- Email: [email protected]
An approach to rock size measurement based on a model of the human visual system
Minerals Engineering, Vol. 10, No. 10, pp. 1085-1093, 1997
Pergamon S0892--6875(97)00095-2
(0 1997 Published by Elsevier Science Ltd All rights reserved. Printed in Great Britain 0892-6875/97 $17.00+0.00
AN A P P R O A C H T O R O C K S I Z E M E A S U R E M E N T B A S E D ON A MODEL OF THE HUMAN VISUAL SYSTEM
R.C. CRIDA and G. de JAGER Department of Electrical Engineering, University of Cape Town, Private Bag, Rondebosch 7700, South Africa. E-mail: [email protected] (Received 14 April 1997; accepted 6 June 1997)
ABSTRACT This paper describes research into the development of an instrument for the purpose of performing online measurement of rock size distributions using machine vision. Such an instrument would have application in the gold mining industry where it could be used to measure the fragmentation of gold ore on a conveyor belt feed to an autogenous mill, for the purpose of controlling the mill. A computation structure has been developed to identify and delineate rocks in an image for the purpose of measuring their areas. It is based on the human visual system in that it consists of a low-level preattentive vision stage and a higher-level stage of attention focusing Multiscalar image processing techniques have also been integrated in order to improve the detection of rocks across a wide range of sizes. A performance advantage can be obtained in this way because all the algorithms can be better matched to the size of objects being detected. © 1997 Published by Elsevier Science Ltd
Keywords Autogenous grinding; sizing; process control
INTRODUCTION Measurement of rock size distributions of fragmentation has application in the mining industry where sophisticated conlxol systems are used to monitor and control autogenous mills. The use of image processing as a non-invasive measurement technique offers advantages over conventional techniques such as: undisturbed feed monitoring, repeatable results and reliability in a harsh measurement enviromnent. Miles and Hall [1], Hunter et al [2] and Kemeny [3] give reviews of rock fragmentation analysis techniques using computer vision with emphasis on the analysis of blast muckpiles. Although encouraging results have been reported in the literature [4,5] there are certain limitations and problems which have been consistently identified. A major complication in all of the methods is that they aim to measure aJtl sizes of rock at one time with the exception of McDermott and Miles [6] who use a two
1085
lO86
R.C. Cridaand G. de Jager
pass process to measure large and small rocks. This problem is compounded by the fact that the segmentation algorithms generally consist of fairly low-level image processing procedures which are generally sensitive to scale and therefore not suitable for detecting a wide size range of objects [7]. The method that is described in this paper attempts to counteract this problem by using a multiscalar approach to create an image pyramid. It is then only necessary to produce a system which is capable of detecting a single size of rock. By applying it to each level of the pyramid, all sizes will effectively be detected using an optimal approach. Furthermore, the method that is described for detecting rocks in the image pyramid is based on a simplified model of the human visual system. According to Treisman [8], the human visual perception system allows the viewer to perceive the world as consisting of coherently organised, recognisable objects. She further states that a model of the visual system containing two stages is accepted in the area of artificial intelligence research. The first stage involves the extraction of features from patterns of light. This is preattentive vision and happens automatically and in parallel for the whole scene. The second stage involves the identification of objects and their settings. This stage is referred to as attention focusing and uses prior knowledge which is typically specific to a domain to examine and classify regions of the scene which were highlighted by the feature detectors in the first stage. In the present application, the preattentive vision stage is accomplished by identifying ellipticaUy shaped target features using intensity gradient information. Attention is then focussed on these regions in order to locate actual rocks. This process involves segmenting the local region based on the orientation and position of the detected ellipse and incorporates knowledge about the visual characteristics of rocks. Finally, the segmented region is analysed using feature classification to determine whether it is a representation of a rock or not. Due to the multiscalar nature of the solution it is necessary to perform a final stage of hierarchical analysis of the results obtained at each level of the image pyramid. In this stage, all the detected rock positions from each level of the pyramid are examined and a most probable list of rocks is generated. Finally, Results and Conclusions are given.
