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Comparison of shape features for the classification of wear particles
Pergamon PII:S0952-1976(97)00017-1
EngngApplic.Artif.lntell.Vol.10,No. 5, pp. 485-493,1997 © 1997ElsevierScienceLtd Printedin GreatBritain.Allrightsreserved 0952-1976/97$17.00+0.00
Contributed Paper
Comparison of Shape Features for the Classification of Wear Particles KUN XU University of Wales, Swansea U.K. A. R. L U X M O O R E University of Wales, Swansea U.K. FARZIN DERAVI University of Wales, Swansea U.K.
(Received July 1996) Wear particle shapes are divided into four classes: Regular, Irregular, Circular and Elongated. They have been classified here using back-propagation neural networks which have been trained using different sets of rotation-, scale- and translation-invariant shape features derived from particle boundaries. The features include: Fourier coefficients based on either boundary curvature analysis or XY co-ordinates of boundary points; statistical moments of the curvature distribution including standard deviation, skewness and kurtosis; and two general shape descriptions, aspect ratio and roundness. In order to evaluate the performances of the features, a series of tests have been carried out on a wear particle database, and the results are compared. The boundary-curvature-based Fourier descriptors produce a shape classifier with the highest performance. The neural network trained by the Fourier features derived from the boundary data provides a slightly lower classification rate which is similar to that achieved using three statistical moments combined with the two general shape features. © 1997 Elsevier Science Ltd. All rights reserved Keywords: Shape, wear particles, neural networks, Fourier, curvature.
1. INTRODUCTION Any machinery that involves moving surfaces in contact will generate a certain amount of wear debris throughout its working life. This debris will consist of small particles that are produced from the interaction of the contacting surfaces. Initially, these wear particles will be benign, arising from small asperities on the surfaces that are removed during the preliminary operation of the machinery (running-in). As the machine ages, or is subjected to incorrect usage, misalignment and excessive forces between the various surfaces will produce certain quantities of other types of wear particles that are indicative of these conditions (Anderson, 1984). The particle characteristics (which include shape, size, concentration, surface and colour, etc.) are sufficiently Correspondenceshould be sent to: Mr A. R. Luxmoore,Departmentof Civil Engineering,Universityof Wales, SingletonPark, Swansea SA2 8PE U.K.
specific to operating wear modes to allow an expert to predict these wear modes from microscopic inspection of the particles. This can help in predicting the future behaviour of the machine, thus preventing failures and their associated costs. The technique is of particular use during the servicing of the sensitive and expensive machinery in aircraft and helicopters. Wear particle analysis is normally carried out in two stages: quantitative analysis and morphological analysis. Quantitative analysis measures the concentration of wear particles in a sample (a debris test index, DT), usually by means of a magnetic instrument, as most wear particles are ferrous. Morphological analysis is normally carried out under a microscope, to inspect the details of the particles, and yields specific information about the mechanism that produced them from their machine component. The debris test is quick and cheap, but morphological study gives more detailed information, albeit at a greatly increased cost.
485
486
KUN XU et al.: SHAPE FEATURES
Practical experience has shown that an increasing DT value can give valuable information concerning the machine condition, but some machines that have been near to failure still had normal DT counts, whereas morphological examination of the same debris picked up a significant number of wear particles caused by a serious wear mode. In other cases, machines were rejected because of their high DT counts, but the microscopic analysis showed that there were no signs of serious wear. Therefore solely using the quantitative analysis can result in unreliable decisions, and morphological analysis is essential for reliable machine condition monitoring. Wear particles fall into several well-defined classes in terms of their formation mechanism and conditions. As an example, Fig. 1 shows four popular types of wear particles from aircraft engines. Rubbing debris (a), which is benign, is in the form of thin, plane particles with smooth edges, produced under the normal operation of lubricated machinery. Fatigue debris (b) is one of the more severe particles, and is characterised by an irregular outline. Cutting wear particles (c) are normally small, no more than 50/zm in length, elongated and usually curved, and are often to be found in a new engine. However, an increase in quantity and size with time would be a cause for concern. Spherical particles (d) are in the form of hollow spheres, typically 8-10/zm in diameter, and usually give evidence of a distressed bearing.
The images in Fig. 1 show that particle shape represents one of the most important features for a wear particle, the different shapes being associated with different wear types. Previous work (Roylance et al., 1992) has shown that shape is one of six particle attributes (the others are edge detail, size, texture, colour and thickness) that can be used to classify the particle uniquely in terms of a particular wear mode. These wear modes produce wear particle shapes which can be split into four classes: Regular, Irregular, Circular and Elongated. Instead of making the assessment visually, wear particle shape identification and classification might be performed more effectively using computer vision and artificial neural-network techniques, leading to the eventual automation of all six attributes.
2. SHAPE RECOGNITION AND CLASSIFICATION Shape recognition and classification are essential problems in many applications concerning computer vision techniques. In recent years there have been a number of investigations on two-dimensional closed-shape analysis and classification, based on a two-stage procedure: feature extraction, and shape recognition/classification. For the feature extraction many new shape-analysis approaches have been proposed. For shape classification in real time, artificial neural networks may be combined with appropriate features.
(a)
(b)
(¢)
(d)
Fig. 1. Wear particles. (a) Rubbing wear platelets. Image size 134 x 91 /xm. (b) Fatigue wear particle. Image size 134 x 91 /zm. (c) Typical cutting wear debris. Image size 54 X 37/xm. (d) Three spherical particles. The smallest one is about 5/zm in diameter.
