Computers & Geosciences 27 (2001) 1081–1089

Mineral identification using artificial neural networks and therotating polarizer stage

Sean Thompsona, Frank Fuetenb,*, David Bockusa

aDepartment of Computer Science, University of Toronto, 10 King’s College Road, Toronto, Ont., Canada M5S 3G4bDepartment of Earth Sciences, Brock University, 500 Glenridge Avenue St. Catharines, Ont., Canada L2S 3A1

Received 14 July 1999; received in revised form 14 February 2000; accepted 17 February 2000

Abstract

An artificial neural network is used for the classification of minerals. Optical data using thin sections is acquired usingthe rotating polarizing microscope stage, which extracts a basic set of seven primary images during each sampling. Aselected set of parameters based on hue, saturation, intensity and texture measurements are extracted from thesegmented minerals within each data set. Parameters such as pleochroism, plane light hue, and gradient homogeneity

were a few that proved to yield class-discriminating properties. Texture parameters are shown to have the ability toclassify colourless minerals. The neural network is trained on manually classified mineral samples. The most successfulartificial network to date is a three-layer feed forward network using generalized delta error correction. The network

uses 27 distinct input parameters to classify 10 different minerals. Testing the network on previously unseen mineralsamples yielded successful results as high as 93%. # 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Petrography; Genetic algorithm; Texture; Colour; Image analysis

1. Introduction

Artificial neural networks (ANN) have wide use in

artificial intelligence. They have been shown to beparticularly useful in visual systems (e.g. Pandya andMacy, 1996), where the input can naturally be expressedas measurements. ANNs are models for expressing

knowledge using a connectionist paradigm, which iscapable of representing non-linear continuous functions.The knowledge of the system is represented by the

trained weights of the connections between the indivi-dual neurons. The weights are derived by presentingtraining data to the input and output layer of the ANN.

A standard back-propagation algorithm (Kosko, 1991)is then applied to the ANN and the weights are modifieduntil a low global error condition is achieved.

The use of ANNs in geology has been limited. Theyhave been used in a variety of applications (WangShuoru et al., 1997; Brown et al., 1998; Pendock et al.,

1991) but have not been employed in the identification ofminerals using a petrographic microscope. The petro-graphic microscope is a commonly used tool for manualmineral identification in thin sections; however, its use

for image processing has been limited (Fabbri, 1984;Launeau et al., 1990; Pfleiderer et al., 1992; Petruk, 1989;Starkey and Samantary, 1993). The main problem in

automating the mineral identification process using thepetrographic microscope is that in plane-polarized lightmany minerals are colourless, while in cross-polarized

light the interference colour depends on a variety offactors in addition to mineral type. Hence, automatedmineral identification systems (e.g. Marschallinger,

1997; Launeau et al., 1994) are based on scanned imagesand use the natural colour of the mineral.The rotating polarizer microscope stage (Fueten,

1997) was specifically designed as an addition to the

standard petrographic microscope to overcome some of

*Corresponding author.

E-mail addresses: seant@cs.toronto.edu (S. Thompson),

ffueten@craton.geol.brocku.ca (F. Fueten), dbockus@spartan.

ac.brocku.ca (D. Bockus).

0098-3004/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 9 8 - 3 0 0 4 ( 0 0 ) 0 0 1 5 3 - 9

its inherent problems. The stage works in conjunctionwith a video capture board and allows the thin section to

remain fixed while the polarizers are rotated. Thisgreatly enhances the usage of standard image processingtechniques on thin sections for the segmentation,

measurement and mineral identification.This paper reports some positive results on the

attempt to identify minerals using an ANN. It illustratesthat an ANN using texture and colour parameters can

identify minerals with accuracy exceeding 90%.

2. The rotating polarizer stage and data set

The fully automated rotating polarizing stage (Fueten,1997) for a petrographic microscope allows a thin section

to remain fixed while the polarizers are rotated. Henceany point within a grain is registered to the same pixel atall positions of the polarizers, greatly simplifying thecomputational requirements. Sampling is performed by

repeatedly grabbing a frame, extracting data, and rotatingthe polarizers. The normal sampling procedure rotates thepolarizers from 0 to 1808 in 0.98 increments (200 steps)

under both plane- and crossed-polarized light. A compo-site data set is then constructed from this information.

