities. These must be taken into cognizance,
for example the shape of mesh holes can vary, and so can the sieving time, on which the amount of material passing through a sieve is dependent. (AlIen, 1981). Chord-Length Measurements and Stereology Some common derived diameters, such as Martin's or Ferret's diameter and projected areal diameter, can be used to describe the size of rocks. The application of most of these derived diameters assumes that an accurate outline of the particles to be sized exists. However, after experimentation with various edge-detection schemes, it was concluded that there was little likelihood that complete and correct outlines of the rock scenes typically found on autogenousmill sites could be obtained. In addition, the computational requirements needed for the calculation of these commonly used diameters is very high. It was therefore decided that chord lengths would be measured, and statistical and stereological techniques would be used, in the estimation of size. Stereology, according to 'is a body of methods microstructure as seen in or projection plane to quantities' .
Underwood (1970), for relating the the random section the true spatial
stereologyl provides tools that allow measurements on a two-dimensional plane to be related to a three-dimensional structure or, as in this case, allow one-dimensional chord data to be extrapolated to three- dimensional size data (sieve size). statistically exact stereological solutions to the measurement of size from profiles or cho rd lengths are possible for regularly shaped particles such as spheres. However, this is not the case for real particles of irregular shape like those found on au togenous-mill conveyor belts. Also, group properties such as size distribution can be evaluated by use of these techniques only if a large enough number of random sections, or samples of a group of particles, to be characterized, is available. In tuitively, it appears to be more correct to calculate size from the projected areas of the rocks than from the measurement of chord lengths. However, this is not so, since stereological techniques allow zero, one-, o r two-dimensional measurements to be used in the prediction of high-order dimensional quantities, (within limits, of course). Hence chord lengths were chosen because they are more easily computed than proj ected areas, and because projected areas are also more sensitive to edge errors in the rock outline than chords. IMAGE PROCESSING AND ANALYSIS As discussed above, the images of the rock scenes as captured on camera are not in a form that allows for the direct measurement of chord length. These 'raw' images (Io) have to be processed or reduced to a form (I t) where chord probe I ines can be appl ied (11.) , and the chord lengths can be measured (m) .
1.
Strictly speaking the term stereology may be replaced by stereometry.)
Sill' Distrii>lItioll of R()ck>
The obj ective of image processing is the stripping away of all unwanted information (Williams 1988) , so that only the outlines of the rocks remain. For this to be done it is important to ensure that the images are captured with the highest possible degree of accuracy and with little or no noise. Thus, most of the processing effort can be directed towards edge detection rather than image restoration or correction. This strategy also helps to reduce the processing time per image. Design Methodology and Philosophy The accuracy of each stage in image processing is affected by the previous stage. The principle employed is similar to the generation and propagation of noise in a series of amplifiers. Each stage not only amplifies the noise from the previous stage; it introduces its own noise, which tends to decrease the ratio of information (signal) to noise. Therefore the design methodology adopted in the present work involved the specification of the role of each sequential stage (starting at the front with the capture of the image), followed by optimization of the algorithm developed so that it would be as fast and as accurate as possible. Another reason for the development of each stage sequentially was that it was difficult to analyse and model the dynamics of the total system, and to describe the propagation as well as the accuracy of the information through the system. For example, what is the relationship between the angle of illumination and the creation of unwanted edges and the detection of unwanted chords? A number of image-processing architectures have been designed and tried and the fundamental strategy by which the edges are extracted is as follows (Fig. 5).
(1)
The image is captured and filtered as required.
(2)
The edges are detected.
(3)
Any missing gaps in the edges are closed, and unwanted edges are removed.
q
GR,W B.i lter FG
_ _ _ _.....J
9
E_d__e_---' improvement
L __
L
G
Edg_
imag e
Fig. 5. Block diagram of the main parts of the image-processing system.
stage 4
The system fills in gaps in the edges and removes unwanted edges.
stage 5
The system measures chord lengths.
This sequence of stages is based on imageprocessing and object- recognition systems wi th typical archi tectures. However, it must be pointed out that this structure has, and wil l be, changed many times. An option that is under investigation is the use of feedback to al ter control parameters to the various stages based on a knowledge base of the expected chord distributions and other heuristic information. This may be neccesary because of the wide variation in the rock scenes to be analysed. Identification of the Rock and its Edges It has been found that rock-edge detection is the most critical part of the whole system since the c hord lengths are measured from these edges. The chord lengths are very sensitive to the accuracy of the detected edges, however, statistics can be used to minimize this sensitivity, but at the cost of resolution and accuracy. since the conveyor belt is generally covered entirely with rocks, the main task is to segment th e edges from the rocks and their interiors. As in most image-processing applications , the biggest problem is the selection of the quickest and most accurate algorithms to perform the filtering, objec t-recognition, and extraction proces ses required for this segmentation. Gurari and Wechsler (1982) conclude that the usual approach to such a problem is an ad hoc, approac h, i. e. the use of heuristic methods. The traditional trade-off between speed and accuracy manifests itself very strongly here, in th at h ighly accurate edge detection requires a lot of processing time, and a rapid edge-detection algorithm will be very prone to errors . Low-pass spatial filtering is required initially to remove impulse (spot) noise, and to smooth the interiors of the rocks while preserving their true outlines. These are conflicti ng goals, and tests have shown that simple, neighbourhood, averaging convolutions appear to work best for this initial filtering. Spatial frequency-domain filters, median filters (Bovik, 1987; Arce and Stevenso n, 1987), and recursive filters (Shanks, and Justice, 1972; Hu and Rabiner, 1972) have been tried, but disadvantages such as large computation times and instability with the recursive filters caused these techniques to be discarded.
s t ag e 1
The system captures the rock images with as little noise, distortion, blurring, and other unwanted effects as possible.
stage 2
The system f il ters out any spurious noise such as spot n01se and smoothes out the irregular features on each rock while preserving the edge information.
Segme ntation and edge detection for object recognition and extraction has been widely researched by a great many workers, in a large number of different applications, (Torre and Poggio , 1986; Garbay, 1986; Pratt, 1978). Commercial instruments are available that perform edge detection and segmentation on images (Sanz, 1988). Applications range from the segmentation of different cells or parts of a cell in medical applications (Jain and colleagues, 1980) to the segmentation of tanks from background bushes in military applications.
stage 3
The system recognises and defines each rock in the image as accurately as possible, and then extracts the edges.
In many segmentation applications, the objects to be segmented from the background are of a different intensity and are easily discernible. This is not the case with rock
A more detailed expansion on strategy is described below:
the
above
30
T. B.
images. As a result most segmentation techniques described in the literature could not be applied in the present work. A number of segmentation and edge-detection techniques were examined for edge detection. The next paragraphs describe these tests briefly and explain why the various techniques were rej ected. It should be noted that the future use of these techniques is being reviewed continuously as technology improves. Rule Bases. The geometry of the shape and size of the entities in the image captured are random, and vary tremendously. This randomness eliminates a large selection of image-processing techniques-including template matching - that make use a priori of the expected shape and size of the objects to be found. This does not mean that no heuristic information can be used. On the contrary, the rocks themselves have a unique description that allows certain shapes to be excluded. Berger (1985) designed a rule-based system for the measurement of rock size, but, the processing time per image was about threequarters of an hour on a minicomputer, which is obviously unacceptable. Thresholding. The grey-level histogram of typical scenes from the conveyor belts are unimodal, and are more difficul t to process,(Bhanu and Faugers, 1982). This is unfortunate because a great many segmentation teChniques using thresholding for segmentation of the images cannot be used (Weszka, 1978). Convolution and Templates. This class of edge-detection methods is very well established, and does have potential. They include for example, the Soble and Roberts edge detector, the integrated directional derivative gradient operator (Zuniga and Haralick, 1987), and the calculation of the first and second derivatives (Laplacian) of the image. The grey levels in the image can be regarded as a surface in three dimensions, with hills, valleys, troughs, etc. However, a large variety of edges is present in rock images and experiments have shown that the application of one edge detector is inadequate. This is because each edgedetector template is a function of the shape, size and slope of the edge, and detects only a subset of all the edges, which implies multiple passes with many edge templates of different size and shape. This is very intensive computationally and demands a large amount of memory. Such methods may be more viable with powerful parallel hardware systems. Also these methods are intrinsically sensitive to noise (differentiate), and it is difficult to find a balance between the correct pre-filters (integrator) and edge detector, particularly in view of the wide range of input images. Frequency-Domain and Texture-Analysis Techniques. These methods were also rejected, mainly because the image patterns vary too much for these processes to. be u~ed effectively, and because the processlng tlme is again too long. Laplacian operator. The only traditional technique that proved to be very useful in the detection of a large proportion of the edges was the Laplacian operator. This edge detector is quick, and found an estimated 50 to 80 per cent of the edqes because it is less
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sensitive to edge direction than most other operators. This edge detector was ul timately also abandoned in favour of morphological edge detectors. Completing the Resultant Edge Patterns The edge detectors that were tested or selected, extracted on average about twothirds of all the required edges. A portion of the entities (edges) produced by these edge-detection algorithms also consist of noise, which includes valid edges that are not part of the true rock perimeter, as well as gaps in the true perimeter. The chordlength distributions derived from such edge patterns are therefore full of errors and some post-processing is required for the removal of this noise. A number of methods were developed in an attempt to fill in the missing edges and erase unwanted edges. This is where most (70 to 80 per cent) of the processing time was taken up, and traditional techniques using heuristic knowledge and artifical intelligence were implemented. Figure 6 illustrates one of the first teChniques that was developed in an effort to close the gaps and remove unwanted edges. This method used a rule base, the design of which was based on the most probable shapes of the rock outl ines, to complete the edges. The method was abandoned in favour of morphological teChniques, which are discussed below.
a
c
b
d
Fig. 6. Illustration of a rule-based method method designed for the closing of edge gaps. a. Orig inal; b. After edge detection; c and d. Two results with varying rule parameters.
:11 Mathematical Morphology From an inspection of the resultant binary edge patterns produced by segmentation and edge detection (Fig. 6b), it is relatively easy to analyse the shape of the rocks and perceive the rock edges. It is bel ieved that in the processing of these image entities to improve the edge patterns, mathematical morphology approaches most closely the processes of the human mind, because morphological operators relate directly to shape. Mathematical morphology was introduced by Matheron (1975) and Serra (1982) as a set theoretical method for image analysis whose purpose is the quantitative description of geometrical structures. According to Haralick and co-workers (1987), 'morphological operations tend to simplify image data preserving their essential shape characteristics and eliminating irrelevancies' . At present these techniques provide the means by which most of the gaps are filled and unwanted edges are removed. The implementation of morphological techniques is beyond the scope of this paper, and will not be discussed here. However, the reader is referred to Maragos (1985, 1987); Maragos and Schafer (1986) ; and Haralick and co-workers, (1987) . Fig. 7 shows how the morphological operation of opening helps to remove impulse noise from an edge pattern, and Fig. 8 shows how the morphological operation of closing helps to remove small gaps in the edges detected. b
Fig.
7.
Filtering of noise by use of morphological opening. a. Before opening; b. After opening.
At first, morphological methods were used only for the improvement of resul tant binary edge patterns as detected by the Laplacian operator. However, additional research indicated that mathematical morphology could also be used for edge detection. A morphological edge detector operates on grey-scale images and uses grey-scale morphological techniques instead of binary morphology (Maragos, 1985, 1987; Maragos and SChafer, 1986; and Haralick and co-workers, 1987) .
8. Use of morphological closing to close edge gaps. a. Before closing; b. After closing I~DWARE
CONSIDERATIONS
The choice of algorithms for the system was influenced by real-time constraints, and the requirement that they should be implemented at a relatively low cost. Time constants in the mineral-processing industry are typically 15 minutes, and range from 1 minute to hours. (This is very different from military applications where real-time can be considered in milliseconds.) These real-time specifications allow for the use of general-purpose computing hardware as opposed to specialized hard,oJare where the algorithms are built into custom circuits and integrated circuits. So far, all development work has been undertaken on machines using the Intel 80286 or 80386 type microprocessors with Data Translation imaging boards, which allow for a great deal of flexibility in software developement. Because high sampling rates of images are required, the processing speeds are still too slow (60 seconds per image). However, powerful accelerator cards and co-processors for the AT-type microcomputer can be used to improve performance to levels approaching supercomputing. In particular, the Transputers from Inmos have great potential because of their fairly high power, as well as their ability to be linked in parallel. It is important to note that many hardware systems are available in which morphological operations as well as other well-known traditional image-processing algorithms are implemented. other options that may prove useful in future are the use of optical processors and neural networks, which could be 'taught' to recognise rocks in an image. TEST RESULTS At first, the testing and development of this instrument appeared to be straightforward, the only problem being the development of the software. However, in retrospect, this was not the case as difficulties were encountered wi th dynamic image capture and, as a result, most tests were done on static images in the laboratory. A closed-loop conveyor-bel t test bed is currently being set up for the testing of continuous on-line measurements. Figures 9, 10 show the typical cumulative chord-length distributions obtained for grani te rocks by the image system in the laboratory. These curves show that the system can distinguish between different sieve sizes as well as different distributions of sieve sizes.
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T. B.
is made up of two fields, one of which consists of the even lines and the other of the odd lines. These fields are sensed 20ms apart and, since the rock scene is moving relative to the camera, one field is displaced relative to the other, rendering the image useless. Realignment software, as well as the use of one field, was investigated but, because of perspective and quantization errors, the use of these cameras was abandoned.
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30
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Chord length, pixels
Fig. 9. Cumulative chord-length distributions for sieved rock piles
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0 . 50 1. 00 1. 50 1. 75 2 . 00
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i
Illumination The best method of illumination of the belt is still a subject of serious contention regarding such factors as intensity, the type of light (diffuse or direct), colour, polarization, and the number of lights as well as their arrangement relative to one another and the belt scene. For example, angled lighting dramatically improves the quantity and quality of the outlines of the rocks, but increases the number of unwanted edges. CONVERSION OF CHORD LENGTH TO SIZE
0.75
'tI
~
Varying Belt Speed and Geometric Distortion The use of a line-scan camera sol ved both the blurring and interlacing problems. A custom controller was built for the line-scan camera to compensate for problems due to different belt speeds and sizes. The controller also controls the aspect ratio and size of the pixels, as well as the image.
N fa c tor.
o ';'0.4
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0"-'~-'T--~'----""""--_~_-----1
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10
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The last stage of the measurement system is the transformation of the chord-length distributions into a form more acceptable to the metallurgist, e.g. sieve size. This stage may be unnecessary if the chord-length distribution can be fed directly into the control system of the mill.
Chord length, pixels
Fig.lO. Cumulative chord-length distributions for mixed rock piles For the different rock distributions used in the tests (Fig. 10), different portions (by mass) of sieved rock fractions were mixed according to the Rosin-Rammler function, and by varying n to produce different rock piles, i. e.