KUN XU et al.: SHAPE FEATURES
487
curvature, and for each segment the normalised approximate curvature sequence was sampled and averaged. Then In the design of a shape classifier using neural networks, the mean curvature values were taken as the features for the important factor is feature extraction, i.e. how an object neural-network training which was aimed at line shape is presented to the neural network. The input vector for the recognition. In this approach a threshold value plays a neural network should carry essential shape information, crucial role in the curvature approximation. In the proposed method, which is not aimed at recognisand must be normalised to provide a unique value ing particular shapes but at classifying all wear particles into irrespective of basic shape transformations such as translafour shape classes, the curvature variations have been tion, rotation and scaling (Pal et al., 1993; Hush and Home, calculated for each boundary point, so that no boundary 1993). Among the large number of two-dimensional closedpoint is omitted from the feature extraction. As curvature is shape analysis algorithms, or feature-extraction schemes, essentially invariant to position and rotation, but not scalepolygon approximations are popular. In 1993, based on a invariant (Katagiri and Nagura, 1994), an edge-smoothing review of existing methods, Pal et al. (1993) suggested a approach was investigated, not only for acquiring a polygon approximation operation which divides a shape reasonable curvature estimation, but also for the curvature into constant-point segments and then approximates each segment by a line segment joining the two end points. The normalisation. Then the DFT was applied to the curvatures angle variation between two consecutive lines is modelled to obtain a set of Fourier descriptors which are invariant by an autoregressive (AR) process, and the derived AR with respect to translation, rotation and size. Because it is a vector is then used for neural-net training and classification. common feature of Fourier descriptors that normally only a The technique is applicable to both concave and convex few low-order terms are essential for global shape recognishapes, and experimental results from four shapes of tion (this can be appreciated by regenerating the shapes various sizes showed that the scheme worked quite well. from the low-order terms), Fourier descriptors are well The constant-point number for the segmentation has to be suited for use as a feature vector in neural networks. This is decided carefully with respect to shape and size, otherwise essential for minimising the size of the neural networks and too much shape information is lost. In 1993 Mitzias and reducing the computation times. Mertzios (1994) presented a new polygonal approximation technique. A shape is approximated by a polygon with a 2.2. Shape classification--neural networks predefined number of vertices, which form the most critical Neural networks have become popular for classification points of the contour for the shape. Then, based on this purposes because of their high computational rates, robustapproximate polygon, two feature vectors are generated, ness and ability to learn. Artificial neural networks are viz. internal angles and normalised errors, which are used connectionist systems, with the neurones normally divided for the neural-network training. This method is also into layers and all the outputs from one layer connected to dependent on the initial selection, as the larger the number the input of the next. A multi-layer perceptron (MLP) has an of vertices chosen, the more detailed the representation of input layer, one or more hidden layers, and an output layer, the original shape that is achieved, leading to larger see Fig. 2. An artificial neurone applies a weight to each computation times, which may not be practicable. The input, then sums those inputs and applies a threshold above techniques face the same problem. No matter how function, for example a sigmoid function, to the output. A well the polygon-approximation algorithm works, there is successful training process should find a single set of always some information that is lost during the procedure, weights and threshold values (or biases) that satisfy all the as the number of vertices is limited. In the application of input and output pairs of training data presented to it. these techniques, the neural networks were employed to recognise only particular shapes. T3 T4 TI T2 Fourier descriptors are powerful tools for shape analysis and feature extraction. Kim and Nam (1995) described the shape classification of industrial tools that have only one degree of freedom. In their approach, a discrete Fourier output layer transform (DFT) was applied to the co-ordinates of all boundary points for feature extraction, and then the loweights order Fourier coefficients were used as the inputs for neural-network training. Their experimental results show a hidden layer very high classification accuracy on four kinds of tools, outperforming the two popular statistical classifiers, which eights are based on either the nearest-neighbour rule, or the input layer minimum-mean-distance rule. Curvature analysis has also been used in boundary feature extraction. Katagiri and Nagura (1994) defined and calcuFI F2 Fn lated the "approximate curvature" along a boundary. The boundary was divided into segments by the points with zero Fig. 2. A neuralnetworkwith a single hiddenlayer.
2.1. Shape analysis and feature extraction
KUN XU et al.: SHAPE FEATURES
488
l@
Fig. 3. Profiles with different boundary shapes.
Having been trained, when the net is presented with data it has never seen before, it can decide the appropriate output (Hush and Home, 1993). In order to determine the best feature number for an input vector, up to eight initial Fourier descriptors (amplitudes only) were used in the neural-network training for the boundary curvature analysis, and the classification rates tested. A similar neural network was trained using loworder Fourier amplitudes calculated directly from the co-ordinates of the boundary points (the XY Fourier), and the test results also compared. In addition to the two Fourier descriptors, some statistical descriptors, i.e. standard deviation, skewness and kurtosis, and general shape descriptors such as aspect ratio and roundness, were also used as feature vectors for the neural-network training, and the test results are presented.
4. BOUNDARY CURVATURE As curvature variation gives important information about the boundary shape, there should be significant differences between the curvatures for the boundaries with different types of shapes. Figure 3 shows four boundary profiles, each illustrating a different shape category. For discrete curvature analysis, a curvature-estimation technique, derived by Freeman and Davies (1977) for comer finding, was employed and applied to the digitised boundaries. The angular difference between two successive vectors was calculated and taken as the estimated curvature value for the intersection point of the two vectors. As shown in Fig. 4, for a boundary with N pixels, the curvature of the point Pj (O<-j<-N- 1) is defined by the angular difference between two vectors P~_j and P~'÷,. As the co-ordinates are known for each boundary point, the slopes can easily be derived by:
3. DATA COLLECTION Wear particles were examined using an Olympus microscope at a magnification of 100 × (for some small cutting wear particles 400 × was used). As only boundaries were of interest, transmission illumination was used. Particle images were taken by a CCD camera attached to the microscope, and this was connected to a Leica Quantimet 500 image processing system. Images were captured with 8-bit grey level resolution, and were processed and analysed by an application software package CAVE (Computer Aided Vision Engineering) (Roylance et al., 1994), which was adapted to MS-Windows for the Quantimet 500 system. For shape classification, particle boundaries are traced using four neighbours. Most images were taken from real wear samples, prepared from the debris found on aircraft engine magnetic drain plugs. As only a very few spherical particles had been found during the trial, some artificial objects were used for the circular class. Images were captured and stored in 512×512 pixels. The particle size is normally about 10/.tm-200 ram. It was assumed that all wear particles neither touched nor overlapped each other in the data collection. All sample images were classified into the four shape categories: Regular, Irregular, Circular and Elongated, by A. L. Price, an expert from the Swansea Tribology Centre of the University of Wales, Swansea. These class labels were chosen as they represent the normal particle types used by tribologists in classifying wear particles.
(1)
O)~-'=tan-'( )Xj--Xj-m-, yj-yj-"-'
O2~+~=tan-'(yj+~+I-yj ) .... x ,-xj j and the curvature of point Pj is calculated by:
kj= 07+1- OT_i ( - 90°-
(2)
The parameter m is normally referred to as a "smoothing factor". It is clear that the greater the value of m, the heavier
ej
(m=3) m
Fig. 4. Computation of discrete curvatures.
KUN XU et al.: SHAPE FEATURES the smoothing would be. However, if a large value of m (or a longer line segment) is chosen, the curvature estimate derived by, eq. (2) may not reflect the original fine features of the digital curve. On the other hand, if m is smaller, there will not be enough smoothing applied to the data: noise and quantization errors may be reflected in the derived curvature. Therefore it is very important to choose an appropriate smoothing factor for a specific application. As wear particles are quite different in size, if any fixed value of m were used, the curvature would depend not only on the boundary shape, but also on the size (curvature is normally not scale-invariant), so the smoothing factor m must be related to the boundary size, or scale. This problem was solved by normalising the successive vectors. The basic idea is to select a value of m corresponding to a fixed proportion of the 360 ° angle enclosed by a profile. From experiment, an angular segment of 10 ° was found to be satisfactory, and m was determined by (number of boundary points)/36. In this way, if any two profiles are of the same shape, their curvature diagram would be the same no matter how different their sizes, as the boundary size only determines the density. This keeps the curvature scaleinvariant. For a demonstration, two image pictures were taken from one wear particle using a microscope with two different lenses ( × 100 and × 50 respectively). Figure 5
489
shows the boundary profiles extracted from these two images and their curvatures. The two images do not appear to have identical shapes because of the difference in the depth of field for the two lenses, leading to slight differences between the two curvature diagrams, which is also reflected in the derived statistical values. For the four types of profile shown in Fig. 3, the curvature diagrams are shown in Fig. 6. The four profiles exhibit significantly different curvature curves. In order to extract the information with a finite number of features, a Fourier transform was carried out on the boundary curvatures.