3. Data collected using crossed-polarized light

The maximum intensity image contains the maximumintensity values as defined in hue, saturation, and

intensity (HIS) space. These correspond to the max-imum interference colour for every pixel attained duringa 1808 rotation of the polarizers. Intensity variations aredirectly related to the orientation of the crystal latticewith respect to the plane of the thin section. Variationsin intensity due to the orientation of the polarizers,which are seen in single images, have been eliminated by

the sampling procedure. The maximum position image isa gray-scale image (with a 0–200 intensity range)indicating the polarizer position at which each pixel

reached the maximum intensity. Position values recordthe orientation of the polarizing filters, i.e. the stepnumber, when a pixel reaches its maximum value. The

gradient image is a representation of the accumulatedsum of the maximum difference in intensity between thehorizontal and vertical directions. The image is then

rescaled to a 0–255 range (for display purposes) andserves as the input of the segmentation routine aspresented by Goodchild and Fueten (1998).

4. Data collected using plane-polarized light

A maximum intensity image is obtained under plane-

polarized light. In addition, a minimum intensity imageand a minimum position image are constructed similar to

the maximum intensity and position images undercrossed-polarized light. The advantage to having both

maximum and minimum intensity images is that they canbe used to obtain a measure of pleochroism, the variationin colour of a mineral during plane light rotation.

5. Test data set

Forty-four thin sections of relatively unaltered rockswere selected from the departmental teaching set. Thesections were taken from igneous, metamorphic and

sedimentary rocks (Table 1) and a total of 10 commonminerals were used in this study. The same operatorsampled sections over the course of several days.

Samples were segmented using the edge detectionalgorithm of Goodchild and Fueten (1998) and mineralswere identified manually. Any individual mineral was

identified in several sections if possible to get a widerange of data for each mineral. Table 1 shows acomplete listing of the type and number of mineralsidentified. No effort was made to obtain the same

number of each mineral. Hence, the data reflect the typeof abundance ranges one could expect to see in real-world application.

6. Neural network parameters

Finding a set of useful parameters for mineralidentification is a difficult process. It is relatively easy

for the human brain to distinguish between differentminerals by looking at qualitative features, but notobvious which numerical measurements can accomplishthe same task. Visual identification of objects in images

using ANNs is frequently accomplished by using shapeextraction. While their shape can on occasions identifyminerals, this is not generally the case. Hence, it was

decided that identification should restrict itself to visualparameters, such as colour and texture which can beextracted from each mineral. A variety of colour and

texture parameters were chosen as potential inputparameters to an ANN.

7. Colour parameters

Each image is captured using red, green and blue

(RGB) components. However, experimentation deter-mined that the RGB colour model was very sensitive tofluctuations of the light source. Converting the RGB

components to hue, saturation and intensity space (HSI)detaches the intensity component from the colourinformation and reduces the effects of variable lighting.

In addition, the hue and saturation components areclosely related to the way in which human beings

S. Thompson et al. / Computers & Geosciences 27 (2001) 1081–10891082

Table 1

Rock types and number of mineral samples used in this study

Rocktype (no. of sections) Quartz K-Feldspar Plagioclase Biotite Hornblende Clinopyroxene Olivine Garnet Calcite Opaque