IMAGE PYRAMID FORMATION The most important factor to consider when generating the image pyramid is how to perform image smoothing before resampling in order to obtain desirable visual characteristics at each level of the pyramid. Lifshitz and Pizer [9] have demonstrated that Gaussian smoothing is a solution for the diffusion equation and as such, ensures that no new extrema are introduced to the image as smoothing occurs. This is significant in many multiscalar applications which follow extrema through scale-space. In this application, the creation of new extrema would not be critical, because the segmentation algorithm is more dependent on the macro structure of the image in a region, and the choice of a Gaussian filter was based on two further factors: (1) Smoothing can be cascaded since convolution of a Gaussian with a Gaussian is another Gaussian and (2) the modulation Uansfer function or frequency response of the imaging system can be reasonably approximated using a Gaussian. It is conunon in multiscalar applications to create a dyadic pyramid, i.e. the size of each level of the pyramid is an integer power of two. In this case, the rock detection algorithm described in the next three stages is optimised to fred rocks of a particular size. Obviously, the algorithm will respond to rocks which are also slightly larger or smaller than the optimum size and so there is a narrow band of rock sizes which can be detected on one layer of the image pyramid. It is therefore necessary to ensure that the scale
Rock size measurement
1087
difference between adjacent layer of the pyramid is less than the bandwidth of the detection algorithm with the result that the ,;tandard pyramid scale factor of 0.5 might not be appropriate. In practice, experimentation showed that best results are obtained when the scale factor is 0.85. Figure 1 shows four levels of an example pyramid created using a scale factor of 0.8. Each level was appropriately smoothed before subsampling to result in an image which appears to have been convolved with a Gaussian with t~ = 1.
iii i
Fig.1 An image pyramid created using a scaling factor of 0.8 and Gaussian smoothing with t~=l.
PREATTENTIVE VISION The preattentive vision stage is responsible for scanning each level of the image pyramid to detect target features for further analysis in the following operations. To facilitate this procedure, the basic assumption is made that the shape of a rock can be reasonably accurately modelled using an ellipse. This is implemented by performing edge detection of a level of the: pyramid and using the Hough transform to detect ellipses. Since only one size of rock is to be detected at a particular level of the pyramid, the edge detection process
1088
R.C. Crida and G. de Jager
has been optimised to respond most strongly and accurately to objects of that size. The Hough transform also need only detect ellipses of various eccentricity, but one size (ellipse size is defined here to be area). An analysis of lighting and the appearance of rocks was used to create a suitable edge detection algorithm which is demonstrated in Figure 2. It was determined that under a diffuse light source, the intensity at the edge of an Object would be less than a fraction of the intensity of a horizontal surface on the object with the result that a form of adaptive thresholding could be used to detect the shadows around the edges of rocks in the image [10].
(a) Smoothed image using local mean.
(b) Dilated image to make intensity maxima as large as expected rock size.
(c) Thresholded rock image using 0.7 times the dilated image value.
";...
•
(d) The Hough transform of the rock edge image to detect ellipses with an aspect ratio of 1.2 and an orientation of 0. Fig.2
¢
(e) Clipped image which only keeps strong ellipse responses.
(f) Detection of peaks for tinal target selection.
Example of the stages of processing that are performed during the preattentive vision stage for one level of the image pyramid.
ATTENTION FOCUSING The purpose of attention focusing is to analyse each of the detected target features from the preattentive vision stage in order to determine the extent of the object in the image. This is achieved, using a segmentation algorithm which incorporates information about the expected size and shape of the rock in the form of an ellipse model with known position, size, aspect ratio and orientation. Furthermore, the rock will be lighter than its immediate background due to shadows east by the lighting system. The rock is a physical object and sliould therefore comply with the following two roles: it must have a continuous boundary and a simply connected interior. The segmentation algorithm that was developed consists of three sections: firstly, edge points are detected using the ellipse model and knowledge that intensity decreases radially at the edge of the rock; secondly, edge points are linked to create a continuous boundary; and thirdly, the interior of the boundary is filled to produce a labelled region which corresponds to the object in the image.