5. F O U R I E R D E S C R I P T O R S OF CURVATURE Curvature k~ (j=0, 1..... N - 1) is a discrete signal, so a discrete Fourier transform (DFT) was employed. A discrete signalfk (O<--k<--N - 1) can be represented as a trigonometric series: N-I
fk=A0+ E ( A , c o s ( 2 ~ k n l N ) + N ) + B n s i n ( 2 z r k n / N ) )
where the Fourier coefficients are defined as follows:
(a)
(b)
Mean: FIA : Rq : Rsk : Rku :
10.249110 33.634533 44.172844 0.496645 3.516201
Mean: FILA : FILq : Rsk ;
10.369712 30.490973 39.686660 0.T00491 3.7271194
RJ(u :
~
Fig. 5. Curvatureanalysis-sizenormalisation.(a) Boundaryprofilesof a wear particle with different size. (b) The curvatures of two profiles.
(3)
490
KUN XU et al.: SHAPE FEATURES
9O
'
""
.....
~
"-"
'r
_lWr
""
V
---m,-
"wr"
-4s -90
Fig. 6. Curvaturevariationsfor differentboundaryshapes. 1
2
(4)
N-I
A.= ~ ~__°Xf, cos(2crkn/N) 2
Figure 7 shows that the Fourier coefficients for the four shape classes are distinguishable from each other. The circular shape produces a very low value for all eight harmonics: the regular shape gives a similar value for each harmonic; the irregular shape has higher components on high frequencies; and the elongated profile only gives priorities to the even harmonics (2, 4, 6, 8). The results indicate that the Fourier coefficients based on the curvature analysis provide very distinct features and representations for the four types of boundary shape.
N-I
Ao=~/ L~oA
(5)
N-I
B,= ~/ ,__E ° ftsin(2~rkn/N)
(6)
and C , = 2~
2
( l < - - n < N - 1).
(7) 6. OTHER SHAPE FEATURES 6.1. XY Fourier descriptors
Applying equations (4)-(6) to the curvature variable kj, then the c~ (i= 1-8) for the four different profiles (shown in Fig. 2) are calculated using equation (7), and shown in Fig. 7.
A boundary pixel is represented by a two-dimensional array of (x, y). Treating the co-ordinates x and y as independent, it is advantageous to treat the 2D array as two
• Circular I'1 Irregule t • F.JeeSated • Regular
_JJ 1
2
3
4
5
6
7
Harmonlo Number
Fig. 7. The Fouriercoefficientsfor fourprofiles.
8
KUN XU et al.: SHAPE FEATURES
491
Kurtosis, the fourth moment, measures the "peakedness" 1D arrays, i.e. to deal with the two co-ordinates separately. of a distribution relative to with the normal one: In this way, instead of the two-dimensional DFT, only a one-dimensional DFT is carried out, on xk and Yk (O<-k<--N- 1) respectively. Based on this idea, a set of XY Fourier descriptors were developed by Badreldin et al. (15) Kurt= ~[ i=l (1980). In trigonometric terms the Fourier series descriptors for x~ are given by: 2 N-I
Ax.= ~ k=~oxkcos(2~'knIN) 2
N-I
Bx~= ~ kX=oxksin(2~kn/N)
(8)
(9)
The dc components Ax0 and Bxo can be ignored since they only carry information about the x position of the image centre. From Ax, and Bx,, the Fourier descriptor Cx, for xk can be derived:
C x . = ~ ( n =2 l , 2
2
.... ).
Also, two general shape features, aspect ratio and roundness, were used. The aspect ratio is the ratio of the longest feret divided by the shortest feret; and the roundness is a shape factor which gives a minimum value of unity for a circle:
Roundness =
Perimeter 2 41rX Area × 1.064
(16)
where the adjustment factor of 1.064 corrects the perimeter for the effect of the corners produced by the digitisation of the image (Leica Cambridge Ltd, 1993).
(10) 7. EXPERIMENTS AND RESULTS
The same procedure could be carried out on Yk to obtain the Fourier coefficients of Cyn . The parameters Cx~ and Cy, are not rotation- or shift-invariant, but for each nth harmonic a invariant Fourier descriptor C~ can be derived from Cx~ and Cy~ (Badreldin et al., 1980): 2
c.=
+ Cy 2.
(11)
In order to further refine Cn to be a scale-invariant descriptor, a normalisation operation was applied: an ~ Cn
.
Cl '
(12)
then S. (n= 1, 2 .... ) is invariant to rotation, shift and size (Shridhar and Badreldin, 1984).
6.2. Statistical moments and general shape descriptors Statistical analysis of a set of data also provides important information about that data; therefore, based on the boundary curvatures, three higher moments were derived and used for the neural-network training:
Standard deviation, the second moment, characterises the data distribution around its mean value: 1 or=
-
N
N -- 1 "=Xl(xi - 3) 2.
(13)
Skewness, the third moment, characterises the degree of asymmetry of a distribution around its mean value:
Skew= ~ i=l
(14)
The neural networks utilised in this work are static, multilayer pereeptrons (MLP) with only one hidden layer. There are four output nodes for the output layer corresponding to the four shape classes, but the node number for the hidden layer is dependent on the number of input features. When the number of input features is over six, the number of nodes for the hidden layer is equal to or slightly less than the number of input nodes, otherwise there are slightly more hidden nodes. The neural networks were trained using a supervised, back-propagation learning algorithm. Given a set of sample input-output pairs, the neural networks were trained to match the samples as closely as possible. Altogether 200 wear particles were assessed, with 100 for training, and 100 for test. As there were fewer samples of spherical particles than for the other shapes, only 10% of the samples were available for the circular class (the test results showed that this number is enough for the circular class training), leaving 30% each for regular, irregular and elongated respectively.
7.1. Classification using curvature Fourier descriptors Experiments were carded out to train the nets using different numbers of the Fourier coefficients based on the curvature analysis, and then the same test samples (100) were used for classification. The test result shows that using the first seven Fourier coefficients as the inputs (with six nodes in the hidden layer) gives the highest classification rate of 97%, see Fig. 8.
