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Morphological analysis and classification of types of surface corrosion damage by digital image processing
Corrosion Science 47 (2005) 1–15 www.elsevier.com/locate/corsci
Morphological analysis and classification of types of surface corrosion damage by digital image processing K.Y. Choi
a,*
, S.S. Kim
b,1
a
b
Chemical Department, Belarusian State University, 14, Leningradskaya Street, Minsk 220050, Belarus School of Mechanical Engineering, Kyungpook National University, Daegu 702-701, South Korea Received 16 October 2002; accepted 18 May 2004 Available online 2 July 2004
Abstract This paper examines a new concept of corrosion surface damage analysis by using the digital image processing. Corrosion phenomena are analyzed using a digital value for morphological surface damages instead of electrochemical methods. Initial images are characterized by three categories: color, texture and shape features. To calculate corrosion surface damages color we use the interpretation of HIS model. For the texture attributes, the method of co-occurrence matrix is used. Five types of corrosion damage are examined. Multidimensional scaling procedure is used to define the classification plane. This study suggests a probabilistic method of decision-making. This analysis develops a method for automated identification system of corrosion damages and is supposed to be more advantageous than that of electrochemical techniques. 2004 Elsevier Ltd. All rights reserved. Keywords: Corrosion damage; Morphology; Digital image processing; Classification
1. Introduction Corrosion damage monitoring is an important aspect of a number of industrial technologies related to both serviceability provision and various mechanisms safe *
Corresponding author. Tel.: +375-297-308219; fax: +375-17-226-4696. E-mail addresses: [email protected] (K.Y. Choi), [email protected] (S.S. Kim). 1 Tel.: +82-53-950-5577; fax: +82-53-950-6650.
0010-938X/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2004.05.007
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operation [1–3]. Methods, based on corrosion kinetics estimation by corrosion current, are supposed to be the most widespread to measure corrosion damage in industry. Electric resistance and various modifications of potentiometric techniques are used for these purposes [4,5]. To measure corrosion by electrochemical polarization several methods are available. Using either the Tafel extrapolation or polarization resistance, commercial corrosion monitoring probes have been introduced to the industry [6]. EIS enables a valid measurement of polarization resistance and corrosion rate after correcting ohmic interferences from solution resistance [7,8]. However, it is not always perfect. At the low-frequency end of the spectra where the polarization resistance is measured, corrosion potential and corrosion rate may vary in the middle of the measurement [9]. Intricacy of the problem stems from the specific features of corrosion phenomena, i.e., influences of various factors and great diversity of corrosion types. To quantify galvanic corrosion rate, for example, there are great many controlling factors [10]. Although Evans diagrams, suitably amended to take into account the differences in corrosion areas of metals presence, the extrapolation of laboratory behavior into large-scale engineering situations is extremely difficult to model [11]. Recently, Scanning Reference Electrode Technique (SRET), which applies computer analysis and display of data collection program, has been developed. It allows the precise identification of probe position above the surface of specimen [12]. It has been shown that this technique is powerful in many different applications, such as using a calibration technique by which localized current densities can be measured by mapping corrosion surface damage [13,14]. But it can be applied only for special-purpose corrosion area localization not to the entire corrosionmonitoring system, which can compare and analyze the full corrosion process and phenomena. The NACE (National Association of Corrosion Engineers) has set up a task group (T-3T-3), who prepares a report on various on-line technologies. The report has categorized the on-line monitoring methods into three groups: Group 1 measures, either on a sensing element or directly, the change in physical geometry of noncorroded metal. Group 2 controls either the potential or electrical current density across a metal and conductive fluid interface and measures whichever is not controlled as well. Group 3 measures corrosion byproducts, using hydrogen probes or acoustic emission [15]. And nowadays a variety of techniques for corrosion testing is available in industry for on-site monitoring [16–18]. In short, the current techniques are useful mostly for an integral assessment––i.e., the total mass losses of a metal and the rate of corrosion at laboratorial size––or only in some limited cases in large-scale engineering industry. Different effects of various factors on corrosion process cause different damage types and finally result in different morphological damage. At present the following typology of corrosion damages is generally used by NACE: general or uniform corrosion, localized corrosion (or pitting, crevice corrosion), galvanic corrosion, cracking phenomena (stress corrosion cracking, hydrogen embrittlement), velocity effects (erosion–corrosion, cavitation, fretting), intergranular corrosion, dealloying, high temperature corrosion