Rock size measurement
1089
It is possible that many of the targets which were detected in preattentive vision do not actually correspond to a rock and so there will be many instances in which the ellipse model does not correspond to what is actually present in the image. What is important at this stage is to ensure that if a rock is actually present, that it is segmented as accurately as possible. Figure 3 shows the various stages of segmentation for six example targets which do actually contain rocks. It can be seen from these results that when a rock is present, it is accurately segmented.
,~ii'ii
(a) Image of target region. '~i~'
i~;:il i:
i'
I,.
,I
'I.
......
I' ~1 ~-._..~ i.
(b) Ellipsemodel for each region.
!'t °o %
F"
!i,
~,
(c) Detected edge points.
,,,t,
"S--'o r
"II •
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i"
i
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I
|,°L I'"!
mli •
ij |
(d) Continuous boundary. ~!::
f-'-',?
iF~:¸ IX'=.,-.
If w
"l,..,,,ll~
i
"1~. ! ii!i (e) Labelled region and outline.
Fig.3 Stages of segmentation for 6 example target regions containing rocks.
1090
R.C. Crida and G. de Jager OBJECT IDENTIFICATION
Because it is possible that the preattentive vision stage detected targets that do not correspond to rocks, it is necessary to identify which of the regions that have been segmented could be a rock. This is achieved by means of a classification process and is therefore similar to a second function of attention focusing in the human visual system which compares the current object to an internal representation in order to perform identification.
In practice, this is achieved by analysing characteristics of the segmented regions to determine whether or not they could correspond to a rock which matches the predicted ellipse model. Note that no information concerning the context of the rock (the arrangement of rocks in the image) is considered at this stage. It is therefore possible that there may be several adjacent hits on a rock (due to close hits on the same object during preattentive vision) or in contradictory positions in the image (due to classification error). See Crida and de Jager [11] for a more complete explanation of the segmentation and classification processes. The next stage of hierarchical analysis is responsible for consolidating all of the detected rock positions into a final realistic list of rocks.
H I E R A R C H I C A L ANALYSIS The aim of the hierarchical analysis is to determine the final list of rocks in the image from the results of the identification process from each level of the pyramid. This stage is necessary because the preattentive vision process typically highlights more positions in the image where there are not actually rocks than where there are rocks. Unfortunately, although the identification process removes a large proportion of the false ,alarms from the list of targets, there still remains the possibility of multiple hits on each rock and further false alarms. False alarms occur in situations where a group of rocks is merged together, or a single rock is split at relatively high resolution such that its comers appear as individual rocks. The result of these factors is that there are many extraneous detections of rocks in the image pyramid which must be removed before a size distribution can be calculated. A tree structure has been used for this purpose by representing the appearance and disappearance of rocks in the scale structure of the image. The tree structure may be complicated since there can be more than one point corresponding to each rock which will result in multiple branches at that level. Each tree represents a possible rock in the image, All trees are processed to form a normalised representation before ranking using a weighting function in order to delete overlapping trees. The remaining trees represent the most probable collection of rocks in the image. Trees are grown in the following way: Each detected target which was identified as representing a rock becomes a node with information about its ellipse position, aspect ratio and orientation, and strength of detection during preattentive vision. Each node becomes the root of its own tree which can then grow towards the base of the pyramid. All nodes on the next level of the pyramid within a certain footprint become children of the node. The depth to which a tree may grow is limited. The result of this process is that the trees that are generated will have the following characteristics: There are as many trees as there are nodes. The root of a tree occurs at the highest pyramid level and it grows downward toward the base of the pyramid. Each node may have multiple branches to the level below. Each node may appear in several different trees or even in different branches of the same tree.