7.2. Comparison with XY Fourier descriptors Based on the XY Fourier descriptors, a trained neural network worked very well in the recognition of one-DOF tools (Kim and Nam, 1995), so it was employed in this work for wear particle shape classification. As the Fourier descriptors (coefficients) were normalised by the first Fourier coefficient, equation (12), this coefficient was
492
K U N X U et al.: S H A P E F E A T U R E S 100 95 90 85 80 75 70 65 60 55 50
I
I
2
I
3
I
4
5
I
I
I
6
7
S
Input Feature Numbel
Fig. 8. Performance vs different number of inputs.
omitted, and the next seven coefficients (S2-Ss) were used for net training with the same structure (one hidden layer with six nodes and four outputs). The result shows that the classification rate of the classifier based on the XY Fourier descriptors is lower:
groups, being robust for the irregular and circular classes, but not as reliable for the regular and, in particular, the elongated class. For the two training strategies based on the boundary curvatures and boundary data, the classification and normalised system errors vs the number of iterations also show that the Fourier descriptors based on the curvature analysis present a high and stable classification rate, with lower system error during the training process, and the neural net trained by the XY Fourier descriptors reaches its highest performance (91%) after 200 iterations, after which the classification rate drops down again, see Fig. 9.
Curvature Fourier 97% XY-coordinates Fourier 91%. The classification rates for the four individual shape classes were also compared for the two Fourier systems. The results are shown in Table 1. For the four shape classes, the neural network trained by the Fourier coefficients based on boundary curvature analysis outperforms the net trained by the XY Fourier coefficients. The former gives more consistent results, but the latter presents a different performance for the different
7.3. Results of other shape descriptors Three higher statistical moments derived from boundary curvatures and two general shape descriptors were also used for the neural-net training, but the feature vectors were composed of different features----~e classification rates are compared as follows:
Table 1. Confusion matrices showing the performances of two nets True setkassigned set
Regular
Irregular
Elongated
(a) Curvature Fourier classifications Regular 29 Irregular 1 Elongated Circular
30
2 28
(b) XY Fourier classifications Regular 27 Irregular 1 Elongated Circular 2
30
70 .2 50
5 1 24
20 U 10 o o
I 200 ~
I
ox.. . I
I
92 (aspect ratio, roundness, sd, skew and kurt.) 89 (aspect ratio, roundness) 54 (sd, skew, and kurt.).
For the four individual shape classes, the performances of the classifiers trained using the five features and two features are shown in Table 2.
00'
Curv. Fourier
I
Classification Rate (%)
O'o, o
i
• Curv. Fourier n XY Fourier
~ 015 ~ - \ \
ox.... •
40 ~ 30--
2 features 3 features
10
:
60
Training Features 5 features
10
100 90 80 =
Circular
i
i
I
i
I
600 800 1000 i200 1400 1600 1800 2000 N u m b e r 0:f ite~'a~ions
01i
0.3 0.2 ~ O.
~'
z
t
0
200
400
~
600 800 1000 1200 1400 1600 1800 2000 N u m b e r o f iterations
Fig. 9. Classification rate and normalised system error vs number of iterations for two feature sets.
KUN XU et al.: SHAPE FEATURES Table 2. Confusion matrices of two nets trained using other shape features True setkassigned set
Regular
Irregular
(a) Classifications based on five features Regular 28 2 Irregular 1 28 Elongated 27 Circular 1
Elongated
Circular
1 2
(b) Classifications based on roundness and aspect ratio Regular 27 2 Irregular 2 28 1 Elongated 29 Circular 1
9 3 2 5
493
A series of experiments were also carried out to compare the performance with that of the neural networks trained by other shape features. Despite the reported success (Katagiri and Nagura, 1994) of neural networks trained using Fourier coefficients of boundary data for one-DOF tool recognition, for wear particle classification this approach did not work as well as the curvature Fourier (for the same number of coefficients), particularly for the elongated shape category. This is most probably due to the initial smoothing (filtering) in the curvature process. The two general shape features, aspect ratio and roundness, provide most of the shape information, but for a high classification rate, some more information is required, particularly for circular shapes.
The system trained by five features (aspect ratio, roundness, standard deviation, skewness, and kurtosis)
REFERENCES
gives a good performance of 92%, and the use of two features of aspect ratio and roundness also gives a reasonable rate, 89%. The main difference between these two systems is for the circular class. The results indicate that aspect ratio and roundness carry most information for a 2D closed profile, but for spherical shape recognition, the two general shape features are not so reliable (probably because the aspect ratio is dependent on each individual point, including any "noise" which might be a single outlier), and some more information is needed. The performance of the neural net trained with only the three higher moments is very low.
Anderson, D. P. (1984) Wear Particle Atlas (Revised). Report NAEC92-163 Prepared for Advanced Technology Office, Support Equipment Engineering Department, Naval Air Engineering Center, Lakehurst, New Jersey. Badreldin, A., Wang, A. K. C., Prasad, T. and Ismail, M. (1980) Shape descriptors for N-dimensional curves and trajectories. IEEE Proceedings on Cybernetics and Society, pp. 713-717. Freeman, H. and Davies, L. S. (1977) A comer-finding algorithm for chaincoded curves. IEEE Transactions on Computers, C-26, 297-303. Hush, D. and Home, B. G. (1993) Progress in supervised neural networks, What's new since Lipomann. IEEE Signal Processing Magazine, pp. 8-39. Katagiri, M. and Nagura, M. (1994) Recognition of line shapes using neural networks. IEICE Transactions on Information and System, E77D(7), 754-760. Kim, H. and Nam, K. (1995) Object recognition of one-DOF tools by a back-propagation neural net. IEEE Transactions on Neural Networks,
6(2), 484--487. 8. CONCLUSIONS
This paper has presented a classification system for wear particle shape classification through the use of a backpropagation neural network, which was trained using the feature vectors composed of a number of low-order DFT descriptors derived from boundary curvatures. The classifier presents a high classification rate, and exhibited robust and consistent performances for the four shape categories. The average time consumed on the curvature calculation and Fourier analysis is about 100 ms, depending on the size, and about 50 ms for the shape classification, using a PC486 running at 66 MHz.
Leica Cambridge Ltd (1993) Quantimet 500+ User Manual. Leica Cambridge Ltd, Cambridge, U.K. Mitzias, D. A. and Mertzios, B. G. (1994) Shape recognition with a neural classifier based on a fast polygon approximation technique. Pattern Recognition, 27(5), 627-636. Pal, N. R., Pal, P. and Basu, A. K. (1993) A new shape representation scheme and its application to shape discrimination using a neural network. Pattern Recognition, 26(4), 543-551. Roylance, B. J., Albidewi, I. A., Luxmoore, A. R. and Price, A. L. (1992) The development of a computer-aided systematic particle analysis procedure--CASPA. Lubrication Engineering, 48(12), 940-946. Roylance, B. J., Albidewi, I. A., Laghari, M. S., Luxmoore, A. R. and Deravi, E (1994) Computer-aided vision engineering (CAVE)---quantification of wear particle morphology. Lubrication Engineering, 50(2) Shridhar, M. and Badreldin, A. (1984) High accuracy character recognition algorithm using Fourier and topological descriptors. Pattern Recognition, 17(5), 515-524.