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[19,20]. Combined types of damage can also arise when several factors interact, e.g., uniform corrosion with pits [21]. Corrosion damages morphology, surface distribution, shape and depth are strictly dependent on the nature of characteristics in connection with a final concrete operation of corrosion mechanisms. However, given the same corrosion rate and, also, given the same amount of mass loss in metal, localized corrosion or SCC seems to be a more dangerous damage type compared to uniform corrosion owing to more localized failure that brings about catastrophic fracture [22]. Therefore, an adequate estimation of corrosion damages degree requires the study of damages morphology in addition to the corrosion process integral kinetic characteristics. At present, there exists a concrete morphological definition only for pitting made by ASTM Practice G-46. It detects the measurement of pit density, size, depth, and characterization of the cross-sectional shape of pits [23]. Even though this is a useful and strong evaluation tool for pitting corrosion analysis, it has lots of limitations. Among them are difficulties in automatic recognition of pitting changing phases, difficulties in comparing morphological cross-sectional shape of pits, complexity of automatic distinguishing between various corrosion types when pitting arises together with other corrosions like uniform type or intergranular type and, furthermore, difficulties in predicting corrosion rate, etc. Expert visual examination is the most common and simple method of assessing corrosion damages morphology. Among the drawbacks of the method are the necessities to employ qualified staff and to use of subjective criteria for decisionmaking. However, progress in hardware and software made in the last several years allows us to facilitate this approach in a new direction. Methods of digital images processing, classification and analysis are currently in considerable use in various fields of science. Yet, despite the apparent advantages of this approach, it is not used to analyze corrosion processes. The main reason for this lies, in our opinion, in the problem of describing of corrosion damage by morphology, i.e., color, texture and shape. If we are able to analyze and describe, through image processing method to conform qualified state of digital value, all kinds of corrosion morphological damages and their mechanism. Apart from original electrochemical approach it is another powerful tool to evaluate the corrosion process. Also, the combination of digital image processing method with mathematical analysis techniques (Finite Element, Finite Difference, Boundary Element Method, etc.) for corrosion phenomena will enable us to apply the digital image processing method to dynamic corrosion monitoring and simulation system with new idea. The aim of this paper is to develop corrosion damages automated classification method by their optical images. It allows detecting a representative set of morphological attributes of damages and making corresponding classification rules, which enable us to divide the damages into several types. Corrosion damages typology is as follows: uniform corrosion, crevice corrosion, pitting corrosion, fretting corrosion, intergranular corrosion. These types of corrosion damages are selected according to the significance when solving problems of diagnostics in engineering and in
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accordance with the possibility of their use in the analysis of optical methods of surface examination as well.
2. Sampling specimens A sample of 197 images has been selected to solve the problem. Among them 97 images have been used for exercise, the remaining images have served for validating the decision-making rules. The images were obtained from accelerated corrosion tests [24] including scientific papers, textbooks and Internet. The images of the specimens after corrosion tests were taken by an optical microscope [25]. Other images of the objects adopted from publications and Internet were scaled to the size identical to that of the images obtained by microscopy. The magnification range of all images is from 50 to 500. Fig. 1 shows the examples of corrosion damage images used in the paper.
3. Corrosion damage images description Like any other problem of image analysis, the solution of the problem of computer-aided identification and classification of corrosion damage can be split up into several stages. During the first stage a model suitable to describe the morphology of
Fig. 1. Examples of corrosion damage images: (a) non-corroded pure surface of mild steel (100X); (b) uniform corrosion of mild steel (X300); (c) crevice corrosion of stainless steel under barnacles growing in seawater (X200); (d) pitting in stainless steel (X50); (e) Fretted corrosion steel surface (X480); (f) Intergranular SCC of an Inconel heat exchanger tube with the crack following the grain boundaries (X500).
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defects is to be identified. In relation to visually interpretable objects, the morphology comprises the notions of texture, color and shape of the objects under analysis. At present, no integrated theory exists to show how to assign parameters to a visually perceived object [26]. Each specific application has its own approach to the interpretation of images of observed objects which is governed to a substantial degree by morphological formations and their relation to the physical models in this application. Hence, parameters of selection of morphological parameters representative set require, in each specific case, an individual analysis, as well as the methods of their description of attributes computation and optimization. To deal with the quantitative description of such parameters as color, texture and shape of corrosion defects. Color and texture can be formulated as follows: selection of a set of quantitative attributes in accordance with the discrimination between a corroded elementary surface and non-corroded surface portion. Shape characteristic is basically solved from the results obtained from the solution of the two previous parameters. In general it is formulated as a problem of localizing and describing of defects. Algorithmically its solution is derived from the determination of relations between the identified color and texture characteristics of elementary surface portions, the coordinates of the identified regions (corrosion defects) and description of their shape and mutual arrangement. 3.1. Color characteristics of corrosion defects Attributes of color characteristics of corroded objects should be determined in order to identify them quantitatively based on a definite color model. The HSI model is the best suitable model for this purpose since it allows describing color characteristics separately from brightness characteristics. The values H (hue), S (saturation) and I (intensity, brightness) for the R (Red), G (Green) and B (Blue) components were specified as follows: 1 I ¼ ðR þ G þ BÞ 3 3 ½minðR; G; BÞ S ¼1 ðR þ G þ BÞ 1 ½ðR GÞ þ ðR BÞ 2 H ¼ cos1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðR GÞ þ ðR BÞðG BÞ These formulas have been optimized for the computer format of data interpretation. Hence, registration of a signal in the RGB computer format allows transforming it into the HSI color space [27]. A test sample of objects has been grouped in order to choose the color parameters and to investigate the space of attributes they produce. Each object has been the image of a surface portion obtained for corrosion damage. The surface portions 10 · 10 pixels were selected for analysis. We can take the separation of primary attributes of objects on the base of strong correlation between original attributes for