Gabbro (3) 0 0 180 3 0 71 0 0 0 3

Granite (2) 23 21 35 0 0 0 0 0 0 0

Hornblende Andesite 0 0 0 0 9 0 0 0 0 0

Hornblende biotite Dacite 0 0 12 1 17 0 0 0 0 0

Dunite (4) 0 0 0 0 0 0 666 0 0 0

Olivine Gabbro (3) 0 0 88 0 0 10 0 0 0 64

Sandstone (4) 559 0 0 0 0 0 0 0 92 0

Blue marble (6) 0 0 0 0 0 0 0 0 428 10

Nepheline synite (6) 0 341 0 0 0 0 0 0 0 2

Olivine Diabase 0 0 10 1 0 0 6 0 0 0

Sillimanite garnet staurolite schist (4) 0 0 0 0 0 0 0 307 0 0

Granodiorite (2) 0 0 40 64 60 0 0 0 0 9

Staurolite garnet Schist 0 0 0 4 0 0 0 4 4 0

Foliated granite (3) 0 0 2 1 0 0 0 0 0 57

Coronitic Gabbro 0 0 0 0 0 0 0 0 0 0

Olivine porphyritic basalt (2) 0 0 0 0 0 0 13 0 0 44

Total 582 369 372 74 86 81 685 311 520 189

S.Thompsonet

al./Computers

&Geoscien

ces27(2001)1081–1089

1083

perceive colour. The hue of the colour, as described bywavelength, provides a measurement that directly

determines the colour of the grain, for example, thedistinction between red and yellow. The saturation isthe amount of colour that is present, or the degree to

which a pure colour is diluted by white light. Forexample, saturation provides the distinction between redand pink.Pleochroism is a fundamental mineral characteristic

that provides important information during manualmineral identification. Hence, a pleochroism parameterwas defined as the difference between the modes of the

intensity of the maximum intensity and the minimumintensity of the plane light images. For simplicity sake,any changes in the hue or saturation between the two

plane light intensity images were ignored.

8. Texture parameters

Colour is not a uniquely identifying characteristicof minerals alone. Several characteristics of mineralsrequire special tests, which involve the insertion of

the Bertrand lens and an interference plate (e.g. sign,uniaxial/biaxial, axial angle). However, an experiencedpetrologist can in many cases identify mineralsusing subtle colour-independent features such as un-

dulatory extinction or small amounts of alterationwithout having to resort to specialized tests. Featuressuch as undulatory extinction would not manifest

themselves in colour images, but would appear inposition images and can be quantified by texturalparameters. Autio et al. (1999) successfully used texture

parameters to classify rock textures for a variety ofpurposes.The intensity component of the colour images was

used to calculate four standard texture parameters.Texture parameters are calculated using a co-occurrencematrix that is calculated for each grain. A co-occurrencematrix, representing a two-dimensional histogram,

defines a P[i, j] value which corresponds to the numberof pixels with the values i and j separated by thedisplacement vector (1,1). This displacement expressed

as an image mask is the 2� 2 identity matrix. Using thisnormalized matrix (P) the following measurements arecalculated (Jain et al., 1995):

Contrast ¼XX

ði�jÞ2P½i; j�

Entropy ¼ �XX

P½i; j� logðP½i; j�Þ

Energy ¼XX

P2½i; j�

Homogeneity ¼XX

P½i; j�=ð1þ ji � jjÞ

9. Artificial neural network

The type of ANN used here is a three-layer (Fig. 1)standard feed forward network with back-propagationerror correction. The ANN used in this project is based

on the ANN presented by Rumelhart et al. (1986). Ingeneral, the network consists of a series of inputneurons, a hidden layer and a layer of output neurons,

where adjacent layers are fully connected. Each inputparameter is represented by an input neuron and eachoutput neuron represents a distinct mineral type. Inputparameters are scaled to a range of 0–1 and the output

values for each mineral are presented as probabilities inthe range of 0–1. The mineral identified by the networkis that with the highest probability. The connection

between any two neurons is governed by a thresholdfunction, which is essentially sigmoidal, and an asso-ciated weighted connection represented within a

weighted matrix. The exact nature of each functionand each weight within the network is determinedduring the training process. The supervised training of

the network is done using parameters of example grainsand their corresponding mineral type. By propagatingcorrections based on the squared error back through thenetwork, successive cycles modify the sigmoidal func-

tions and weight matrices until the network converges toa correct solution. In order for a network to converge itis essential that the input parameters have some class-

discriminating properties.Because the average image contains little unique data

it was not used for this study. Three colour parameters,

as well as four texture parameters were extracted fromeach intensity image. The two position images yieldedfour texture parameters each, while the gradient imageyielded an intensity parameter in addition to the four

texture parameters. With the addition of the pleochro-ism parameter, a total of 35 input parameters wereavailable for the ANN. The network was designed to

accommodate a total of 15 output minerals, though only10 minerals were used in this study. This was designed toallow for a future expansion of the mineral test set.