EngngApplic.Artif.lntell.Vol.10,No. 5, pp. 485-493,1997 © 1997ElsevierScienceLtd Printedin GreatBritain.Allrightsreserved 0952-1976/97$17.00+0.00
Contributed Paper
Comparison of Shape Features for the Classification of Wear Particles KUN XU University of Wales, Swansea U.K. A. R. L U X M O O R E University of Wales, Swansea U.K. FARZIN DERAVI University of Wales, Swansea U.K.
(Received July 1996) Wear particle shapes are divided into four classes: Regular, Irregular, Circular and Elongated. They have been classified here using back-propagation neural networks which have been trained using different sets of rotation-, scale- and translation-invariant shape features derived from particle boundaries. The features include: Fourier coefficients based on either boundary curvature analysis or XY co-ordinates of boundary points; statistical moments of the curvature distribution including standard deviation, skewness and kurtosis; and two general shape descriptions, aspect ratio and roundness. In order to evaluate the performances of the features, a series of tests have been carried out on a wear particle database, and the results are compared. The boundary-curvature-based Fourier descriptors produce a shape classifier with the highest performance. The neural network trained by the Fourier features derived from the boundary data provides a slightly lower classification rate which is similar to that achieved using three statistical moments combined with the two general shape features. © 1997 Elsevier Science Ltd. All rights reserved Keywords: Shape, wear particles, neural networks, Fourier, curvature.
1. INTRODUCTION Any machinery that involves moving surfaces in contact will generate a certain amount of wear debris throughout its working life. This debris will consist of small particles that are produced from the interaction of the contacting surfaces. Initially, these wear particles will be benign, arising from small asperities on the surfaces that are removed during the preliminary operation of the machinery (running-in). As the machine ages, or is subjected to incorrect usage, misalignment and excessive forces between the various surfaces will produce certain quantities of other types of wear particles that are indicative of these conditions (Anderson, 1984). The particle characteristics (which include shape, size, concentration, surface and colour, etc.) are sufficiently Correspondenceshould be sent to: Mr A. R. Luxmoore,Departmentof Civil Engineering,Universityof Wales, SingletonPark, Swansea SA2 8PE U.K.
specific to operating wear modes to allow an expert to predict these wear modes from microscopic inspection of the particles. This can help in predicting the future behaviour of the machine, thus preventing failures and their associated costs. The technique is of particular use during the servicing of the sensitive and expensive machinery in aircraft and helicopters. Wear particle analysis is normally carried out in two stages: quantitative analysis and morphological analysis. Quantitative analysis measures the concentration of wear particles in a sample (a debris test index, DT), usually by means of a magnetic instrument, as most wear particles are ferrous. Morphological analysis is normally carried out under a microscope, to inspect the details of the particles, and yields specific information about the mechanism that produced them from their machine component. The debris test is quick and cheap, but morphological study gives more detailed information, albeit at a greatly increased cost.
485
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Practical experience has shown that an increasing DT value can give valuable information concerning the machine condition, but some machines that have been near to failure still had normal DT counts, whereas morphological examination of the same debris picked up a significant number of wear particles caused by a serious wear mode. In other cases, machines were rejected because of their high DT counts, but the microscopic analysis showed that there were no signs of serious wear. Therefore solely using the quantitative analysis can result in unreliable decisions, and morphological analysis is essential for reliable machine condition monitoring. Wear particles fall into several well-defined classes in terms of their formation mechanism and conditions. As an example, Fig. 1 shows four popular types of wear particles from aircraft engines. Rubbing debris (a), which is benign, is in the form of thin, plane particles with smooth edges, produced under the normal operation of lubricated machinery. Fatigue debris (b) is one of the more severe particles, and is characterised by an irregular outline. Cutting wear particles (c) are normally small, no more than 50/zm in length, elongated and usually curved, and are often to be found in a new engine. However, an increase in quantity and size with time would be a cause for concern. Spherical particles (d) are in the form of hollow spheres, typically 8-10/zm in diameter, and usually give evidence of a distressed bearing.
The images in Fig. 1 show that particle shape represents one of the most important features for a wear particle, the different shapes being associated with different wear types. Previous work (Roylance et al., 1992) has shown that shape is one of six particle attributes (the others are edge detail, size, texture, colour and thickness) that can be used to classify the particle uniquely in terms of a particular wear mode. These wear modes produce wear particle shapes which can be split into four classes: Regular, Irregular, Circular and Elongated. Instead of making the assessment visually, wear particle shape identification and classification might be performed more effectively using computer vision and artificial neural-network techniques, leading to the eventual automation of all six attributes.
2. SHAPE RECOGNITION AND CLASSIFICATION Shape recognition and classification are essential problems in many applications concerning computer vision techniques. In recent years there have been a number of investigations on two-dimensional closed-shape analysis and classification, based on a two-stage procedure: feature extraction, and shape recognition/classification. For the feature extraction many new shape-analysis approaches have been proposed. For shape classification in real time, artificial neural networks may be combined with appropriate features.
(a)
(b)
(¢)
(d)
Fig. 1. Wear particles. (a) Rubbing wear platelets. Image size 134 x 91 /xm. (b) Fatigue wear particle. Image size 134 x 91 /zm. (c) Typical cutting wear debris. Image size 54 X 37/xm. (d) Three spherical particles. The smallest one is about 5/zm in diameter.