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their identification [28]. The original set of attributes is transformed into a secondary set, and optimized by the classic statistical approach. The purpose of these transformations is to discriminate between the correlating and non-correlating portions of the set of attributes. The method of moments has been employed to calculate the second set of attributes [29]. For this purpose the final H and S values for each element of the image are represented as histograms of distribution of their values. It is known that one method of describing the distribution of random values is to use their moments of the nth order. If hðxÞ is a histogram, the moment of the nth order xi against its mean value is calculated as X ðxi xÞn pðxi Þ; n > 1 ð1Þ ln ¼ i
where pðxi Þ is the probability of incidence of the ith value of the attribute x. The set of the secondary attributes includes the moments up to the 4th order: X 2 ðxi xÞ pðxi Þ; x ¼ fH ; S; Ig ð2Þ l2 ¼ i
l3 ¼
X
3
ðxi xÞ pðxi Þ;
x ¼ fH ; S; Ig
ð3Þ
ðxi xÞ4 pðxi Þ;
x ¼ fH ; S; Ig
ð4Þ
i
l4 ¼
X i
Additionally the distributed mean, median and geometrical median original attributes have been included into the set 1X x ¼ xi ; x ¼ fH ; Sg ð5Þ n i xm ¼ xi ;
i
i X j¼0
xg ¼
Y 1 ; xni i
xj ¼
n X
xj ;
x ¼ fH ; Sg
ð6Þ
j¼i
x ¼ fH ; Sg
ð7Þ
Attributes (5)–(7) have been calculated for the value of the brightness component ðIÞ of the HSI color field in order to avoid problems induced by the irregularity and inconstancy of the parameters of illumination when registering images. The method of main components has been applied to optimize the set of attributes and to eliminate insignificant attributes [30]. Full-factor space, which has over 50% of the dispersion of the attributes, can be minimized to two factors. Varimax focuses on cleaning up the factors for this purpose. Varimax method for the rotation of the space of attributes has been used to calculate the significance of the attributes. Varimax rotation produces factors that have high correlations with one smaller set of variables and little or no correlation with another set of variables [31,32]. Fig. 2 shows the graph of significance of the attributes by Varimax.
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1 0.8 0.6
2 4
9
8
Factor 2
0.4 6
0.2
5 10
3
0
14 1
13
-0.2
11 7 15
-0.4
12
-0.6 -0.8 -1 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Factor 1
Fig. 2. Factorial loads. Figures designate attributes: (1, 2) mean values; (3, 4) median values; (5, 6) geometrical mean values of H and S; (7, 8, 9) dispersion; (10, 11, 12) asymmetry and (13, 14, 15) excess of distribution of H , S and I values.
The circumference on the graph shows the boundary of the significance region corresponding to 0.75. The maximum variability of attributes is observed along the axis of factor 1. This behavior of the data is commonly interpreted as linear discriminability of objects classes. A threshold of 0.75 has been used to rank the values of attributes and to select five most significant secondary attributes. Consequently, the set of secondary attributes reflecting corrosion damage color characteristics can be reduced from 15 to 5 elements (2, 4, 1, 15, 14). This set has the following parameters: mean H value; mean S value; median S value; skews S distribution; skews I distribution. 3.2. Texture and shape characteristics of corrosion defects Corrosion process produces a certain texture or a typical rough surface structure on the metal. This surface texture features are distinct for various types of corrosion damage. It is important to obtain a quantitative system of rating reflecting the visual perception of various textures of the objects under analysis. With this consideration in mind the texture analysis should be performed by the brightness parameters of rough surface images relating to the visual perception characteristics rather than to the sizes of projections. To describe the texture features of corrosion damage we use the method disclosed in [33–35]. According to this method, the term ‘‘texture’’ implies the result of three-dimensional relations between brightness degrees in the rough surface image [36]. The characteristics of these relations are represented by co-occurrence matrix: M ¼ ka; qk
ð8Þ
Each element of the matrix (8) is equal to the number of pairs of texture elements with the azimuth difference a and the spacing q between them (Fig. 3). The routine of calculating the matrix of mutual incidence comprises several steps. First, the azimuth angle a of each element of the digital image is calculated. Then the
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Fig. 3. Diagram of description of corrosion damage texture.
difference between the coordinates of texture elements is calculated in pairs. To reduce calculation time and to save resources the range of possible a values is quantified into 10 levels. The spacing q is calculated in pixels. The maximum spacing of 10 has been selected to make the texture elements discernible. Hence, calculations are made in the sliding window 11 11. Co-occurrence matrix elements values are determined by calculating the numbers of pairs with relevant combinations of the a and q values Mði; jÞ ¼ #pði; jÞ
ð9Þ
The routine is competed by matrix normalization: Mði; jÞ mði; jÞ ¼ P i;j Mði; jÞ
ð10Þ
Images texture properties are characterized by the following set of attributes [37]: X X lx ¼ i mði; jÞ ly ¼ r2x ¼
i
j
j
i
X X j mði; jÞ X
ði lx Þ
2
i
r2y ¼
X
X
ði ly Þ2
X
j
I¼
mði; jÞ
i
XX i
mði; jÞ
j
j
2
ði jÞ mði; jÞ
ð11Þ
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The set comprising (11) attribute of flat object shape recommended in [38] is used to describe corrosion damage morphology. The set includes the following characteristics: area, perimeter, length, shape factor, dimension of the maximum axis, dimension of the minimal axis, ratio between the axes, the mean radius, the maximum radius, the minimal radius, the ratio between the radiuses.