The transformation can be considered a deconvolution of the integral equation (simplified), as shown below, in order to solve for f ( D) where p(L ) and P(L/D) are known. P (L)
where (4 )
where
P (L ) f(D) P(L/D )
X f (X ) b,n
is size distribution, and characteristic constants
Practical problems experienced during tests on static and dynamic images are listed below. Wet material causes problems with respect to reflection and contrast. Blurring Conveyor belts on mineralprocessing plants have velocities ranging from about O. 1 m/ s to over 2 m/ s. Al though a CCD camera with a high shutter speed (1 ms) ~ol ved most of the problems due to blurring, l.t was effective only on belts moving at less than 0.75 m/so Interlacing Commercial cameras using an interlacing format could not be used for dynamic image capture. A television frame
r
P(L / D ) f ( D ) dD,
(5)
o
is the chord-length distribution as measured the size distribution required, and the conditional probability density function relating chord-length to size.
The solution for f ( D ) is not a trivial exercise, and has been researched by King (1982), and by Yu and Gentry (1987). Chen and colleagues (1987) have shown that constrained linear inversion can be used for this transformation, and initial work in the present investigation showed that this method has potential. Figure 11 shows the resul ts for the conversion of chord distribution to size by use of constrained linear inversion. Only five images were processed for each of the five size ranges shown. The errors in the above measurement are attributed mainly to the small number of samples processed here.
Size Distribution of Roc ks 1. 0
I'Zl Calculated distribution
0 .8
-
0.8
True distribution
0 .4
33
irregularly shaped rocks and, more seriously, that only simulations with realistically shaped particles will contribute any real information to the interpretation of the chord distributions.
0 .2
f~ ~~_L'2~'-0~8m-m- ~~~5L'-'2~m-m--~-~~'~8~"~5-m-m--~~-~25~'-'~9m-m---u-31I ~.-'2~5~m~m o
Sieve size range
Fig.ll.
Results of constrained linear inversion for the conversion of chord-length to sieve size
Sampling Sampling is an important factor influencing this measurement technique. Examination of the chord-length distributions measured in tests, as well as the results of the constrained linear inversion, show that the number of chord samples processed is critical to the accuracy or validity of the measurement_ Monte Carlo simulations carried out on circles in the present work, and work done by Kawakami and co-workers (1987), confirm this. The Monte Carlo simulations showed that measurements of 100 000 samples yield fairly low deviations (less than 3 per cent) , which is also indicative of the potential accuracy that can be obtained. It also indicates, as emphasized previously, that the image-processing rate of the system has to be fast as well, particularly if the size statistics are not stationary. The Monte Carlo simulations were also used as a test of the effect of various factors on c hord distributions and as an aid in the understanding and derivation of the kernel P (L/ DJ of equation (4) required for the transformation equation (3). These factors are: (a)
the relationship between different distributions of circles (e_g. single sizes, normal, and log normal) and the chord distributions,
(b)
the effect of overlapping, spacing and packing (i.e. occlusion), and
(c)
chord probe-line spacing.
This work indicated that, for circles, a single size can be read off directly from the chord distribution. This is not the case for more- complex distributions of circles, such as log normal distributions, although there is a strong correlation between the shape of the size distribution and of the chord distribution. Overlapping of circles, and oversampling by probe lines being placed too close to each other, also biases the distribution, although this biasing does not appear to affect the shape of the distribution. It is believed that these factors will affect the chord distributions, as measured from
Another point that arises from these simulations, and from observations, is that the surface distribution of rocks is not representative of the actual size distribution of the whole volume of material on the belt. This is because of the sorting and packing processes experienced by these particles. This was simulated to a limited extent with circles, and initial studies have indicated that this 'packing' factor could possibly be predicted. CONCLUSION A system that measures the size distribution of rocks on a conveyor belt in real-time is currently under development. Problems such as dynamic image capture, rock recognition, rock-edge detection, and size measurement have been addressed and largely solved. The image processing was aided greatly by the use of mathematical morphology, and stereology. Constrained linear inversion provides a simple yet effective tool for the transformation of chord-length measurements to sieve size. There are problems due to the overlapping and occluding of rocks, and these phenomena must be taken into account. At present, the system can differentiate between different sieve sizes, as well as different distributions. The system must process as many samples as quickly as possible in order to achieve improved accuracy, reduced variations, and operate in real-time. Instrument specifications such as those for range and accuracy are therefore dependent on the hardware as well as the software. Since technology is advancing rapidly it should not take long for the ideal instrument is realized. ACKNOWLEDGEMENT This paper is published by permission of the Council for Mineral Technology (Mintek). REFERENCES AlIen, T. (1981). Particle size measurement. 3rd ed. Chapman and Hall, London, Chap. 4 . Arce, G. R., and R.L . Stevenson, (1987). On the synthesis of median filter systems. IEEE Tra n s. on Circuits Systems., Berger, G. F. (1985). So ftware for a particle size analys er bas ed on image analysis te c hniques . M.Sc. Dissertation, University of the Witwatersrand, Johannesburg. Bhanu, B., and o. D. Faugers (1982) . Segmentation of images having unimoda1 distributions. IEEE Trans. on Pattern Analysis Machine Intelligence, Vol. PAMI-4, No.4, 408-419. Bovik, A. C., T.S. Huang. and D.C. Munson. (1987). The effect of median filtering on edge estimation and detection. IEEE Trans. on Pattern Analysis Machine Intelligence, Vol. PAMI-9, No.2, pp 181194.
T. B. l.all,!.(C
Chen Luh Lin, J.D.Miller, and J.A.Herbst (1987) . Solutions to the transformation equation for volumetric grade distribution from linear and/or areal grade distributions. Powder Technol.50, 5563. Eriksen, O. (1978). In-stream measurements of grain size distribution by random intercepts. International Symposium on In-Stream Measurementsof Particulate Solid Properties, Bergen, Norway. Garbay, C. (1986). Image structure representation and processing: A discussion of some segementation methods in cytology. IEEE Trans. on Pattern Analysis Machine Intelligence, Vol.PAMI-8, NO.2, 140-146. Grannes, S.G. (1986). Determining size distribution of moving pellets by computer processing. 19th Application of Computers and Operations Research in the Mineral Industry. pp.545-552. Gurari, E. M., and H.Wechsler, (1982). On difficulties involved in the segmentation of pictures. IEEE Trans. on Pattern Analysis Machine Intelligence. Vol.PAMI-4, No.3, 304-306. Haralick, R. M., S.R.Sternberg, X.Zhuang, (1987) . Image analysis using mathematical morphology. IEEE Trans. on Pattern Analysis Machine Intelligence. Vol.PAMI-9, No.4, 532-550. Hu, J. V., and L.R.Rabiner, (1972). Design techniques for two dimensional digital filters. IEEE Trans. on Audio and Electroacoustics, Vol.AU-20, No.4, 249-257. Jain, A. K., S.P.Smi th, and E.Backer, (1980). Segmentation of muscle cell pictures: A preliminary study. IEEE Trans. on Pattern Analysis Machine Intelligence. Vol .PAMI-2, No.3, 232-242. Kawakami, M., N.Tomimoto, and Y.Kitazawa, (1988). Estimation of size distribution of bubbles in iron melt from the chord length distribution. Trans. Iron and Steel Insti. Jap., Vol.28 271-277. Keller , J . M., R.M.Crownover, and R.Y.Chen, (1987). Characteristics of natural scenes related to th e fractal dimensions. IEEE Trans. Pattern Analysis Machine Intelligence. Vo l.PAMI-9, No.5, 62 1-6 27 . King, R.P. (1982). Determination of th e distribution of size of irregularly shaped particles from measurements on sections or proj ected areas. Powder Techn. 32 , 87-100. Lantuejoul, C., and J.Serra (1982). M filters. IEEE International Conference on Acoustics, Speech and Signal Processing. pp. 2063-2066. Levialdi, S. (1980). Finding the edge. Digital Image Processing, Proc NATO, Bonas France. pp.105-148. Luerkens, D. W., J.K. Beddow, and A.F.Vetter (1987). Structure and morphologythe science of form applied to particle characterization. Powder Techn. 50.9310l. Maragos, P. A. (1985). A unified theory of translation-invariant systems with applications to morphological analysis and coding of images. Ph.D. Thesis. Georgia Institute of Technology, Atlanta. Maragos, P. A. (1987). Tutorial on advances in morphological image processing and analysis. Optical Eng. Vol. 26,No.7.