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curvature, and for each segment the normalised approximate curvature sequence was sampled and averaged. Then In the design of a shape classifier using neural networks, the mean curvature values were taken as the features for the important factor is feature extraction, i.e. how an object neural-network training which was aimed at line shape is presented to the neural network. The input vector for the recognition. In this approach a threshold value plays a neural network should carry essential shape information, crucial role in the curvature approximation. In the proposed method, which is not aimed at recognisand must be normalised to provide a unique value ing particular shapes but at classifying all wear particles into irrespective of basic shape transformations such as translafour shape classes, the curvature variations have been tion, rotation and scaling (Pal et al., 1993; Hush and Home, calculated for each boundary point, so that no boundary 1993). Among the large number of two-dimensional closedpoint is omitted from the feature extraction. As curvature is shape analysis algorithms, or feature-extraction schemes, essentially invariant to position and rotation, but not scalepolygon approximations are popular. In 1993, based on a invariant (Katagiri and Nagura, 1994), an edge-smoothing review of existing methods, Pal et al. (1993) suggested a approach was investigated, not only for acquiring a polygon approximation operation which divides a shape reasonable curvature estimation, but also for the curvature into constant-point segments and then approximates each segment by a line segment joining the two end points. The normalisation. Then the DFT was applied to the curvatures angle variation between two consecutive lines is modelled to obtain a set of Fourier descriptors which are invariant by an autoregressive (AR) process, and the derived AR with respect to translation, rotation and size. Because it is a vector is then used for neural-net training and classification. common feature of Fourier descriptors that normally only a The technique is applicable to both concave and convex few low-order terms are essential for global shape recognishapes, and experimental results from four shapes of tion (this can be appreciated by regenerating the shapes various sizes showed that the scheme worked quite well. from the low-order terms), Fourier descriptors are well The constant-point number for the segmentation has to be suited for use as a feature vector in neural networks. This is decided carefully with respect to shape and size, otherwise essential for minimising the size of the neural networks and too much shape information is lost. In 1993 Mitzias and reducing the computation times. Mertzios (1994) presented a new polygonal approximation technique. A shape is approximated by a polygon with a 2.2. Shape classification--neural networks predefined number of vertices, which form the most critical Neural networks have become popular for classification points of the contour for the shape. Then, based on this purposes because of their high computational rates, robustapproximate polygon, two feature vectors are generated, ness and ability to learn. Artificial neural networks are viz. internal angles and normalised errors, which are used connectionist systems, with the neurones normally divided for the neural-network training. This method is also into layers and all the outputs from one layer connected to dependent on the initial selection, as the larger the number the input of the next. A multi-layer perceptron (MLP) has an of vertices chosen, the more detailed the representation of input layer, one or more hidden layers, and an output layer, the original shape that is achieved, leading to larger see Fig. 2. An artificial neurone applies a weight to each computation times, which may not be practicable. The input, then sums those inputs and applies a threshold above techniques face the same problem. No matter how function, for example a sigmoid function, to the output. A well the polygon-approximation algorithm works, there is successful training process should find a single set of always some information that is lost during the procedure, weights and threshold values (or biases) that satisfy all the as the number of vertices is limited. In the application of input and output pairs of training data presented to it. these techniques, the neural networks were employed to recognise only particular shapes. T3 T4 TI T2 Fourier descriptors are powerful tools for shape analysis and feature extraction. Kim and Nam (1995) described the shape classification of industrial tools that have only one degree of freedom. In their approach, a discrete Fourier output layer transform (DFT) was applied to the co-ordinates of all boundary points for feature extraction, and then the loweights order Fourier coefficients were used as the inputs for neural-network training. Their experimental results show a hidden layer very high classification accuracy on four kinds of tools, outperforming the two popular statistical classifiers, which eights are based on either the nearest-neighbour rule, or the input layer minimum-mean-distance rule. Curvature analysis has also been used in boundary feature extraction. Katagiri and Nagura (1994) defined and calcuFI F2 Fn lated the "approximate curvature" along a boundary. The boundary was divided into segments by the points with zero Fig. 2. A neuralnetworkwith a single hiddenlayer.
2.1. Shape analysis and feature extraction
KUN XU et al.: SHAPE FEATURES
488
l@
Fig. 3. Profiles with different boundary shapes.
Having been trained, when the net is presented with data it has never seen before, it can decide the appropriate output (Hush and Home, 1993). In order to determine the best feature number for an input vector, up to eight initial Fourier descriptors (amplitudes only) were used in the neural-network training for the boundary curvature analysis, and the classification rates tested. A similar neural network was trained using loworder Fourier amplitudes calculated directly from the co-ordinates of the boundary points (the XY Fourier), and the test results also compared. In addition to the two Fourier descriptors, some statistical descriptors, i.e. standard deviation, skewness and kurtosis, and general shape descriptors such as aspect ratio and roundness, were also used as feature vectors for the neural-network training, and the test results are presented.
4. BOUNDARY CURVATURE As curvature variation gives important information about the boundary shape, there should be significant differences between the curvatures for the boundaries with different types of shapes. Figure 3 shows four boundary profiles, each illustrating a different shape category. For discrete curvature analysis, a curvature-estimation technique, derived by Freeman and Davies (1977) for comer finding, was employed and applied to the digitised boundaries. The angular difference between two successive vectors was calculated and taken as the estimated curvature value for the intersection point of the two vectors. As shown in Fig. 4, for a boundary with N pixels, the curvature of the point Pj (O<-j<-N- 1) is defined by the angular difference between two vectors P~_j and P~'÷,. As the co-ordinates are known for each boundary point, the slopes can easily be derived by:
3. DATA COLLECTION Wear particles were examined using an Olympus microscope at a magnification of 100 × (for some small cutting wear particles 400 × was used). As only boundaries were of interest, transmission illumination was used. Particle images were taken by a CCD camera attached to the microscope, and this was connected to a Leica Quantimet 500 image processing system. Images were captured with 8-bit grey level resolution, and were processed and analysed by an application software package CAVE (Computer Aided Vision Engineering) (Roylance et al., 1994), which was adapted to MS-Windows for the Quantimet 500 system. For shape classification, particle boundaries are traced using four neighbours. Most images were taken from real wear samples, prepared from the debris found on aircraft engine magnetic drain plugs. As only a very few spherical particles had been found during the trial, some artificial objects were used for the circular class. Images were captured and stored in 512×512 pixels. The particle size is normally about 10/.tm-200 ram. It was assumed that all wear particles neither touched nor overlapped each other in the data collection. All sample images were classified into the four shape categories: Regular, Irregular, Circular and Elongated, by A. L. Price, an expert from the Swansea Tribology Centre of the University of Wales, Swansea. These class labels were chosen as they represent the normal particle types used by tribologists in classifying wear particles.
(1)
O)~-'=tan-'( )Xj--Xj-m-, yj-yj-"-'
O2~+~=tan-'(yj+~+I-yj ) .... x ,-xj j and the curvature of point Pj is calculated by:
kj= 07+1- OT_i ( - 90°-
(2)
The parameter m is normally referred to as a "smoothing factor". It is clear that the greater the value of m, the heavier
ej
(m=3) m
Fig. 4. Computation of discrete curvatures.
KUN XU et al.: SHAPE FEATURES the smoothing would be. However, if a large value of m (or a longer line segment) is chosen, the curvature estimate derived by, eq. (2) may not reflect the original fine features of the digital curve. On the other hand, if m is smaller, there will not be enough smoothing applied to the data: noise and quantization errors may be reflected in the derived curvature. Therefore it is very important to choose an appropriate smoothing factor for a specific application. As wear particles are quite different in size, if any fixed value of m were used, the curvature would depend not only on the boundary shape, but also on the size (curvature is normally not scale-invariant), so the smoothing factor m must be related to the boundary size, or scale. This problem was solved by normalising the successive vectors. The basic idea is to select a value of m corresponding to a fixed proportion of the 360 ° angle enclosed by a profile. From experiment, an angular segment of 10 ° was found to be satisfactory, and m was determined by (number of boundary points)/36. In this way, if any two profiles are of the same shape, their curvature diagram would be the same no matter how different their sizes, as the boundary size only determines the density. This keeps the curvature scaleinvariant. For a demonstration, two image pictures were taken from one wear particle using a microscope with two different lenses ( × 100 and × 50 respectively). Figure 5
489
shows the boundary profiles extracted from these two images and their curvatures. The two images do not appear to have identical shapes because of the difference in the depth of field for the two lenses, leading to slight differences between the two curvature diagrams, which is also reflected in the derived statistical values. For the four types of profile shown in Fig. 3, the curvature diagrams are shown in Fig. 6. The four profiles exhibit significantly different curvature curves. In order to extract the information with a finite number of features, a Fourier transform was carried out on the boundary curvatures.