4. Classification of corrosion damage 4.1. Model of the space of attributes To classify the descriptions of color, objects texture and morphology are represented as an ordered sequence of numerical values. In relation to our specific case, to identify image surface corrosion damage, the image under analysis is represented by a vector of 18 elements (5 color, 2 texture and 11 morphological shape attributes): Fs ¼ ½f1 ; f2 ; . . . ; f18
ð12Þ
Prior to the analysis the vector of the attributes of all the objects in the test sample is integrated into a single table and normalized. To check if the parameters meet the criterion of non-homogeneity r2 > 0 [39], integrity parameters are analyzed. If this condition is satisfied, object attributes description parameters can be treated as the coordinates of some n-dimensional space. Resting on this approach, the object under analysis can be represented by a point on the n-dimensional space. The closer the distance between the attributes (point) of an object on the space are, the more is the similarity of the objects. On the same token, the farther the distances between the attributes are, the less alike they are in terms of the attributes. In accordance with this, clusters are formed on the space of attributes. The task of classification is to determine the ranges of the clusters corresponding to various objects and to set the rules being the functions of the attributes, which are used to divide the objects into classes. The function of calculating the measure of distance in some abstract space should satisfy the following four axioms [40]: (1) (2) (3) (4)
Identity: qðF1 ; F2 Þ ¼ 0jF1 ¼ F2 . Symmetry: qðF1 ; F2 Þ ¼ qðF2 ; F1 Þ. Positiveness: qðF1 ; F2 Þ P 0. Triangular inequality: qðF1 ; F3 Þ 6 qðF1 ; F2 Þ þ qðF2 ; F3 Þ.
The function satisfying these conditions is termed a metric space. It allows us to use the attributes with different physical sense or content. For example, one dimension can characterize color, another dimension––size, still another can present the characteristics of the environment at the moment the object is being analyzed. It is possible, because the location of a point as some mathematical abstraction has its own attribute; meanwhile the distance is meaningful only as its difference from another point.
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There is one more essential factor relating to the features of the metrical space. It has been demonstrated [41] that linear transformations of the space coordinates in no way alter the topological structure of arbitrarily arranged points within it. In particular, it is impossible to alter the mutual arrangement of objects in the space using affined transformations of the type xi ¼ a0i þ a1i f1 þ þ ani fn
ð13Þ
where 1 6 i < n, ani is the matrix of transformation coefficients specifying the operations of displacement, rotation, scale or shear alterations. This conclusion has an essential practical significance in the problems of classification, since no transformation is capable to alter the discriminability of classes. In order to avoid this problem, the metric of Minkovskii method is the most suitable. This metric space is specified in the following form with Euclidean measure [42]: " #1=2 d X 2 qE ðk; mÞ ¼ ðfik fim Þ ð14Þ i¼1
This measure is the most frequently used for the problems of classification, primarily because it gives the values intuitively understandable and easy to interpret. Hence, a multidimensional space of attributes has been selected as a model to formalize the presentation of corrosion damage image data. 4.2. Clustering in the space of attributes At present the multidimensional scaling for clustering is the most common approach in visualizing the multidimensional data [43]. Shepard–Kruskal method of projecting and minimizing discrepancies is used for this purpose [44]. This method is effective in determining the projection coordinates by solving the equations, which are describing the mutual arrangement of points on the plane. The discrepancy function has been calculated as: w¼
n1 X n X
ðoÞ
ðqkl qkl Þ
2
ð15Þ
k¼1 l¼kþ1 ðoÞ
where qkl , qkl are the distances between the points in the original multidimensional space and on the projection plane, respectively. In order to obtain the solution the discrepancy w is specified as 10% of the original sum of distances between objects. Fig. 4 presents the results of multidimensional scaling of objects of the exercise sample corresponding to the objects affected and unaffected by corrosion and the clustering of various types of corrosion defects. This graph corresponds to the division of the regions under analysis into two classes, i.e., those affected and those unaffected by corrosion. Presented data analysis allows the following conclusion: six clusters can be identified on the classification plane, which is conventionally divided into two parts. Region ‘‘A’’ has the cluster corresponding to the specimens unaffected by corrosion. The region ‘‘B’’ has the groups with different types of corrosion damage.
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Fig. 4. Multidimensional scaling results: division of objects into two classes damaged or undamaged by corrosion (Papvepyocnm D1 ¼ Dimension D1, Papvepyocnm D2 ¼ Dimension D2).
4.3. Classification of corrosion defects In order to obtain the functional relationship between objects coordinates on the classification plane and their coordinates (attributes) in the original multidimensional space, linear regression model has been selected: X Dj ¼ a0 þ ai Fi ; fj ¼ 1; 2g ð16Þ i
where a0 ; a are the required coefficients of the model, Fi is the ith attribute of the objects in the exercise sample. In general, the boundaries between two arbitrary classes can be determined in the following way: D2 ¼ b0 þ b1 D1
ð17Þ
where b0 , b1 are the coefficients of linear interpolation. This line divides the classification plane into two semi-spaces, and validates the following condition: 1jd < D12 c¼ ð18Þ 2jd > D12 where D12 is the coordinates of the interclass boundary, and d is the coordinates of the analyzed object. This approach can be expanded to cover the case of n linearly distinguishable classes: c ¼ ijDi1;i < d < Di;iþ1 ;
i ¼ 1; . . . n;
D0;i ¼ 1;
Dn;nþ1 ¼ þ1
ð19Þ
The lines of the relevant boundaries of the classes and clusterization of corrosion damage by calculation of the space of attributes are shown in Fig. 5. This graph is shown to classify the clusters according to the corrosion damage types within a class and reflects a detailed analysis of the region B shown in Fig. 4.