Rock size measurement
1091
Each tree is then pruned to form a normalised representation by selecting the core tree which has the highest possible score and is therefore most likely to represent a rock. The following simple recursive algorithm describes how the pruning process is achieved: .
2.
Determine which branch of the current node has the highest branch score and delete all other branches. Apply the pruning algorithm to the remaining branch until there are no branches.
Finally, all the rocks that are represented by each of the trees are compared. For each pair of rocks that overlap by more than a certain amount, the scores of the trees are compared and the rock with a weaker score is deleted. This is repeated until there are no more overlapping rocks. Note that a small amount of overlap is allowed because the ellipse representation of the rocks are compared and they may not accurately model the edge of the rock at all points. Figure 4 shows the steps of hierarchical analysis. In (a), all the detected rocks are represented using the ellipse which is shaded using the score of the tree. High scores correspond to bright ellipses. In (b), overlapping ellipses have been deleted and in (c), the segmentation algorithm has been used to determine the actual shape of the rocks.
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-
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i:
(a) Rocks represented by all possible trees displayed using a intensity weighted ellipse.
(b) Ellipse representation of final rock list after deletion of overlapping rocks.
(c) Final rock list showing detected boundaries.
Fig.4 Stages of hierarchical analysis.
RESULTS The aim of the research was to produce an instrument for measuring rock size distribution that is tolerant of the following conditions in that it should be able to achieve correct results in their presence:
(l)
It should correctly identify all rocks in the image regardless of their individual intensity. Specifically, it should not be biased against dark rocks or rocks in the shadow of larger, lighter rocks.
(2)
It should find the same result regardless of rotation, reflection, magnification and translation of the image or rocks in the image.
(3)
The instrttment should not confuse areas of fines in the image for larger rocks.
Figure 5 shows some sample results obtained with the procedure described in this paper. Note that in each case, the same op(~ating parameters have been used which indicates that the method is robust and capable of handling changimg conditions successfully. It can also be seen that the goals of the system appear to have been satisfied. Computation time was approximately 10 minutes on a Sun Spare 20 processor in each case.
1092
R.C. Crida and G. de Jager
(a) Real rock scene.
(b) Rock scene with fines.
(c) Laboratory scene.
Fig.5 Boundaries of detected rocks for three example scenes.
CONCLUSIONS A need has been identified in the mining industry for an instrument for measuring rock fragmentation. A measure of rock fragmentation will be useful for increasing the efficiency of the gold extraction process by improving control over comminution using autogenous mills. A computational framework based on the structure of the human visual system and multiscalar image analysis has been implemented. The results in the previous section indicate that this approach has provided a method which is capable of producing accurate results with a relatively high degree of flexibility with regard to image capture conditions and the appearance of the rock material.
ACKNOWLEDGEMENTS
The authors acknowledge the support of MINTEK who have sponsored this research.
REFERENCES o
2.
.
4. 5.
.
7. 8. 9.
10.
Miles, N.J. & Hall, S.T., Image Processing: Diagnostic and control applications in mineral processing, tech. rep., University of Nottingham, Nottingham, England. Hunter, G.C., McDermott, C., Miles, N.J., Singh, A. & Scoble, M.J., A review of image analysis techniques for measuring blast fragmentation. Mining Science and Technology, 11, 19-36 (July 1990). Kemeny, J.M., Practical technique for determining the size distribution of blasted benches, waste dumps and heap leach sites. Mining Engineering, 1281-1284 (Nov. 1994). Berger, G. F.-M., Software for a particle-size analyser based on image analysis techniques. Master's Thesis, University of the Witwatersrand, (1985). Wu, X. & Kemeny, J.M., A segmentation method for multi-connected particle delineation, in IEEE Workshop on Applications of Computer Vision, no. 92TH0446-5, (Palm Springs, CA, USA), 240-247 (Nov. 1992). McDermott, C. &, Miles, N.J., The measurement of rock fragmentation using image analysis. Departmental Magazine, Department of Mining Engineering, 49-61 (1988). Mart, D. & Hildreth, E., Theory of edge detection. Royal Society of London Proceedings B, 207, 187-217 (1980). Treisman, A., Features and objects in visual processing. Scientific American, 255, 106-115 (Nov. 1986). Lifshitz, L.M. & Pizer, S.M., A multiresolution hierarchical approach to image segmentation based on intensity extrema. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 529-540 (June 1990). Crida, R.C., A Machine Vision Approach to Rock Fragmentation Analysis. PhD Thesis, University of Cape Town, (Sept. 1995).