5. F O U R I E R D E S C R I P T O R S OF CURVATURE Curvature k~ (j=0, 1..... N - 1) is a discrete signal, so a discrete Fourier transform (DFT) was employed. A discrete signalfk (O<--k<--N - 1) can be represented as a trigonometric series: N-I
fk=A0+ E ( A , c o s ( 2 ~ k n l N ) + N ) + B n s i n ( 2 z r k n / N ) )
where the Fourier coefficients are defined as follows:
(a)
(b)
Mean: FIA : Rq : Rsk : Rku :
10.249110 33.634533 44.172844 0.496645 3.516201
Mean: FILA : FILq : Rsk ;
10.369712 30.490973 39.686660 0.T00491 3.7271194
RJ(u :
~
Fig. 5. Curvatureanalysis-sizenormalisation.(a) Boundaryprofilesof a wear particle with different size. (b) The curvatures of two profiles.
(3)
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KUN XU et al.: SHAPE FEATURES
9O
'
""
.....
~
"-"
'r
_lWr
""
V
---m,-
"wr"
-4s -90
Fig. 6. Curvaturevariationsfor differentboundaryshapes. 1
2
(4)
N-I
A.= ~ ~__°Xf, cos(2crkn/N) 2
Figure 7 shows that the Fourier coefficients for the four shape classes are distinguishable from each other. The circular shape produces a very low value for all eight harmonics: the regular shape gives a similar value for each harmonic; the irregular shape has higher components on high frequencies; and the elongated profile only gives priorities to the even harmonics (2, 4, 6, 8). The results indicate that the Fourier coefficients based on the curvature analysis provide very distinct features and representations for the four types of boundary shape.
N-I
Ao=~/ L~oA
(5)
N-I
B,= ~/ ,__E ° ftsin(2~rkn/N)
(6)
and C , = 2~
2
( l < - - n < N - 1).
(7) 6. OTHER SHAPE FEATURES 6.1. XY Fourier descriptors
Applying equations (4)-(6) to the curvature variable kj, then the c~ (i= 1-8) for the four different profiles (shown in Fig. 2) are calculated using equation (7), and shown in Fig. 7.
A boundary pixel is represented by a two-dimensional array of (x, y). Treating the co-ordinates x and y as independent, it is advantageous to treat the 2D array as two
• Circular I'1 Irregule t • F.JeeSated • Regular
_JJ 1
2
3
4
5
6
7
Harmonlo Number
Fig. 7. The Fouriercoefficientsfor fourprofiles.
8
KUN XU et al.: SHAPE FEATURES
491
Kurtosis, the fourth moment, measures the "peakedness" 1D arrays, i.e. to deal with the two co-ordinates separately. of a distribution relative to with the normal one: In this way, instead of the two-dimensional DFT, only a one-dimensional DFT is carried out, on xk and Yk (O<-k<--N- 1) respectively. Based on this idea, a set of XY Fourier descriptors were developed by Badreldin et al. (15) Kurt= ~[ i=l (1980). In trigonometric terms the Fourier series descriptors for x~ are given by: 2 N-I
Ax.= ~ k=~oxkcos(2~'knIN) 2
N-I
Bx~= ~ kX=oxksin(2~kn/N)
(8)
(9)
The dc components Ax0 and Bxo can be ignored since they only carry information about the x position of the image centre. From Ax, and Bx,, the Fourier descriptor Cx, for xk can be derived:
C x . = ~ ( n =2 l , 2
2
.... ).
Also, two general shape features, aspect ratio and roundness, were used. The aspect ratio is the ratio of the longest feret divided by the shortest feret; and the roundness is a shape factor which gives a minimum value of unity for a circle:
Roundness =
Perimeter 2 41rX Area × 1.064
(16)
where the adjustment factor of 1.064 corrects the perimeter for the effect of the corners produced by the digitisation of the image (Leica Cambridge Ltd, 1993).
(10) 7. EXPERIMENTS AND RESULTS
The same procedure could be carried out on Yk to obtain the Fourier coefficients of Cyn . The parameters Cx~ and Cy, are not rotation- or shift-invariant, but for each nth harmonic a invariant Fourier descriptor C~ can be derived from Cx~ and Cy~ (Badreldin et al., 1980): 2
c.=
+ Cy 2.
(11)
In order to further refine Cn to be a scale-invariant descriptor, a normalisation operation was applied: an ~ Cn
.
Cl '
(12)
then S. (n= 1, 2 .... ) is invariant to rotation, shift and size (Shridhar and Badreldin, 1984).
6.2. Statistical moments and general shape descriptors Statistical analysis of a set of data also provides important information about that data; therefore, based on the boundary curvatures, three higher moments were derived and used for the neural-network training:
Standard deviation, the second moment, characterises the data distribution around its mean value: 1 or=
-
N
N -- 1 "=Xl(xi - 3) 2.
(13)
Skewness, the third moment, characterises the degree of asymmetry of a distribution around its mean value:
Skew= ~ i=l
(14)
The neural networks utilised in this work are static, multilayer pereeptrons (MLP) with only one hidden layer. There are four output nodes for the output layer corresponding to the four shape classes, but the node number for the hidden layer is dependent on the number of input features. When the number of input features is over six, the number of nodes for the hidden layer is equal to or slightly less than the number of input nodes, otherwise there are slightly more hidden nodes. The neural networks were trained using a supervised, back-propagation learning algorithm. Given a set of sample input-output pairs, the neural networks were trained to match the samples as closely as possible. Altogether 200 wear particles were assessed, with 100 for training, and 100 for test. As there were fewer samples of spherical particles than for the other shapes, only 10% of the samples were available for the circular class (the test results showed that this number is enough for the circular class training), leaving 30% each for regular, irregular and elongated respectively.
7.1. Classification using curvature Fourier descriptors Experiments were carded out to train the nets using different numbers of the Fourier coefficients based on the curvature analysis, and then the same test samples (100) were used for classification. The test result shows that using the first seven Fourier coefficients as the inputs (with six nodes in the hidden layer) gives the highest classification rate of 97%, see Fig. 8.