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Fig. 5. (a) Boundaries of corrosion damage classes: ab, crevice corrosion and all other corrosion damage classes; cd, uniform corrosion/fretting; ce, fretting/pitting; fg, pitting/intergranular. (b) Clusterization of corrosion damaged objects according to types: 1, crevice corrosion; 2, intergranular; 3, pitting; 4, fretting; 5, uniform corrosion.
4.4. Evaluation of the probability and accuracy of classification results In order to achieve the probabilistic classification, objects distribution density within clusters is calculated. Corrosion damage tested sample coordinates serve as parameters. For this purpose the histograms of distributions are approximated along the curves of normal distribution. To facilitate the problem a map of classes has been calculated as a matrix with each element corresponding to a certain region of the classification plane, the value of the element is the probability of matching the class. Fig. 6 shows the map of classes for the problem in question. A test sample of 100 images serves to evaluate the accuracy of classification of corrosion defects using the above-mentioned methods. Tests results are summarized in Table 1. The sum of the elements in each line is equal to the number of particles of a relevant class analyzed in the test. In other words, the values in ði; jÞth cells of the table at i 6¼ j are equal to the number of particles classified erroneously.
0.6
6
0.4 0.2
5
0
4 1
-0.2 -0.4
3
-0.6
2
-0.8
-1
-0.5
0
0.5
1
1.5
Fig. 6. Bidimensional map of probabilities of corrosion damage classification: 1, non-corroded specimen; 2, crevice corrosion; 3, intergranular; 4, pitting; 5, fretting; 6, uniform corrosion.
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Table 1 Results of testing of method 1
2
17 2
3 13 2
1 2 3 4 5 6
3 1 13 1
4
5
1 12 3
3 13
6
1 15
Legend: 1, non-corroded specimen; 2, crevice corrosion; 3, intergranular corrosion; 4, pitting; 5, fretting corrosion; 6, uniform corrosion.
All test images have been verified by experts. The degree of agreement between the experts’ views is rated resting upon the method of consensus [45]. The obtained consensus factor equals 0.91. We can conclude that the experts’ views did not differ significantly. The presented data prove that the objects have been classified quite accurately (85%). Hence, the accuracy of the new method of classification is actually the maximum achievable for the class of objects in question.
5. Conclusions Morphological attributes analysis resulted in the formulation and validation of the optimum set of attributes. It will allow us to perform the probabilistic identification of surface corrosion damages using their images. Applicability of pattern recognition theory for automated classification of surface corrosion damage has been developed. Our results have shown, that apart from electrochemical method, corrosion can be evaluated by digital image processing in morphology: color, texture, and shape. Machine vision methods are applied to the analysis of corrosion surface damage for the first time. The analysis of corrosion damage by digital image processing is an important step in the promising direction in corrosion diagnostics.
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[33]
[34] [35]
K.Y. Choi, S.S. Kim / Corrosion Science 47 (2005) 1–15 F. Mansfeld, M.W. Kendig, S. Tsai, Corrosion 38 (1982) 570. D.C. Silverman, J.E. Carrico, Corrosion 44 (1988) 280. Denny A. Jones, Principles and Prevention of Corrosion, Prentice Hall, 1996, p. 165. K.R. Trethewey, J. Chamberlain, Corrosion for Science and Engineering, Longman, 1995, p. 139. D.J. Astley, Use of the microcomputer for calculation of the distribution of galvanic corrosion and cathodic protection in seawater system, in: H. Hack (Ed.), Galvanic Corrosion, ASTM, Philadelphia, 1988, pp. 53–78. H.S. Isaacs, V. Brijesh, Scanning reference electrode techniques in localized corrosion, in: F. Mansfeld, U. Bertocci (Eds.), Electrochemical Corrosion Testing, ASTM, Philadelphia PA, 1981, pp. 3–33. K.R. Trethewey, D.A. Sargeant, D.J. Marsh, S. Haines, New methods of quantitative analysis of localized corrosion using scanning electrochemical probes, in: K.R. Trethewey, P.R. Roberge (Eds.), Modeling Aqueous Corrosion, Kluwer Academic, Dordrecht, The Netherlands, 1994, pp. 417–426. K.R. Trethewey, D.A. Sargeant, D.J. Marsh, Quantitative measurement of localized corrosion using the scanning reference electrode technique. Paper 317 in Corrosion 94, Baltimore MD, NACE International, Houston, TX, 1994. A.J. Perkins, ‘New developments in on-line corrosion monitoring systems’, Corrosion/93, paper no. 185, NACE, Houston, TX, 1993. ASM Metals Handbook, Corrosion, vol. 13, ASM International, Metals Park, OH, 1987, p. 197. G.C. Moran, P. Labine (Eds.), Corrosion Monitoring in Industrial Plants using Nondestructive Testing and Electrochemical Methods, STP 908, ASTM, 1986. NACE, in: Laboratory Corrosion Testing of