Rock size measurement
ll.
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Crida, R.C. & de Jager, G., Rock recognition using feature classification, in 1994 IEEE South African Symposium on Communications and Signal Processing (COMSIG'94), no. IEEE Cat No 94TH0665-0, (University of Stellenbosch), 152-157 (Oct. 1994).
Pergamon S0892--6875(97)00095-2
(0 1997 Published by Elsevier Science Ltd All rights reserved. Printed in Great Britain 0892-6875/97 $17.00+0.00
AN A P P R O A C H T O R O C K S I Z E M E A S U R E M E N T B A S E D ON A MODEL OF THE HUMAN VISUAL SYSTEM
R.C. CRIDA and G. de JAGER Department of Electrical Engineering, University of Cape Town, Private Bag, Rondebosch 7700, South Africa. E-mail: [email protected] (Received 14 April 1997; accepted 6 June 1997)
ABSTRACT This paper describes research into the development of an instrument for the purpose of performing online measurement of rock size distributions using machine vision. Such an instrument would have application in the gold mining industry where it could be used to measure the fragmentation of gold ore on a conveyor belt feed to an autogenous mill, for the purpose of controlling the mill. A computation structure has been developed to identify and delineate rocks in an image for the purpose of measuring their areas. It is based on the human visual system in that it consists of a low-level preattentive vision stage and a higher-level stage of attention focusing Multiscalar image processing techniques have also been integrated in order to improve the detection of rocks across a wide range of sizes. A performance advantage can be obtained in this way because all the algorithms can be better matched to the size of objects being detected. © 1997 Published by Elsevier Science Ltd
Keywords Autogenous grinding; sizing; process control
INTRODUCTION Measurement of rock size distributions of fragmentation has application in the mining industry where sophisticated conlxol systems are used to monitor and control autogenous mills. The use of image processing as a non-invasive measurement technique offers advantages over conventional techniques such as: undisturbed feed monitoring, repeatable results and reliability in a harsh measurement enviromnent. Miles and Hall [1], Hunter et al [2] and Kemeny [3] give reviews of rock fragmentation analysis techniques using computer vision with emphasis on the analysis of blast muckpiles. Although encouraging results have been reported in the literature [4,5] there are certain limitations and problems which have been consistently identified. A major complication in all of the methods is that they aim to measure aJtl sizes of rock at one time with the exception of McDermott and Miles [6] who use a two
1085
lO86
R.C. Cridaand G. de Jager
pass process to measure large and small rocks. This problem is compounded by the fact that the segmentation algorithms generally consist of fairly low-level image processing procedures which are generally sensitive to scale and therefore not suitable for detecting a wide size range of objects [7]. The method that is described in this paper attempts to counteract this problem by using a multiscalar approach to create an image pyramid. It is then only necessary to produce a system which is capable of detecting a single size of rock. By applying it to each level of the pyramid, all sizes will effectively be detected using an optimal approach. Furthermore, the method that is described for detecting rocks in the image pyramid is based on a simplified model of the human visual system. According to Treisman [8], the human visual perception system allows the viewer to perceive the world as consisting of coherently organised, recognisable objects. She further states that a model of the visual system containing two stages is accepted in the area of artificial intelligence research. The first stage involves the extraction of features from patterns of light. This is preattentive vision and happens automatically and in parallel for the whole scene. The second stage involves the identification of objects and their settings. This stage is referred to as attention focusing and uses prior knowledge which is typically specific to a domain to examine and classify regions of the scene which were highlighted by the feature detectors in the first stage. In the present application, the preattentive vision stage is accomplished by identifying ellipticaUy shaped target features using intensity gradient information. Attention is then focussed on these regions in order to locate actual rocks. This process involves segmenting the local region based on the orientation and position of the detected ellipse and incorporates knowledge about the visual characteristics of rocks. Finally, the segmented region is analysed using feature classification to determine whether it is a representation of a rock or not. Due to the multiscalar nature of the solution it is necessary to perform a final stage of hierarchical analysis of the results obtained at each level of the image pyramid. In this stage, all the detected rock positions from each level of the pyramid are examined and a most probable list of rocks is generated. Finally, Results and Conclusions are given.