Maragos, P. A., and R.W.Schafer (1986). Applications of morphological filtering to image analysis and processing. Conference on Acoustics, Speech and Signal Processing, Tokoyo Japan. pp.2067-2069. Matheron, G. (1975). Random sets and integral geometry. John Wiley, New York. Pratt, W. K. (1978) . Digital image processing. John Wiley, New York. Sanz, J. L. C.Ed. (1988). Special PAMI Issues on Industrial Machine Vision and Computer Technology. Part 1. IEEE Trans. Pattern Analysis Machine Intelligence. Vol.10, No.l. Serra, J. (1982). Image analysis and mathematical morphology. Academic Press, London. Shanks, J. L., and J.H. Justice, (1972) . Stability and synthesis of twodimensional recursive filters. IEEE Trans. Audio electroacoustics, Vol.AU-20, No.2, 115-128. Sresty, G. C., R.Venkateswar, (1980). Particle size analysis - A review. In Proceedings of the International Symposium, Las Vegas, Nev, February. pp. 329 -365. Torre, V., and T.A.Poggio, (1986). On edge detection. IEEE Trans. Pattern Analysis Machine Intelligence, Vol.PAMI-8, No.2, 147-163. Underwood, E. E. (1970). Quantitative stereology. Addison Wesley, Reading, Massachusetts. Vignos, J.H., L.Elbe r, and E. Gallagher,(1 979) . Coarse particle size distribution transmitter. Meeting of SME of AIME, Tucson, Arizona, October 1979. Weszka, J. S. (1978). A survey of threshold selection techniques. Comput. Graphics Image Process. 7, 259-265. Williams, T. (1988). Object recognition opens the eyes of machine vison systems. Comput . Des. 69-84. Yache r C., C. Gonzalez, G. Van Boses, and R. Nobel, (1985). Coarse particle size distribution analizer. Instrumentation in the Mining and Metallurgy ~ndustries. 13th Annual Mining and Metallurgy Synposium. Vol.12, 71-79. Yu, P., andJ. Gentry (1987). Comparison of g ene tic inversion algorithms for characterizing particle size distribution. Powder Techn. 50, 79-89. Zuniga, O.A., and R.M. Haralick (1987). Integrated directional derivative gradient operator. IEEE Trans. Pattern Analysis l-1achine Intelligence, Vol. 17, NO.3.
Tra llS\'aa!. S, ,\rri ('a I\IHH
REAL-TIME MEASUREMENT OF THE SIZE DISTRIBUTION OF ROCKS ON A CONVEYOR BELT T. B. Lange C II/II/I'i/ .1"1' ,\l i Il ITII/ Tn/llw /(Jgy , /' 1'/. '1111' /i llg SJ / 1!5, NIIIII//Jl II }! 21 2'), SIIIIIII ,4/l'il'll
Abstr a ct . An on-line, real-time instrument is currently under d eve l opment for the measurement of the size distribution of rocks on a conveyor b e lt . The system captures images of rocks from conveyor bel ts, and proc esses t hese images to a state from which chord-length distributions a r e measured. These chord-length distributions are then transformed to equivalent s ieve si zes. Experiments have shown that the system can differentiate b e twe e n g r o u ps of rocks of different sizes and size distributions. Owing to diffi c ulties i n sampling! the accuracy and precision of the measurements is not satisfa c t o r y , and statl.stical and stereological aspects must be considered careful l y i f th e resul ts are to be accurate and easily understood. Techniques suc h as mathematical morphology are shown to be more useful than ' c l a ssi ca l' i mage processing in the preparation of the images for the measureme nt of c h o r d length distributions. In addition, the architec ture a nd p owe r of th e h ardware mus t be considered in conjunc tion with th e software and a lgor ithms employed . Only in this way can a practi c al instrume nt b e r ealized , and the spec if i c a tions for the instrument b e sat isf ied . Keywo rds. Autogenous milling; instrume ntation; rock- s iz e dist ribu ti on; image processing; morphology; chord lengths; stereology.
INTRODUCTION In the mining and mineral-processing industry, it is necessary to measure the size distribution of rocks on conveyor belts on1 i ne and in real-time. This measurement has b ecome particularly important in the goldmining industry where new control systems are b e ing applied to the milling stages of mi n e ral-recovery plants. Aut o genous milling is a grinding process in whi c h the ore itself is used as the grinding med ium. This is in contrast to other types of mil l ing such as baIlor rod milling, where stee l rods or balls are introduced into the mill as the grinding me dium. Run-of-mine milling is a process in which mined rock as large 0, 5m, is fed via conveyor belts directly into autogenous mills, and ground into smaller particles. Autogenous mills are becoming more widely used in South Africa, particularly on new plants in the gOld-mining sector and as a result of narrowing profit margins, lower yields , increasing energy costs and other problems, efficient control of these mills, and the optimization of this control is becoming increasingly important. Exactly how the size of the input ore affects the operation of an autogenous mill is not fully understood. However, it is hypothesized that if the size of the ore input to a mill , could be measured, the understanding of autogenous-milling processes would improve, and the measurement could be used as a feedforward input to the control system on the mill.
The i nitial spec ifi ca tion for on-line meas ur e ment of the feed size is the provision of a t least a single-point measurement ind i ca ting the percentage of material sma l le r than 75 or 10 0mm. Obviousl y a more accurate mul tipoint measurement would be mo r e de sirable. Th is paper discusses the feasibility, desig n, and development of a computer-vision sys t em for the measurement of the size dis t r ibution of rocks on a conveyor belt. Some preliminary results are presented, and some fundamental areas where serious p ro bl e ms have arisen and must be solved are d isc u s sed. These problems cover many asp e c ts of engineering and s c ience, and are th e r e f o re only briefly highlighted. Existing Instruments va r io us instruments of which the MSD 95 from Au t ometrics (Vignos and co - workers 1979) is th e best known, have been designed for the online measurement of the size distribution of r o cks and other material on a conveyor bel t. Th e MSD 95 uses photo-detectors to detect the sh a dows between the rocks along a probe line in the centre of the conveyor belt. These s h a dow data are then converted to size me a surements. Other instruments operate on similar principles, except that two- dimensional scenes of rocks are captured by a video camera and then processed by a computer to produce a size measurement. (Grannes, 1986, Yacher and co-workers, 1985) . Another sizing instrument (Eriksen 1978) uses the time during which
T. B. LlIlgc free-falling rocks intercept a laser beam to measure chord lengths. The Council for Mineral Technology was approached by various parties in the mineralprocessing industry to investigate and solve problems experienced with the measurement of the size distribution of rocks. It was fel t that the measurement from the MSD 95 was seriously biased because the instrument ignores the rock material on either side of the probe line, and is sensitive to changes in the levels of ambient light. It was also pointed out that all the methods for the measurement of rock size that use visuallight techniques are very biased because the sensors ( light detectors, video camera) can see only the top layer of the rocks. This, and other aspects such as poor accuracy and correlation with sieve Slzes, led to a request for an in-depth investigation of rock-size measurement.
the true rock scene; i. e. the light eflected off the rocks is a function not only of the height of the rocks above the belt, but also of each rocks I geometric and reflective properties such as shape, as well as its interaction with other rocks (occlusion).