Since a total of 35 parameters were extracted from thedata set, any number of networks containing all or asubset of the input parameters could be constructed.

Experimentation demonstrated that a network, whichincluded all possible parameters, did converge but wascomputationally expensive. Parameters with insignif-icant mineral classification properties tend to confuse

the training algorithm, which prolongs the trainingprocess. To find a computationally less-expensive solu-tion and one containing only useful parameters, several

networks consisting of subsets of the input parameterswere constructed. For these networks parameter evalua-tion was initially performed manually (Fig. 2) and only

parameters that showed separation between individualminerals or groups of minerals were thus selected. It was

S. Thompson et al. / Computers & Geosciences 27 (2001) 1081–10891084

found that a variety of networks containing differentsubsets of input parameters could be constructed thatconverged and performed with accuracy approaching

90%. As 235 networks are possible given the 35 inputparameters, a genetic algorithm (GA) was employed tofind a near-optimal solution. A GA is a heuristic search

technique, which is modelled on the biological conceptof evolution. A GA is capable of evolving a near-optimal solution while only examining a small percen-tage of the search space. One further advantage of using

a GA is that a good ANN may get stuck in a localminimum and not properly converge. However, goodANNs should repeatedly evolve and the repeated

selection or deselection of individual parameters willprovide information on their relative importance. TheGA employed in this study started with a population of

100 networks containing a random selection of inputparameters. The networks were trained using a subset ofthe mineral test set. Networks were then evaluated on

their ability to identify the unknown minerals in thecomplete data set. A new generation of networks wasevolved using the GA that combined characteristics ofthe best networks of the generation. The GA evolved

networks over 50 generations and allowed for some

amount of random mutation. Details of the GA arebeyond the scope of this paper and will be presentedelsewhere. Each net developed by the GA was trained

using a set of 36 samples of each mineral and evaluatedusing the entire data set. The evaluation was weighted tothe number of minerals present in the data set, ensuring

that each mineral had equal contribution to the rankingof the ANN. Otherwise, the GA could produce networksfocused on identifying minerals with a large number ofsamples in the test set.

10. Results

The GA found several nets with roughly the sameaccuracy. The best net (Fig. 1) consists of a total 27

input parameters, of which 18 are texture parametersand nine are colour parameters. The network wastrained with two separate training sets, one consisting

of 36 examples for each mineral while the second setconsisted of 74 samples of each mineral, including allexamples of biotite. Table 2 presents the percentage of

correctly identified minerals in each net. Overall, theaccuracy of the networks is greater for those trained

Fig. 1. Representation of optimal neural network structure used. The full connections are only shown for 2 input and 2 output

parameters. The 27 inputs shown are those of the optimal network.

S. Thompson et al. / Computers & Geosciences 27 (2001) 1081–1089 1085

with the larger training set; in both cases the overall

accuracy exceeds 90%.The ANN is capable of distinguishing coloured as well

as colourless minerals. For some minerals such asquartz, garnet or calcite a training set of approximately

50 minerals appears to be adequate, as accuracy forthese minerals does not increase, as more samples areincluded in the training set. Minerals with variable

birefringence such as clinopyroxene and olivine aredistinguished with greater accuracy as more trainingdata is provided. The ANN’s failure to correctly identify

two biotites, even when all examples are included in thetraining set, may be due to several factors. Theparameter values for some biotites may not be adequateto distinguish the mineral class, thus confusing it with

other minerals. Alternatively, we cannot exclude the

possibility that some minerals were incorrectly manually

identified.Perhaps one of the most interesting results was the

ability of the ANN to identify quartz. Even when thetraining set included less than 10% of the quartz

the ANN was able to identify quartz with greaterthan 95% accuracy. The ANN was somewhat lesscapable of separating K-feldspar from plagioclase, but

still managed an accuracy of greater than 85%. Quartz,K-feldspar and plagioclase are colourless and havebirefringence colours in the gray range. Hence, without

the aid of staining they cannot be separated on the basisof their colour. To determine the usefulness of textureparameters in distinguishing colourless minerals, anetwork was constructed containing only the texture

parameters of the ANN in Fig. 1. This network was

Fig. 2. Plots of four separate input parameters for eight separate minerals used to manually examine their classification ability.