IMAGE PYRAMID FORMATION The most important factor to consider when generating the image pyramid is how to perform image smoothing before resampling in order to obtain desirable visual characteristics at each level of the pyramid. Lifshitz and Pizer [9] have demonstrated that Gaussian smoothing is a solution for the diffusion equation and as such, ensures that no new extrema are introduced to the image as smoothing occurs. This is significant in many multiscalar applications which follow extrema through scale-space. In this application, the creation of new extrema would not be critical, because the segmentation algorithm is more dependent on the macro structure of the image in a region, and the choice of a Gaussian filter was based on two further factors: (1) Smoothing can be cascaded since convolution of a Gaussian with a Gaussian is another Gaussian and (2) the modulation Uansfer function or frequency response of the imaging system can be reasonably approximated using a Gaussian. It is conunon in multiscalar applications to create a dyadic pyramid, i.e. the size of each level of the pyramid is an integer power of two. In this case, the rock detection algorithm described in the next three stages is optimised to fred rocks of a particular size. Obviously, the algorithm will respond to rocks which are also slightly larger or smaller than the optimum size and so there is a narrow band of rock sizes which can be detected on one layer of the image pyramid. It is therefore necessary to ensure that the scale
Rock size measurement
1087
difference between adjacent layer of the pyramid is less than the bandwidth of the detection algorithm with the result that the ,;tandard pyramid scale factor of 0.5 might not be appropriate. In practice, experimentation showed that best results are obtained when the scale factor is 0.85. Figure 1 shows four levels of an example pyramid created using a scale factor of 0.8. Each level was appropriately smoothed before subsampling to result in an image which appears to have been convolved with a Gaussian with t~ = 1.
iii i
Fig.1 An image pyramid created using a scaling factor of 0.8 and Gaussian smoothing with t~=l.
PREATTENTIVE VISION The preattentive vision stage is responsible for scanning each level of the image pyramid to detect target features for further analysis in the following operations. To facilitate this procedure, the basic assumption is made that the shape of a rock can be reasonably accurately modelled using an ellipse. This is implemented by performing edge detection of a level of the: pyramid and using the Hough transform to detect ellipses. Since only one size of rock is to be detected at a particular level of the pyramid, the edge detection process
1088
R.C. Crida and G. de Jager
has been optimised to respond most strongly and accurately to objects of that size. The Hough transform also need only detect ellipses of various eccentricity, but one size (ellipse size is defined here to be area). An analysis of lighting and the appearance of rocks was used to create a suitable edge detection algorithm which is demonstrated in Figure 2. It was determined that under a diffuse light source, the intensity at the edge of an Object would be less than a fraction of the intensity of a horizontal surface on the object with the result that a form of adaptive thresholding could be used to detect the shadows around the edges of rocks in the image [10].
(a) Smoothed image using local mean.
(b) Dilated image to make intensity maxima as large as expected rock size.