7.2. Comparison with XY Fourier descriptors Based on the XY Fourier descriptors, a trained neural network worked very well in the recognition of one-DOF tools (Kim and Nam, 1995), so it was employed in this work for wear particle shape classification. As the Fourier descriptors (coefficients) were normalised by the first Fourier coefficient, equation (12), this coefficient was
492
K U N X U et al.: S H A P E F E A T U R E S 100 95 90 85 80 75 70 65 60 55 50
I
I
2
I
3
I
4
5
I
I
I
6
7
S
Input Feature Numbel
Fig. 8. Performance vs different number of inputs.
omitted, and the next seven coefficients (S2-Ss) were used for net training with the same structure (one hidden layer with six nodes and four outputs). The result shows that the classification rate of the classifier based on the XY Fourier descriptors is lower:
groups, being robust for the irregular and circular classes, but not as reliable for the regular and, in particular, the elongated class. For the two training strategies based on the boundary curvatures and boundary data, the classification and normalised system errors vs the number of iterations also show that the Fourier descriptors based on the curvature analysis present a high and stable classification rate, with lower system error during the training process, and the neural net trained by the XY Fourier descriptors reaches its highest performance (91%) after 200 iterations, after which the classification rate drops down again, see Fig. 9.
Curvature Fourier 97% XY-coordinates Fourier 91%. The classification rates for the four individual shape classes were also compared for the two Fourier systems. The results are shown in Table 1. For the four shape classes, the neural network trained by the Fourier coefficients based on boundary curvature analysis outperforms the net trained by the XY Fourier coefficients. The former gives more consistent results, but the latter presents a different performance for the different
7.3. Results of other shape descriptors Three higher statistical moments derived from boundary curvatures and two general shape descriptors were also used for the neural-net training, but the feature vectors were composed of different features----~e classification rates are compared as follows:
Table 1. Confusion matrices showing the performances of two nets True setkassigned set
Regular
Irregular
Elongated
(a) Curvature Fourier classifications Regular 29 Irregular 1 Elongated Circular
30
2 28
(b) XY Fourier classifications Regular 27 Irregular 1 Elongated Circular 2
30
70 .2 50
5 1 24
20 U 10 o o
I 200 ~
I
ox.. . I
I
92 (aspect ratio, roundness, sd, skew and kurt.) 89 (aspect ratio, roundness) 54 (sd, skew, and kurt.).
For the four individual shape classes, the performances of the classifiers trained using the five features and two features are shown in Table 2.
00'
Curv. Fourier
I
Classification Rate (%)
O'o, o
i
• Curv. Fourier n XY Fourier
~ 015 ~ - \ \
ox.... •
40 ~ 30--
2 features 3 features
10
:
60
Training Features 5 features
10
100 90 80 =
Circular
i
i
I
i
I
600 800 1000 i200 1400 1600 1800 2000 N u m b e r 0:f ite~'a~ions
01i
0.3 0.2 ~ O.
~'
z
t
0
200
400
~
600 800 1000 1200 1400 1600 1800 2000 N u m b e r o f iterations
Fig. 9. Classification rate and normalised system error vs number of iterations for two feature sets.
KUN XU et al.: SHAPE FEATURES Table 2. Confusion matrices of two nets trained using other shape features True setkassigned set
Regular
Irregular
(a) Classifications based on five features Regular 28 2 Irregular 1 28 Elongated 27 Circular 1
Elongated
Circular
1 2
(b) Classifications based on roundness and aspect ratio Regular 27 2 Irregular 2 28 1 Elongated 29 Circular 1
9 3 2 5
493
A series of experiments were also carried out to compare the performance with that of the neural networks trained by other shape features. Despite the reported success (Katagiri and Nagura, 1994) of neural networks trained using Fourier coefficients of boundary data for one-DOF tool recognition, for wear particle classification this approach did not work as well as the curvature Fourier (for the same number of coefficients), particularly for the elongated shape category. This is most probably due to the initial smoothing (filtering) in the curvature process. The two general shape features, aspect ratio and roundness, provide most of the shape information, but for a high classification rate, some more information is required, particularly for circular shapes.
The system trained by five features (aspect ratio, roundness, standard deviation, skewness, and kurtosis)
REFERENCES
gives a good performance of 92%, and the use of two features of aspect ratio and roundness also gives a reasonable rate, 89%. The main difference between these two systems is for the circular class. The results indicate that aspect ratio and roundness carry most information for a 2D closed profile, but for spherical shape recognition, the two general shape features are not so reliable (probably because the aspect ratio is dependent on each individual point, including any "noise" which might be a single outlier), and some more information is needed. The performance of the neural net trained with only the three higher moments is very low.
Anderson, D. P. (1984) Wear Particle Atlas (Revised). Report NAEC92-163 Prepared for Advanced Technology Office, Support Equipment Engineering Department, Naval Air Engineering Center, Lakehurst, New Jersey. Badreldin, A., Wang, A. K. C., Prasad, T. and Ismail, M. (1980) Shape descriptors for N-dimensional curves and trajectories. IEEE Proceedings on Cybernetics and Society, pp. 713-717. Freeman, H. and Davies, L. S. (1977) A comer-finding algorithm for chaincoded curves. IEEE Transactions on Computers, C-26, 297-303. Hush, D. and Home, B. G. (1993) Progress in supervised neural networks, What's new since Lipomann. IEEE Signal Processing Magazine, pp. 8-39. Katagiri, M. and Nagura, M. (1994) Recognition of line shapes using neural networks. IEICE Transactions on Information and System, E77D(7), 754-760. Kim, H. and Nam, K. (1995) Object recognition of one-DOF tools by a back-propagation neural net. IEEE Transactions on Neural Networks,
6(2), 484--487. 8. CONCLUSIONS
This paper has presented a classification system for wear particle shape classification through the use of a backpropagation neural network, which was trained using the feature vectors composed of a number of low-order DFT descriptors derived from boundary curvatures. The classifier presents a high classification rate, and exhibited robust and consistent performances for the four shape categories. The average time consumed on the curvature calculation and Fourier analysis is about 100 ms, depending on the size, and about 50 ms for the shape classification, using a PC486 running at 66 MHz.
Leica Cambridge Ltd (1993) Quantimet 500+ User Manual. Leica Cambridge Ltd, Cambridge, U.K. Mitzias, D. A. and Mertzios, B. G. (1994) Shape recognition with a neural classifier based on a fast polygon approximation technique. Pattern Recognition, 27(5), 627-636. Pal, N. R., Pal, P. and Basu, A. K. (1993) A new shape representation scheme and its application to shape discrimination using a neural network. Pattern Recognition, 26(4), 543-551. Roylance, B. J., Albidewi, I. A., Luxmoore, A. R. and Price, A. L. (1992) The development of a computer-aided systematic particle analysis procedure--CASPA. Lubrication Engineering, 48(12), 940-946. Roylance, B. J., Albidewi, I. A., Laghari, M. S., Luxmoore, A. R. and Deravi, E (1994) Computer-aided vision engineering (CAVE)---quantification of wear particle morphology. Lubrication Engineering, 50(2) Shridhar, M. and Badreldin, A. (1984) High accuracy character recognition algorithm using Fourier and topological descriptors. Pattern Recognition, 17(5), 515-524.