Maximum position homogeneity shows separation of quartz from the remaining minerals, reflecting the property of undulatory

extinction. Biotite shows classification ability for minimum plan light hue and pleochroism. Maximum crossed-polarized light contrast

shows no classifying ability for any of the minerals plotted.

S. Thompson et al. / Computers & Geosciences 27 (2001) 1081–10891086

trained and then evaluated on its ability to distinguishquartz, K-feldspar and plagioclase. Table 3 illustratesthat this net does just as well identifying quartz and

plagioclase using texture parameters only. The ANN’sability to identify K-feldspar decreased from 87 to 82%,which may indicate that minor alterations such as

sericitization contribute some useful colour informationfor identification. These results indicate that the colour-based network connections, which result in the identi-fication of quartz and plagioclase, contribute little to no

information.As mentioned above, the GA evolved several nets that

performed with approximately the same accuracy. The

nets differ in the number and composition of para-meters. Hence, it can be stated that there is no uniqueANN for mineral identification. The ANN which does

marginally better for the mineral suite used in this studymay be outperformed by a different net if anothermineral suite is examined. There were however someconsistencies during the evolution of the ANN by

the GA. Some of the 35 possible parameters were

deselected consistently during the evolution of the netswhile other parameters were consistently included in all

well-performing ANNs (Table 4). A third and the largestset of parameters could either be included or lost duringthe evolution. For some parameters, the geological

reasons for their inclusion or exclusion are readilyapparent. The exclusion of the hue of a mineral in themaximum cross-polarized image can readily be under-

stood, as the hue can have a large range for evenindividual grains in many birefringent minerals such asolivine or clinopyroxene. Pleochroism is a fundamentaloptical property and the parameter that mimics it is

consistently included in good ANNs. Parameters such asthe homogeneity or intensity of the gradient image canbe related directly to the optical smoothness of a mineral

and are thus sensitive to inclusions, cleavage or fracturesand can contribute important information.

11. Discussion

The initial results are encouraging and clearly indicatethat a properly designed and trained ANN can do agood job at identifying minerals based on optical data

extracted with the rotating polarizer stage. While theinput data used is not directly comparable to that usedin previous studies we will argue that an ANN can do abetter job than previously used colour-based classifica-

tion methods. It is perhaps particularly encouraging thatan ANN can distinguish between colourless mineralswhen the input data includes texture parameters. That

the ANN was able to identify data from differentsections which were undoubtedly sampled under slightlydifferent lighting conditions indicates that an ANN is

quite robust and can accurately identify minerals underless than ideal conditions. That ability should make it a

Table 2

Examples of accuracy for training sets using different number of minerals. Neural networks were trained with 74 and 36 samples per

mineral. Training set of 36 samples was chosen in order to be able to use half of biotite samples as training set while other half serves as

test set. Training set of 74 minerals uses all examples of biotite for training and subsequent testing

Mineral (total number) 74 samples used for testing 36 samples used for testing

Quartz (575) 95.30 85.74

K-Feldspar (369) 92.10 52.03

Plagioclase (358) 89.94 49.44

Biotite (74) 95.95 95.95

Hornblende (86) 95.35 84.88

Clinopyroxene (81) 97.53 59.25

Olivine (685) 91.39 45.69

Garnet (311) 95.50 96.78

Calcite (520) 95.39 88.23

Opaque (189) 93.65 81.48

Complete file accuracy 93.53 70.55

Average individual mineral accuracy 94.21 67.22

Table 3

Neural networks trained only with texture parameters to

identify colourless minerals. Data was separated into two

sample sets (231 samples in each) used for training. Complete

file accuracy refers to percentage using all test samples

available. Average individual mineral accuracy refers to average

mineral accuracy from individual experiments using subset of

available samples

Mineral Training set 1 Training set 2

Quartz 96.65 93.30

K-Feldspar 82.05 77.78

Plagioclase 88.55 95.78

S. Thompson et al. / Computers & Geosciences 27 (2001) 1081–1089 1087

perfect candidate for practical applications. While anANN of this configuration would not be able to identifynew unknown minerals it is well suited for an applica-tion in which a large number of thin sections of limited