(c) Thresholded rock image using 0.7 times the dilated image value.
";...
•
(d) The Hough transform of the rock edge image to detect ellipses with an aspect ratio of 1.2 and an orientation of 0. Fig.2
¢
(e) Clipped image which only keeps strong ellipse responses.
(f) Detection of peaks for tinal target selection.
Example of the stages of processing that are performed during the preattentive vision stage for one level of the image pyramid.
ATTENTION FOCUSING The purpose of attention focusing is to analyse each of the detected target features from the preattentive vision stage in order to determine the extent of the object in the image. This is achieved, using a segmentation algorithm which incorporates information about the expected size and shape of the rock in the form of an ellipse model with known position, size, aspect ratio and orientation. Furthermore, the rock will be lighter than its immediate background due to shadows east by the lighting system. The rock is a physical object and sliould therefore comply with the following two roles: it must have a continuous boundary and a simply connected interior. The segmentation algorithm that was developed consists of three sections: firstly, edge points are detected using the ellipse model and knowledge that intensity decreases radially at the edge of the rock; secondly, edge points are linked to create a continuous boundary; and thirdly, the interior of the boundary is filled to produce a labelled region which corresponds to the object in the image.
Rock size measurement
1089
It is possible that many of the targets which were detected in preattentive vision do not actually correspond to a rock and so there will be many instances in which the ellipse model does not correspond to what is actually present in the image. What is important at this stage is to ensure that if a rock is actually present, that it is segmented as accurately as possible. Figure 3 shows the various stages of segmentation for six example targets which do actually contain rocks. It can be seen from these results that when a rock is present, it is accurately segmented.
,~ii'ii
(a) Image of target region. '~i~'
i~;:il i:
i'
I,.
,I
'I.
......
I' ~1 ~-._..~ i.
(b) Ellipsemodel for each region.
!'t °o %
F"
!i,
~,
(c) Detected edge points.
,,,t,
"S--'o r
"II •
iiiill
i"
i
FX |
•Im
I
|,°L I'"!
mli •
ij |
(d) Continuous boundary. ~!::
f-'-',?
iF~:¸ IX'=.,-.
If w
"l,..,,,ll~
i
"1~. ! ii!i (e) Labelled region and outline.
Fig.3 Stages of segmentation for 6 example target regions containing rocks.
1090
R.C. Crida and G. de Jager OBJECT IDENTIFICATION
Because it is possible that the preattentive vision stage detected targets that do not correspond to rocks, it is necessary to identify which of the regions that have been segmented could be a rock. This is achieved by means of a classification process and is therefore similar to a second function of attention focusing in the human visual system which compares the current object to an internal representation in order to perform identification.
In practice, this is achieved by analysing characteristics of the segmented regions to determine whether or not they could correspond to a rock which matches the predicted ellipse model. Note that no information concerning the context of the rock (the arrangement of rocks in the image) is considered at this stage. It is therefore possible that there may be several adjacent hits on a rock (due to close hits on the same object during preattentive vision) or in contradictory positions in the image (due to classification error). See Crida and de Jager [11] for a more complete explanation of the segmentation and classification processes. The next stage of hierarchical analysis is responsible for consolidating all of the detected rock positions into a final realistic list of rocks.