Probe line
It was decided to address this measurement problem using machine vision and image processing after a number of other techniques, some of which utilize lasers and ultrasound, had been examined. A discussion of those techniques, most of which were rejected because they were too expensive or subj ect to technical problems, is beyond the scope of this paper.
b
Advantages of Two-Dimensional Machine Vision 20
Two-dimensional imaging allows the full width of the belt to be sampled, whereas the MSD 95 provides one set of one- dimensional data from a line along the belt. simulation of the MSD 95 on real images led to the conclusion that too many errors occur in the detection of the edges of the rocks when only one line of information is used because only a small part of the rock is available for interpretation. Further simulation indicated that, although the use of a number of probe lines working in parallel on different parts of the belt decreased the sampl ing bias, serious errors still occurred far too often due to incorrect ideJlltification of the rock edges.
1) •
One of the assumptions inherent in the use of many sizing intruments using machine vision is that the grey levels of the image represent the height of the rocks above the belt. This is true within limits. However, there are many features in these images where the grey levels do not correspond to the topology of
60
80
1 00
120
140
160
180
Pixel position
Fig. 1. Example of a profile taken from an from an image. a. Image; b.Profi1e MEASUREMENT OF ROCK SIZE The process for the measurement of rock-size distribution by use of this image system consists of the following main sequential stages: the transformation of the raw image to a form where a parameter related to size can be measured,
(i)
These types of errors can be caused by the shadow cast by the ridges on a single rock, which causes the instrument to sense two chords instead of one. In addi tion, I spot I or impulse noise causes the MSD 95 to sense many short chords. It was hypothesized that twodimensional images, providing a larger amount of information, would improve the detection of valid edges, and eliminate these ambiguities. Sizing systems such as the MSD 95 work well under certain conditions, with certain types of image scenes. However, the output from these instruments often cannot be used since the light-intensity patterns reflected off autogenous rock material,particularly when it .is wet, renders inval id the assumptions on which such instruments are based. (see Fig.
40
(ii) the measurement of this parameter (or parameters) from the transformed image; and (iii)the transformation of the measured parameter to the required measurement output: It = (/)(I o )
m = u.(I t
s
}
= f (m)
where Io It
(/) u. m f
s
is the the the the the the the
original image, transformed image, image transformation, measurement process, measurement parameter, transformation to size and, size measurement.
( 1) (2 ) (3 )
'27 The objective of the design process was the development of suitable transformations, ~,u,f, and the choice of the correct parameter m. In addition, it had to be borne in mind that the transformations should be implemented on hardware of relatively low cost, and that they should operate in realtime (Fig 2).
The most important characteristics of these rock scenes can be summarized as follows. (a)
The rocks overlap (occlude)and hide portions of one another.
(b)
occasionally a large rock Looks like a group of small rocks, and groups of small rocks look like large single rocks.
(c)
The surfaces of these rocks range from very smooth to very rough. The rocks can be described generally as having convex surfaces, but they may have many ridges, indentations, and other features on their surfaces.
(d)
Although not apparent in the images presented, the colour and intensities of these rocks also vary greatly, not only from rock to rock, but within a single rock.
The Rock Scenes to be Analysed
(e)
Figures J and 4 show typical rock scenes from conveyor belts.
The rocks are 'randomly' orientated, but there are packing patterns.
(f)
Some form of classification occurs on the conveyor belts. Small rocks may fall to the bottom of the rocks may be sorted across the width of the belt during loading from the hopper.
Transformation
Image
Parameter
processing
measurement
R'w'--_ _ _---' image
to size ' - - - - - - - - - - ' Size
Edge
Parameter
pattern
distribution
di str ibution
(cnords)
Fig. 2. Block diagram of the main parts of the rock-size instrument
The points above highlight the ambiguity associated with the recognition of individual rocks in the images captured from conveyor bel ts. The examples and images shown in Fig. J and 4 are not exceptions, but typical of the scenes to be analysed.
a
Keller and co-workers (1987) used fractals to analyse natural scenes, and commented, 'many objects in images of natural scenes are so complex, that describing them by the familiar models of classicial geometry is inadequate'. Perhaps new techniques such as those based on fractals may ultimately hold the answer to the analysis of scenes such as those described above. What is Rock Size?
b
Before it can be decided how these raw images of autogenous rock material must be tran sfo rmed, a parameter of the objects (rocks) in the images must be chosen for measurement, e.g. projected area, volume. F i g. J . Images of sieved rock piles a . - J8+25mm; b. - 15+12mm
a
b
Fig. 4. Images of mixed rock piles a. N=2.0; b. N=O.5
However, the following questions arise.
*
What is rock size and how can it be measured?
*
Are there standards for the measurement of rock size that can be used for evaluation of the accuracy of the measurement?
The size of rocks or naturally occurring objects, appears to be an almost subjective observation, and each class of objects appears to have its own standard for size measurement. Luerkens and colleagues (1987) comment, 'there is a major uncertainty in particle characterization which is due to the lack of precision in the definition of the terms which are claimed to be measured'. They continue by stating that the nature of the uncertainty in the measurement of properties (e.g. size) ,as related to their definitions, is fuzzy.
28
T. B. Lallgc
Despi te this uncertainty, Sresty and Venkateswar (1980) provide the following fairly succinct definition of particle size: 'Particle size can be defined as the characteristic dimension of the material that can best represent the state of subdivision of its constituting particles' . Characteristic particle dimensions used in size measurement are generally related to the diameters of spheres. This is because the diameter of a regularly shaped homogeneous particle such as a sphere uniquely defines its size irrespective of whether diameter, area, or volume is being considered. The same holds good for a cube, since the length along one edge defines its size. with other regularly shaped particles it may be necessary to specify more than one dimension, e. g. for acyl inder, length and diameter must be defined (AlIen, 1981). It has been stated (Luerkens and co-workers, 1987) that, although an instrument may measure the size of spheres perfectly from a characteristic dimension, perfect spheres rarely occur in nature, and the instrument still leaves one in doubt as to the worth of its readings for irregularly shaped particles. The characteristic particle dimension chosen to represent the material also depends largely on the technique of measurement and the purpose of measurement. For example, Stokes' diameter is used for particles moving in a fluid, proj ected area is used for particles used in the paint industry, and mass or volume-mean diameter is used in the mineral- processing industry. The size of an object is also dependent on shape and other factors irrespective of the method used and, for a class of objects, a number of different sizing instruments often give different measurements. For example, laser scattering, sieving, and ultrasound attentuation produce different measurements for small particles. This is because different parameters or properties are being sensed, and the different instruments produce different errors. To quote Sresty and Venkateswar (1980) again: 'Due to these factors, a quoted average particle size can be meaningful only if it is substantiated by other pertinent information such as method and calculating procedure employed'. The above points are important and must be borne in mind when the results produced by this imaging system are being evaluated. As will be shown later, the imaging system as developed has produced measurements that are not the same as those from sieving, but do correlate with sieving. However, because no absolute standard exists, it would be difficult to justify the rejection of this method out of hand. Sieving as a Standard In general, sieve sizing is the most widely accepted standard for the measurement of coarse particle size, and it was decided to compare sieve size as an independent standard, with the output of the image system. No realistic alternative for rocksize measurement exists in any case. It should be noted that there are factors in sieving that may also introduce ambiguities. These must be taken into cognizance,
for example the shape of mesh holes can vary, and so can the sieving time, on which the amount of material passing through a sieve is dependent. (AlIen, 1981). Chord-Length Measurements and Stereology Some common derived diameters, such as Martin's or Ferret's diameter and projected areal diameter, can be used to describe the size of rocks. The application of most of these derived diameters assumes that an accurate outline of the particles to be sized exists. However, after experimentation with various edge-detection schemes, it was concluded that there was little likelihood that complete and correct outlines of the rock scenes typically found on autogenousmill sites could be obtained. In addition, the computational requirements needed for the calculation of these commonly used diameters is very high. It was therefore decided that chord lengths would be measured, and statistical and stereological techniques would be used, in the estimation of size. Stereology, according to 'is a body of methods microstructure as seen in or projection plane to quantities' .