Metals for the Process Industries, NACE TM-01-69, NACE, Houston, TX, 1976. NACE, in: Corrosion Basics: An introduction, NACE, Houston, TX, 1984, p. 94. Susan Watkins Borenstein, Microbiologically Influenced Corrosion Handbook, Woodhead, 1994, p. 122. I.I. Vasilenko, V.S. Kropachev. Corrosive Cracking of Stainless Steels (in Russian), Moscow, 1976, p. 174. K.R. Trethewey, J. Chamberlain, Corrosion for Science and Engineering, Longman, 1995, pp. 218– 220. Annual Book of ASTM Standards, Standard Practice G46-76, vol. 3.02, American Society for Testing and Materials, Philadelphia, 1993, p. 197. L.S. Pinchuk, K.Y. Choi, S.V. Bezrukov, Accelerated corrosion tests of inhibited packing materials), Protection of Metals 30 (4) (1994) 434–436 (in Russian). K.Y. Choi, A.Ya. Grigoriev, Hardware and software complex for input, processing and storage of images of engineering objects, Materials, Technologies, Tools 5 (1) (2000) 92–97 (in Russian). A. Rosenfeld, Digital Image Processing, Academic press, NY, 1998, p. 520. C. Connoly, Color Image Processing, UHSE, Huddersfield, 1996, p. 128. J. Tou, Pattern Recognition Principles, Addison-Wesley, MS, 1984, p. 420. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw Hill, NY, 1965, p. 478. I. Jolliffe, Principal Component Analysis, Springer, NY, 1998, p. 537. J. Stevens, Applied Multivariate Statistics for the Behavioral Sciences, third ed., Erlbaum, Mahwah, NJ, 1996. R.D. Hetzel, A primer on factor analysis with comments on patterns of practice and reporting, in: B. Thompson (Ed.), Advances in Social Science Methodology, vol. 4, JAI Press, Greenwich, CT, in press. K.Y. Choi, A.Ya. Grigoriev, N.K. Myshkin, S.A. Chizhik, A Method of visualization of rough surface images similarity/dissimilarity, Metrology and Properties of Engineering Surfaces, Huddersfield, UK, 2000, pp. 302–306. A.Ya. Grigoriev, K.Y. Choi, N.K. Myshkin, Method of comparative analysis of surface textures, Journal of Friction and Wear 21 (2) (2000) 128–133 (in Russian). K.Y. Choi, A.Ya. Grigoriev, N.K. Myshkin, Analysis of tribochemical surface damage by image processing, Tribology Letter 13 (2) (2002) 125–129.
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[36] R. Haralic, L. Shapiro, Survey: image segmentation, Computer Vision, Graphics, Image Proceedings (29) (1989) 100–132. [37] R. Haralic, R. Shanmuganb, I. Dinstein, Texture features for image classification, IEEE Transactions on System, Man and Cybernetics SMC-3 (6) (1989) 610–621. [38] E. Hall, Computer Image Processing and Recognition. NY, 1979, p. 584. [39] I. Chakravarti, I. Roy, Handbook of Methods of Applied Statistics, Wiley, NY, 1967, p. 580. [40] B. Duran, P. Odell, Cluster Analysis, Springer-Verlag, NY, 1974, p. 137. [41] F. Hayes-Roth, F. Waterman, Building Expert Systems, Addison-Wesley, MS, 1983, p. 247. [42] E. Hall, Computer Image Processing and Recognition, Academic Press, NY, 1979, p. 584. [43] W. Togerson, Multidimensional scaling of similarity, Psychometrica 30 (1990) 541–546. [44] F. Yuong, W. Torgerson, TORSA, a Fortran IV program for Sheppard–Kruskal multidimensional scaling analysis, Behavior Science 12 (1967) 498. [45] I. Zagnidze, Experimental Design for Studying Multicomponent Systems, Moscow, 1976, p. 214.
Morphological analysis and classification of types of surface corrosion damage by digital image processing K.Y. Choi
a,*
, S.S. Kim
b,1
a
b
Chemical Department, Belarusian State University, 14, Leningradskaya Street, Minsk 220050, Belarus School of Mechanical Engineering, Kyungpook National University, Daegu 702-701, South Korea Received 16 October 2002; accepted 18 May 2004 Available online 2 July 2004
Abstract This paper examines a new concept of corrosion surface damage analysis by using the digital image processing. Corrosion phenomena are analyzed using a digital value for morphological surface damages instead of electrochemical methods. Initial images are characterized by three categories: color, texture and shape features. To calculate corrosion surface damages color we use the interpretation of HIS model. For the texture attributes, the method of co-occurrence matrix is used. Five types of corrosion damage are examined. Multidimensional scaling procedure is used to define the classification plane. This study suggests a probabilistic method of decision-making. This analysis develops a method for automated identification system of corrosion damages and is supposed to be more advantageous than that of electrochemical techniques. 2004 Elsevier Ltd. All rights reserved. Keywords: Corrosion damage; Morphology; Digital image processing; Classification
1. Introduction Corrosion damage monitoring is an important aspect of a number of industrial technologies related to both serviceability provision and various mechanisms safe *
Corresponding author. Tel.: +375-297-308219; fax: +375-17-226-4696. E-mail addresses: [email protected] (K.Y. Choi), [email protected] (S.S. Kim). 1 Tel.: +82-53-950-5577; fax: +82-53-950-6650.