H I E R A R C H I C A L ANALYSIS The aim of the hierarchical analysis is to determine the final list of rocks in the image from the results of the identification process from each level of the pyramid. This stage is necessary because the preattentive vision process typically highlights more positions in the image where there are not actually rocks than where there are rocks. Unfortunately, although the identification process removes a large proportion of the false ,alarms from the list of targets, there still remains the possibility of multiple hits on each rock and further false alarms. False alarms occur in situations where a group of rocks is merged together, or a single rock is split at relatively high resolution such that its comers appear as individual rocks. The result of these factors is that there are many extraneous detections of rocks in the image pyramid which must be removed before a size distribution can be calculated. A tree structure has been used for this purpose by representing the appearance and disappearance of rocks in the scale structure of the image. The tree structure may be complicated since there can be more than one point corresponding to each rock which will result in multiple branches at that level. Each tree represents a possible rock in the image, All trees are processed to form a normalised representation before ranking using a weighting function in order to delete overlapping trees. The remaining trees represent the most probable collection of rocks in the image. Trees are grown in the following way: Each detected target which was identified as representing a rock becomes a node with information about its ellipse position, aspect ratio and orientation, and strength of detection during preattentive vision. Each node becomes the root of its own tree which can then grow towards the base of the pyramid. All nodes on the next level of the pyramid within a certain footprint become children of the node. The depth to which a tree may grow is limited. The result of this process is that the trees that are generated will have the following characteristics: There are as many trees as there are nodes. The root of a tree occurs at the highest pyramid level and it grows downward toward the base of the pyramid. Each node may have multiple branches to the level below. Each node may appear in several different trees or even in different branches of the same tree.
Rock size measurement
1091
Each tree is then pruned to form a normalised representation by selecting the core tree which has the highest possible score and is therefore most likely to represent a rock. The following simple recursive algorithm describes how the pruning process is achieved: .
2.
Determine which branch of the current node has the highest branch score and delete all other branches. Apply the pruning algorithm to the remaining branch until there are no branches.
Finally, all the rocks that are represented by each of the trees are compared. For each pair of rocks that overlap by more than a certain amount, the scores of the trees are compared and the rock with a weaker score is deleted. This is repeated until there are no more overlapping rocks. Note that a small amount of overlap is allowed because the ellipse representation of the rocks are compared and they may not accurately model the edge of the rock at all points. Figure 4 shows the steps of hierarchical analysis. In (a), all the detected rocks are represented using the ellipse which is shaded using the score of the tree. High scores correspond to bright ellipses. In (b), overlapping ellipses have been deleted and in (c), the segmentation algorithm has been used to determine the actual shape of the rocks.
/, !
-
"
"" k
'~'r2;~e-'-'-.
i:
(a) Rocks represented by all possible trees displayed using a intensity weighted ellipse.
(b) Ellipse representation of final rock list after deletion of overlapping rocks.
(c) Final rock list showing detected boundaries.
Fig.4 Stages of hierarchical analysis.
RESULTS The aim of the research was to produce an instrument for measuring rock size distribution that is tolerant of the following conditions in that it should be able to achieve correct results in their presence:
(l)
It should correctly identify all rocks in the image regardless of their individual intensity. Specifically, it should not be biased against dark rocks or rocks in the shadow of larger, lighter rocks.
(2)
It should find the same result regardless of rotation, reflection, magnification and translation of the image or rocks in the image.
(3)
The instrttment should not confuse areas of fines in the image for larger rocks.
Figure 5 shows some sample results obtained with the procedure described in this paper. Note that in each case, the same op(~ating parameters have been used which indicates that the method is robust and capable of handling changimg conditions successfully. It can also be seen that the goals of the system appear to have been satisfied. Computation time was approximately 10 minutes on a Sun Spare 20 processor in each case.
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(a) Real rock scene.
(b) Rock scene with fines.
(c) Laboratory scene.
Fig.5 Boundaries of detected rocks for three example scenes.
CONCLUSIONS A need has been identified in the mining industry for an instrument for measuring rock fragmentation. A measure of rock fragmentation will be useful for increasing the efficiency of the gold extraction process by improving control over comminution using autogenous mills. A computational framework based on the structure of the human visual system and multiscalar image analysis has been implemented. The results in the previous section indicate that this approach has provided a method which is capable of producing accurate results with a relatively high degree of flexibility with regard to image capture conditions and the appearance of the rock material.
ACKNOWLEDGEMENTS
The authors acknowledge the support of MINTEK who have sponsored this research.
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