Underwood (1970), for relating the the random section the true spatial
stereologyl provides tools that allow measurements on a two-dimensional plane to be related to a three-dimensional structure or, as in this case, allow one-dimensional chord data to be extrapolated to three- dimensional size data (sieve size). statistically exact stereological solutions to the measurement of size from profiles or cho rd lengths are possible for regularly shaped particles such as spheres. However, this is not the case for real particles of irregular shape like those found on au togenous-mill conveyor belts. Also, group properties such as size distribution can be evaluated by use of these techniques only if a large enough number of random sections, or samples of a group of particles, to be characterized, is available. In tuitively, it appears to be more correct to calculate size from the projected areas of the rocks than from the measurement of chord lengths. However, this is not so, since stereological techniques allow zero, one-, o r two-dimensional measurements to be used in the prediction of high-order dimensional quantities, (within limits, of course). Hence chord lengths were chosen because they are more easily computed than proj ected areas, and because projected areas are also more sensitive to edge errors in the rock outline than chords. IMAGE PROCESSING AND ANALYSIS As discussed above, the images of the rock scenes as captured on camera are not in a form that allows for the direct measurement of chord length. These 'raw' images (Io) have to be processed or reduced to a form (I t) where chord probe I ines can be appl ied (11.) , and the chord lengths can be measured (m) .
1.
Strictly speaking the term stereology may be replaced by stereometry.)
Sill' Distrii>lItioll of R()ck>
The obj ective of image processing is the stripping away of all unwanted information (Williams 1988) , so that only the outlines of the rocks remain. For this to be done it is important to ensure that the images are captured with the highest possible degree of accuracy and with little or no noise. Thus, most of the processing effort can be directed towards edge detection rather than image restoration or correction. This strategy also helps to reduce the processing time per image. Design Methodology and Philosophy The accuracy of each stage in image processing is affected by the previous stage. The principle employed is similar to the generation and propagation of noise in a series of amplifiers. Each stage not only amplifies the noise from the previous stage; it introduces its own noise, which tends to decrease the ratio of information (signal) to noise. Therefore the design methodology adopted in the present work involved the specification of the role of each sequential stage (starting at the front with the capture of the image), followed by optimization of the algorithm developed so that it would be as fast and as accurate as possible. Another reason for the development of each stage sequentially was that it was difficult to analyse and model the dynamics of the total system, and to describe the propagation as well as the accuracy of the information through the system. For example, what is the relationship between the angle of illumination and the creation of unwanted edges and the detection of unwanted chords? A number of image-processing architectures have been designed and tried and the fundamental strategy by which the edges are extracted is as follows (Fig. 5).
(1)
The image is captured and filtered as required.
(2)
The edges are detected.
(3)
Any missing gaps in the edges are closed, and unwanted edges are removed.
q
GR,W B.i lter FG
_ _ _ _.....J
9
E_d__e_---' improvement
L __
L
G
Edg_
imag e
Fig. 5. Block diagram of the main parts of the image-processing system.
stage 4
The system fills in gaps in the edges and removes unwanted edges.
stage 5
The system measures chord lengths.
This sequence of stages is based on imageprocessing and object- recognition systems wi th typical archi tectures. However, it must be pointed out that this structure has, and wil l be, changed many times. An option that is under investigation is the use of feedback to al ter control parameters to the various stages based on a knowledge base of the expected chord distributions and other heuristic information. This may be neccesary because of the wide variation in the rock scenes to be analysed. Identification of the Rock and its Edges It has been found that rock-edge detection is the most critical part of the whole system since the c hord lengths are measured from these edges. The chord lengths are very sensitive to the accuracy of the detected edges, however, statistics can be used to minimize this sensitivity, but at the cost of resolution and accuracy. since the conveyor belt is generally covered entirely with rocks, the main task is to segment th e edges from the rocks and their interiors. As in most image-processing applications , the biggest problem is the selection of the quickest and most accurate algorithms to perform the filtering, objec t-recognition, and extraction proces ses required for this segmentation. Gurari and Wechsler (1982) conclude that the usual approach to such a problem is an ad hoc, approac h, i. e. the use of heuristic methods. The traditional trade-off between speed and accuracy manifests itself very strongly here, in th at h ighly accurate edge detection requires a lot of processing time, and a rapid edge-detection algorithm will be very prone to errors . Low-pass spatial filtering is required initially to remove impulse (spot) noise, and to smooth the interiors of the rocks while preserving their true outlines. These are conflicti ng goals, and tests have shown that simple, neighbourhood, averaging convolutions appear to work best for this initial filtering. Spatial frequency-domain filters, median filters (Bovik, 1987; Arce and Stevenso n, 1987), and recursive filters (Shanks, and Justice, 1972; Hu and Rabiner, 1972) have been tried, but disadvantages such as large computation times and instability with the recursive filters caused these techniques to be discarded.
s t ag e 1
The system captures the rock images with as little noise, distortion, blurring, and other unwanted effects as possible.
stage 2
The system f il ters out any spurious noise such as spot n01se and smoothes out the irregular features on each rock while preserving the edge information.
Segme ntation and edge detection for object recognition and extraction has been widely researched by a great many workers, in a large number of different applications, (Torre and Poggio , 1986; Garbay, 1986; Pratt, 1978). Commercial instruments are available that perform edge detection and segmentation on images (Sanz, 1988). Applications range from the segmentation of different cells or parts of a cell in medical applications (Jain and colleagues, 1980) to the segmentation of tanks from background bushes in military applications.
stage 3
The system recognises and defines each rock in the image as accurately as possible, and then extracts the edges.