0010-938X/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2004.05.007
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operation [1–3]. Methods, based on corrosion kinetics estimation by corrosion current, are supposed to be the most widespread to measure corrosion damage in industry. Electric resistance and various modifications of potentiometric techniques are used for these purposes [4,5]. To measure corrosion by electrochemical polarization several methods are available. Using either the Tafel extrapolation or polarization resistance, commercial corrosion monitoring probes have been introduced to the industry [6]. EIS enables a valid measurement of polarization resistance and corrosion rate after correcting ohmic interferences from solution resistance [7,8]. However, it is not always perfect. At the low-frequency end of the spectra where the polarization resistance is measured, corrosion potential and corrosion rate may vary in the middle of the measurement [9]. Intricacy of the problem stems from the specific features of corrosion phenomena, i.e., influences of various factors and great diversity of corrosion types. To quantify galvanic corrosion rate, for example, there are great many controlling factors [10]. Although Evans diagrams, suitably amended to take into account the differences in corrosion areas of metals presence, the extrapolation of laboratory behavior into large-scale engineering situations is extremely difficult to model [11]. Recently, Scanning Reference Electrode Technique (SRET), which applies computer analysis and display of data collection program, has been developed. It allows the precise identification of probe position above the surface of specimen [12]. It has been shown that this technique is powerful in many different applications, such as using a calibration technique by which localized current densities can be measured by mapping corrosion surface damage [13,14]. But it can be applied only for special-purpose corrosion area localization not to the entire corrosionmonitoring system, which can compare and analyze the full corrosion process and phenomena. The NACE (National Association of Corrosion Engineers) has set up a task group (T-3T-3), who prepares a report on various on-line technologies. The report has categorized the on-line monitoring methods into three groups: Group 1 measures, either on a sensing element or directly, the change in physical geometry of noncorroded metal. Group 2 controls either the potential or electrical current density across a metal and conductive fluid interface and measures whichever is not controlled as well. Group 3 measures corrosion byproducts, using hydrogen probes or acoustic emission [15]. And nowadays a variety of techniques for corrosion testing is available in industry for on-site monitoring [16–18]. In short, the current techniques are useful mostly for an integral assessment––i.e., the total mass losses of a metal and the rate of corrosion at laboratorial size––or only in some limited cases in large-scale engineering industry. Different effects of various factors on corrosion process cause different damage types and finally result in different morphological damage. At present the following typology of corrosion damages is generally used by NACE: general or uniform corrosion, localized corrosion (or pitting, crevice corrosion), galvanic corrosion, cracking phenomena (stress corrosion cracking, hydrogen embrittlement), velocity effects (erosion–corrosion, cavitation, fretting), intergranular corrosion, dealloying, high temperature corrosion
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[19,20]. Combined types of damage can also arise when several factors interact, e.g., uniform corrosion with pits [21]. Corrosion damages morphology, surface distribution, shape and depth are strictly dependent on the nature of characteristics in connection with a final concrete operation of corrosion mechanisms. However, given the same corrosion rate and, also, given the same amount of mass loss in metal, localized corrosion or SCC seems to be a more dangerous damage type compared to uniform corrosion owing to more localized failure that brings about catastrophic fracture [22]. Therefore, an adequate estimation of corrosion damages degree requires the study of damages morphology in addition to the corrosion process integral kinetic characteristics. At present, there exists a concrete morphological definition only for pitting made by ASTM Practice G-46. It detects the measurement of pit density, size, depth, and characterization of the cross-sectional shape of pits [23]. Even though this is a useful and strong evaluation tool for pitting corrosion analysis, it has lots of limitations. Among them are difficulties in automatic recognition of pitting changing phases, difficulties in comparing morphological cross-sectional shape of pits, complexity of automatic distinguishing between various corrosion types when pitting arises together with other corrosions like uniform type or intergranular type and, furthermore, difficulties in predicting corrosion rate, etc. Expert visual examination is the most common and simple method of assessing corrosion damages morphology. Among the drawbacks of the method are the necessities to employ qualified staff and to use of subjective criteria for decisionmaking. However, progress in hardware and software made in the last several years allows us to facilitate this approach in a new direction. Methods of digital images processing, classification and analysis are currently in considerable use in various fields of science. Yet, despite the apparent advantages of this approach, it is not used to analyze corrosion processes. The main reason for this lies, in our opinion, in the problem of describing of corrosion damage by morphology, i.e., color, texture and shape. If we are able to analyze and describe, through image processing method to conform qualified state of digital value, all kinds of corrosion morphological damages and their mechanism. Apart from original electrochemical approach it is another powerful tool to evaluate the corrosion process. Also, the combination of digital image processing method with mathematical analysis techniques (Finite Element, Finite Difference, Boundary Element Method, etc.) for corrosion phenomena will enable us to apply the digital image processing method to dynamic corrosion monitoring and simulation system with new idea. The aim of this paper is to develop corrosion damages automated classification method by their optical images. It allows detecting a representative set of morphological attributes of damages and making corresponding classification rules, which enable us to divide the damages into several types. Corrosion damages typology is as follows: uniform corrosion, crevice corrosion, pitting corrosion, fretting corrosion, intergranular corrosion. These types of corrosion damages are selected according to the significance when solving problems of diagnostics in engineering and in
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accordance with the possibility of their use in the analysis of optical methods of surface examination as well.
2. Sampling specimens A sample of 197 images has been selected to solve the problem. Among them 97 images have been used for exercise, the remaining images have served for validating the decision-making rules. The images were obtained from accelerated corrosion tests [24] including scientific papers, textbooks and Internet. The images of the specimens after corrosion tests were taken by an optical microscope [25]. Other images of the objects adopted from publications and Internet were scaled to the size identical to that of the images obtained by microscopy. The magnification range of all images is from 50 to 500. Fig. 1 shows the examples of corrosion damage images used in the paper.