mineralogy need to be examined.This study also indicates the importance of textural

parameters in visual systems. Textural parameters alone

can be used to identify colourless minerals with a greatdegree of accuracy. This suggests that texture para-meters could also add to the accuracy of conventional

mineral identification systems.The performance of any ANN depends on the

quantity and quality of the training data. The trainingdata should be representative of the actual data. As it is

not always obvious if the range of parameters in thetraining data reflects that of the actual data, it isadvisable to train the net with a reasonable large

training set. The nets in this study overall performedbetter with the larger training set. Much care should alsobe taken in selecting the training set. Falsely identified

minerals in the training set can result in a net incapableof proper identification. One of the reasons why theANN failed to identify all biotites correctly even though

all biotites were included in one training set may be thatan incorrectly manually identified biotite has beeninadvertently included in the data set.Results of the GA search can provide some interesting

information in how minerals are optically identified. The35 different parameters can be grouped into three classesthat could be termed useful, useless and sometimes

useful. Because of the interconnectivity of the network,there is no easy way to deduce or rank the importance ofindividual parameters. Parameters that are always

selected are definitely important while parameters thatare always deselected are unimportant. It is interestingto note that ANNs containing different combinations ofthe partially selected parameters could perform nearly

equally well. Several potential explanations can be

advanced. It is possible that some of the parameters inthe intermediate usefulness list, especially in combina-tions, essentially provide duplicate data. One example ofduplicate data would be intensity data of colourless

minerals, obtained from the two plane light images.Depending on the evolutionary path the GA takes, oneof the duplicate combinations is favoured. Another

explanation is that there may be more than one wayof optically identifying minerals. Different combinationsof parameters lead to the same result but consider

different data as identifying criteria. We would arguethat different petrologists are able to identify mineralsby relying on their experience and hence would likelyrely on different subtleties, which they detect in

an image. This is analogous to different networkconfigurations learning using their parameters in subtlydifferent ways.

12. Conclusion

ANNs can be used to identify coloured and colourlessminerals with better than 90% accuracy. Accuracy can

be improved by a larger training set. As ANNs are lesssusceptible to changes in illumination, etc., they are idealfor applications requiring repetitive identification of a

limited set of minerals. There is no single ANN toidentify minerals, hence an ANN should be tailored tothe group of minerals or application.Texture parameters provide important information.

Other mineral identification applications could likely beimproved by the inclusion of textural parameters.Future work should be aimed at expanding the

number of minerals to be examined. For computationalreasons some work should be directed at finding thesmallest ANN that is able to accurately identify

minerals. Such ANNs would be composed of the mostimportant parameters for optical mineral identification.

Table 4

Classification of parameters into three sets based on selection occurrence. Parameters that are always selected contain essential

information for mineral identification. Parameters that are occasionally selected provide useful information in some network

configurations. Parameters that are never selected contain no useful information for mineral identification

Always selected Max Cross Sat, Max Cross Int, Max Plane Int, Max Plane Homog, Min Plane Sat,

Min Plane Int, Max Pos Cont, Min Pos Cont, Min Pos Homog, Grad Int,

Grad Homog, Pleochroism

Sometimes selected Max Cross Cont, Max Cross Entropy, Max Cross Energy, Max Plane Hue, Max Plane Sat,

Max Plane Cont, Max Plane Entropy, Max Plane Energy, Min Plane Hue, Min Plane Cont,

Min Plane Entropy, Min Plane Energy, Min Plane Homog, Max Pos Entropy,

Max Plane Energy,

Max Pos Homog, Min Pos Entropy, Min Pos Energy, Grad Cont, Grad Entropy,

Grad Energy

Always deselected Max Cross Hue, Max Pos Energy

S. Thompson et al. / Computers & Geosciences 27 (2001) 1081–10891088

Acknowledgements

The authors would like to thank Carrie Ross formanually identifying the minerals used in this study.This project was supported by an NSERC operating

grant to F. Fueten. The authors would like to thank twoanonymous reviewers for their helpful suggestions.

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