In many segmentation applications, the objects to be segmented from the background are of a different intensity and are easily discernible. This is not the case with rock
A more detailed expansion on strategy is described below:
the
above
30
T. B.
images. As a result most segmentation techniques described in the literature could not be applied in the present work. A number of segmentation and edge-detection techniques were examined for edge detection. The next paragraphs describe these tests briefly and explain why the various techniques were rej ected. It should be noted that the future use of these techniques is being reviewed continuously as technology improves. Rule Bases. The geometry of the shape and size of the entities in the image captured are random, and vary tremendously. This randomness eliminates a large selection of image-processing techniques-including template matching - that make use a priori of the expected shape and size of the objects to be found. This does not mean that no heuristic information can be used. On the contrary, the rocks themselves have a unique description that allows certain shapes to be excluded. Berger (1985) designed a rule-based system for the measurement of rock size, but, the processing time per image was about threequarters of an hour on a minicomputer, which is obviously unacceptable. Thresholding. The grey-level histogram of typical scenes from the conveyor belts are unimodal, and are more difficul t to process,(Bhanu and Faugers, 1982). This is unfortunate because a great many segmentation teChniques using thresholding for segmentation of the images cannot be used (Weszka, 1978). Convolution and Templates. This class of edge-detection methods is very well established, and does have potential. They include for example, the Soble and Roberts edge detector, the integrated directional derivative gradient operator (Zuniga and Haralick, 1987), and the calculation of the first and second derivatives (Laplacian) of the image. The grey levels in the image can be regarded as a surface in three dimensions, with hills, valleys, troughs, etc. However, a large variety of edges is present in rock images and experiments have shown that the application of one edge detector is inadequate. This is because each edgedetector template is a function of the shape, size and slope of the edge, and detects only a subset of all the edges, which implies multiple passes with many edge templates of different size and shape. This is very intensive computationally and demands a large amount of memory. Such methods may be more viable with powerful parallel hardware systems. Also these methods are intrinsically sensitive to noise (differentiate), and it is difficult to find a balance between the correct pre-filters (integrator) and edge detector, particularly in view of the wide range of input images. Frequency-Domain and Texture-Analysis Techniques. These methods were also rejected, mainly because the image patterns vary too much for these processes to. be u~ed effectively, and because the processlng tlme is again too long. Laplacian operator. The only traditional technique that proved to be very useful in the detection of a large proportion of the edges was the Laplacian operator. This edge detector is quick, and found an estimated 50 to 80 per cent of the edqes because it is less
LIII)..((,
sensitive to edge direction than most other operators. This edge detector was ul timately also abandoned in favour of morphological edge detectors. Completing the Resultant Edge Patterns The edge detectors that were tested or selected, extracted on average about twothirds of all the required edges. A portion of the entities (edges) produced by these edge-detection algorithms also consist of noise, which includes valid edges that are not part of the true rock perimeter, as well as gaps in the true perimeter. The chordlength distributions derived from such edge patterns are therefore full of errors and some post-processing is required for the removal of this noise. A number of methods were developed in an attempt to fill in the missing edges and erase unwanted edges. This is where most (70 to 80 per cent) of the processing time was taken up, and traditional techniques using heuristic knowledge and artifical intelligence were implemented. Figure 6 illustrates one of the first teChniques that was developed in an effort to close the gaps and remove unwanted edges. This method used a rule base, the design of which was based on the most probable shapes of the rock outl ines, to complete the edges. The method was abandoned in favour of morphological teChniques, which are discussed below.
a
c
b
d
Fig. 6. Illustration of a rule-based method method designed for the closing of edge gaps. a. Orig inal; b. After edge detection; c and d. Two results with varying rule parameters.
:11 Mathematical Morphology From an inspection of the resultant binary edge patterns produced by segmentation and edge detection (Fig. 6b), it is relatively easy to analyse the shape of the rocks and perceive the rock edges. It is bel ieved that in the processing of these image entities to improve the edge patterns, mathematical morphology approaches most closely the processes of the human mind, because morphological operators relate directly to shape. Mathematical morphology was introduced by Matheron (1975) and Serra (1982) as a set theoretical method for image analysis whose purpose is the quantitative description of geometrical structures. According to Haralick and co-workers (1987), 'morphological operations tend to simplify image data preserving their essential shape characteristics and eliminating irrelevancies' . At present these techniques provide the means by which most of the gaps are filled and unwanted edges are removed. The implementation of morphological techniques is beyond the scope of this paper, and will not be discussed here. However, the reader is referred to Maragos (1985, 1987); Maragos and Schafer (1986) ; and Haralick and co-workers, (1987) . Fig. 7 shows how the morphological operation of opening helps to remove impulse noise from an edge pattern, and Fig. 8 shows how the morphological operation of closing helps to remove small gaps in the edges detected. b
Fig.
7.
Filtering of noise by use of morphological opening. a. Before opening; b. After opening.
At first, morphological methods were used only for the improvement of resul tant binary edge patterns as detected by the Laplacian operator. However, additional research indicated that mathematical morphology could also be used for edge detection. A morphological edge detector operates on grey-scale images and uses grey-scale morphological techniques instead of binary morphology (Maragos, 1985, 1987; Maragos and SChafer, 1986; and Haralick and co-workers, 1987) .
8. Use of morphological closing to close edge gaps. a. Before closing; b. After closing I~DWARE
CONSIDERATIONS
The choice of algorithms for the system was influenced by real-time constraints, and the requirement that they should be implemented at a relatively low cost. Time constants in the mineral-processing industry are typically 15 minutes, and range from 1 minute to hours. (This is very different from military applications where real-time can be considered in milliseconds.) These real-time specifications allow for the use of general-purpose computing hardware as opposed to specialized hard,oJare where the algorithms are built into custom circuits and integrated circuits. So far, all development work has been undertaken on machines using the Intel 80286 or 80386 type microprocessors with Data Translation imaging boards, which allow for a great deal of flexibility in software developement. Because high sampling rates of images are required, the processing speeds are still too slow (60 seconds per image). However, powerful accelerator cards and co-processors for the AT-type microcomputer can be used to improve performance to levels approaching supercomputing. In particular, the Transputers from Inmos have great potential because of their fairly high power, as well as their ability to be linked in parallel. It is important to note that many hardware systems are available in which morphological operations as well as other well-known traditional image-processing algorithms are implemented. other options that may prove useful in future are the use of optical processors and neural networks, which could be 'taught' to recognise rocks in an image. TEST RESULTS At first, the testing and development of this instrument appeared to be straightforward, the only problem being the development of the software. However, in retrospect, this was not the case as difficulties were encountered wi th dynamic image capture and, as a result, most tests were done on static images in the laboratory. A closed-loop conveyor-bel t test bed is currently being set up for the testing of continuous on-line measurements. Figures 9, 10 show the typical cumulative chord-length distributions obtained for grani te rocks by the image system in the laboratory. These curves show that the system can distinguish between different sieve sizes as well as different distributions of sieve sizes.
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is made up of two fields, one of which consists of the even lines and the other of the odd lines. These fields are sensed 20ms apart and, since the rock scene is moving relative to the camera, one field is displaced relative to the other, rendering the image useless. Realignment software, as well as the use of one field, was investigated but, because of perspective and quantization errors, the use of these cameras was abandoned.
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Chord length, pixels
Fig. 9. Cumulative chord-length distributions for sieved rock piles
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Illumination The best method of illumination of the belt is still a subject of serious contention regarding such factors as intensity, the type of light (diffuse or direct), colour, polarization, and the number of lights as well as their arrangement relative to one another and the belt scene. For example, angled lighting dramatically improves the quantity and quality of the outlines of the rocks, but increases the number of unwanted edges. CONVERSION OF CHORD LENGTH TO SIZE
0.75
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~
Varying Belt Speed and Geometric Distortion The use of a line-scan camera sol ved both the blurring and interlacing problems. A custom controller was built for the line-scan camera to compensate for problems due to different belt speeds and sizes. The controller also controls the aspect ratio and size of the pixels, as well as the image.
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The last stage of the measurement system is the transformation of the chord-length distributions into a form more acceptable to the metallurgist, e.g. sieve size. This stage may be unnecessary if the chord-length distribution can be fed directly into the control system of the mill.
Chord length, pixels
Fig.lO. Cumulative chord-length distributions for mixed rock piles For the different rock distributions used in the tests (Fig. 10), different portions (by mass) of sieved rock fractions were mixed according to the Rosin-Rammler function, and by varying n to produce different rock piles, i. e.
The transformation can be considered a deconvolution of the integral equation (simplified), as shown below, in order to solve for f ( D) where p(L ) and P(L/D) are known. P (L)
where (4 )
where
P (L ) f(D) P(L/D )
X f (X ) b,n
is size distribution, and characteristic constants
Practical problems experienced during tests on static and dynamic images are listed below. Wet material causes problems with respect to reflection and contrast. Blurring Conveyor belts on mineralprocessing plants have velocities ranging from about O. 1 m/ s to over 2 m/ s. Al though a CCD camera with a high shutter speed (1 ms) ~ol ved most of the problems due to blurring, l.t was effective only on belts moving at less than 0.75 m/so Interlacing Commercial cameras using an interlacing format could not be used for dynamic image capture. A television frame
r
P(L / D ) f ( D ) dD,
(5)
o
is the chord-length distribution as measured the size distribution required, and the conditional probability density function relating chord-length to size.
The solution for f ( D ) is not a trivial exercise, and has been researched by King (1982), and by Yu and Gentry (1987). Chen and colleagues (1987) have shown that constrained linear inversion can be used for this transformation, and initial work in the present investigation showed that this method has potential. Figure 11 shows the resul ts for the conversion of chord distribution to size by use of constrained linear inversion. Only five images were processed for each of the five size ranges shown. The errors in the above measurement are attributed mainly to the small number of samples processed here.
Size Distribution of Roc ks 1. 0
I'Zl Calculated distribution
0 .8
-
0.8
True distribution
0 .4
33
irregularly shaped rocks and, more seriously, that only simulations with realistically shaped particles will contribute any real information to the interpretation of the chord distributions.
0 .2
f~ ~~_L'2~'-0~8m-m- ~~~5L'-'2~m-m--~-~~'~8~"~5-m-m--~~-~25~'-'~9m-m---u-31I ~.-'2~5~m~m o
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Fig.ll.
Results of constrained linear inversion for the conversion of chord-length to sieve size
Sampling Sampling is an important factor influencing this measurement technique. Examination of the chord-length distributions measured in tests, as well as the results of the constrained linear inversion, show that the number of chord samples processed is critical to the accuracy or validity of the measurement_ Monte Carlo simulations carried out on circles in the present work, and work done by Kawakami and co-workers (1987), confirm this. The Monte Carlo simulations showed that measurements of 100 000 samples yield fairly low deviations (less than 3 per cent) , which is also indicative of the potential accuracy that can be obtained. It also indicates, as emphasized previously, that the image-processing rate of the system has to be fast as well, particularly if the size statistics are not stationary. The Monte Carlo simulations were also used as a test of the effect of various factors on c hord distributions and as an aid in the understanding and derivation of the kernel P (L/ DJ of equation (4) required for the transformation equation (3). These factors are: (a)
the relationship between different distributions of circles (e_g. single sizes, normal, and log normal) and the chord distributions,
(b)
the effect of overlapping, spacing and packing (i.e. occlusion), and
(c)
chord probe-line spacing.
This work indicated that, for circles, a single size can be read off directly from the chord distribution. This is not the case for more- complex distributions of circles, such as log normal distributions, although there is a strong correlation between the shape of the size distribution and of the chord distribution. Overlapping of circles, and oversampling by probe lines being placed too close to each other, also biases the distribution, although this biasing does not appear to affect the shape of the distribution. It is believed that these factors will affect the chord distributions, as measured from
Another point that arises from these simulations, and from observations, is that the surface distribution of rocks is not representative of the actual size distribution of the whole volume of material on the belt. This is because of the sorting and packing processes experienced by these particles. This was simulated to a limited extent with circles, and initial studies have indicated that this 'packing' factor could possibly be predicted. CONCLUSION A system that measures the size distribution of rocks on a conveyor belt in real-time is currently under development. Problems such as dynamic image capture, rock recognition, rock-edge detection, and size measurement have been addressed and largely solved. The image processing was aided greatly by the use of mathematical morphology, and stereology. Constrained linear inversion provides a simple yet effective tool for the transformation of chord-length measurements to sieve size. There are problems due to the overlapping and occluding of rocks, and these phenomena must be taken into account. At present, the system can differentiate between different sieve sizes, as well as different distributions. The system must process as many samples as quickly as possible in order to achieve improved accuracy, reduced variations, and operate in real-time. Instrument specifications such as those for range and accuracy are therefore dependent on the hardware as well as the software. Since technology is advancing rapidly it should not take long for the ideal instrument is realized. ACKNOWLEDGEMENT This paper is published by permission of the Council for Mineral Technology (Mintek). REFERENCES AlIen, T. (1981). Particle size measurement. 3rd ed. Chapman and Hall, London, Chap. 4 . Arce, G. R., and R.L . Stevenson, (1987). On the synthesis of median filter systems. IEEE Tra n s. on Circuits Systems., Berger, G. F. (1985). So ftware for a particle size analys er bas ed on image analysis te c hniques . M.Sc. Dissertation, University of the Witwatersrand, Johannesburg. Bhanu, B., and o. D. Faugers (1982) . Segmentation of images having unimoda1 distributions. IEEE Trans. on Pattern Analysis Machine Intelligence, Vol. PAMI-4, No.4, 408-419. Bovik, A. C., T.S. Huang. and D.C. Munson. (1987). The effect of median filtering on edge estimation and detection. IEEE Trans. on Pattern Analysis Machine Intelligence, Vol. PAMI-9, No.2, pp 181194.
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Maragos, P. A., and R.W.Schafer (1986). Applications of morphological filtering to image analysis and processing. Conference on Acoustics, Speech and Signal Processing, Tokoyo Japan. pp.2067-2069. Matheron, G. (1975). Random sets and integral geometry. John Wiley, New York. Pratt, W. K. (1978) . Digital image processing. John Wiley, New York. Sanz, J. L. C.Ed. (1988). Special PAMI Issues on Industrial Machine Vision and Computer Technology. Part 1. IEEE Trans. Pattern Analysis Machine Intelligence. Vol.10, No.l. Serra, J. (1982). Image analysis and mathematical morphology. Academic Press, London. Shanks, J. L., and J.H. Justice, (1972) . Stability and synthesis of twodimensional recursive filters. IEEE Trans. Audio electroacoustics, Vol.AU-20, No.2, 115-128. Sresty, G. C., R.Venkateswar, (1980). Particle size analysis - A review. In Proceedings of the International Symposium, Las Vegas, Nev, February. pp. 329 -365. Torre, V., and T.A.Poggio, (1986). On edge detection. IEEE Trans. Pattern Analysis Machine Intelligence, Vol.PAMI-8, No.2, 147-163. Underwood, E. E. (1970). Quantitative stereology. Addison Wesley, Reading, Massachusetts. Vignos, J.H., L.Elbe r, and E. Gallagher,(1 979) . Coarse particle size distribution transmitter. Meeting of SME of AIME, Tucson, Arizona, October 1979. Weszka, J. S. (1978). A survey of threshold selection techniques. Comput. Graphics Image Process. 7, 259-265. Williams, T. (1988). Object recognition opens the eyes of machine vison systems. Comput . Des. 69-84. Yache r C., C. Gonzalez, G. Van Boses, and R. Nobel, (1985). Coarse particle size distribution analizer. Instrumentation in the Mining and Metallurgy ~ndustries. 13th Annual Mining and Metallurgy Synposium. Vol.12, 71-79. Yu, P., andJ. Gentry (1987). Comparison of g ene tic inversion algorithms for characterizing particle size distribution. Powder Techn. 50, 79-89. Zuniga, O.A., and R.M. Haralick (1987). Integrated directional derivative gradient operator. IEEE Trans. Pattern Analysis l-1achine Intelligence, Vol. 17, NO.3.