3. Corrosion damage images description Like any other problem of image analysis, the solution of the problem of computer-aided identification and classification of corrosion damage can be split up into several stages. During the first stage a model suitable to describe the morphology of
Fig. 1. Examples of corrosion damage images: (a) non-corroded pure surface of mild steel (100X); (b) uniform corrosion of mild steel (X300); (c) crevice corrosion of stainless steel under barnacles growing in seawater (X200); (d) pitting in stainless steel (X50); (e) Fretted corrosion steel surface (X480); (f) Intergranular SCC of an Inconel heat exchanger tube with the crack following the grain boundaries (X500).
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defects is to be identified. In relation to visually interpretable objects, the morphology comprises the notions of texture, color and shape of the objects under analysis. At present, no integrated theory exists to show how to assign parameters to a visually perceived object [26]. Each specific application has its own approach to the interpretation of images of observed objects which is governed to a substantial degree by morphological formations and their relation to the physical models in this application. Hence, parameters of selection of morphological parameters representative set require, in each specific case, an individual analysis, as well as the methods of their description of attributes computation and optimization. To deal with the quantitative description of such parameters as color, texture and shape of corrosion defects. Color and texture can be formulated as follows: selection of a set of quantitative attributes in accordance with the discrimination between a corroded elementary surface and non-corroded surface portion. Shape characteristic is basically solved from the results obtained from the solution of the two previous parameters. In general it is formulated as a problem of localizing and describing of defects. Algorithmically its solution is derived from the determination of relations between the identified color and texture characteristics of elementary surface portions, the coordinates of the identified regions (corrosion defects) and description of their shape and mutual arrangement. 3.1. Color characteristics of corrosion defects Attributes of color characteristics of corroded objects should be determined in order to identify them quantitatively based on a definite color model. The HSI model is the best suitable model for this purpose since it allows describing color characteristics separately from brightness characteristics. The values H (hue), S (saturation) and I (intensity, brightness) for the R (Red), G (Green) and B (Blue) components were specified as follows: 1 I ¼ ðR þ G þ BÞ 3 3 ½minðR; G; BÞ S ¼1 ðR þ G þ BÞ 1 ½ðR GÞ þ ðR BÞ 2 H ¼ cos1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðR GÞ þ ðR BÞðG BÞ These formulas have been optimized for the computer format of data interpretation. Hence, registration of a signal in the RGB computer format allows transforming it into the HSI color space [27]. A test sample of objects has been grouped in order to choose the color parameters and to investigate the space of attributes they produce. Each object has been the image of a surface portion obtained for corrosion damage. The surface portions 10 · 10 pixels were selected for analysis. We can take the separation of primary attributes of objects on the base of strong correlation between original attributes for
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their identification [28]. The original set of attributes is transformed into a secondary set, and optimized by the classic statistical approach. The purpose of these transformations is to discriminate between the correlating and non-correlating portions of the set of attributes. The method of moments has been employed to calculate the second set of attributes [29]. For this purpose the final H and S values for each element of the image are represented as histograms of distribution of their values. It is known that one method of describing the distribution of random values is to use their moments of the nth order. If hðxÞ is a histogram, the moment of the nth order xi against its mean value is calculated as X ðxi xÞn pðxi Þ; n > 1 ð1Þ ln ¼ i
where pðxi Þ is the probability of incidence of the ith value of the attribute x. The set of the secondary attributes includes the moments up to the 4th order: X 2 ðxi xÞ pðxi Þ; x ¼ fH ; S; Ig ð2Þ l2 ¼ i
l3 ¼
X
3
ðxi xÞ pðxi Þ;
x ¼ fH ; S; Ig
ð3Þ
ðxi xÞ4 pðxi Þ;
x ¼ fH ; S; Ig
ð4Þ
i
l4 ¼
X i
Additionally the distributed mean, median and geometrical median original attributes have been included into the set 1X x ¼ xi ; x ¼ fH ; Sg ð5Þ n i xm ¼ xi ;
i
i X j¼0
xg ¼
Y 1 ; xni i
xj ¼
n X
xj ;
x ¼ fH ; Sg
ð6Þ
j¼i
x ¼ fH ; Sg
ð7Þ
Attributes (5)–(7) have been calculated for the value of the brightness component ðIÞ of the HSI color field in order to avoid problems induced by the irregularity and inconstancy of the parameters of illumination when registering images. The method of main components has been applied to optimize the set of attributes and to eliminate insignificant attributes [30]. Full-factor space, which has over 50% of the dispersion of the attributes, can be minimized to two factors. Varimax focuses on cleaning up the factors for this purpose. Varimax method for the rotation of the space of attributes has been used to calculate the significance of the attributes. Varimax rotation produces factors that have high correlations with one smaller set of variables and little or no correlation with another set of variables [31,32]. Fig. 2 shows the graph of significance of the attributes by Varimax.
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7
1 0.8 0.6
2 4
9
8
Factor 2
0.4 6
0.2
5 10
3
0
14 1
13
-0.2
11 7 15
-0.4
12
-0.6 -0.8 -1 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Factor 1
Fig. 2. Factorial loads. Figures designate attributes: (1, 2) mean values; (3, 4) median values; (5, 6) geometrical mean values of H and S; (7, 8, 9) dispersion; (10, 11, 12) asymmetry and (13, 14, 15) excess of distribution of H , S and I values.
The circumference on the graph shows the boundary of the significance region corresponding to 0.75. The maximum variability of attributes is observed along the axis of factor 1. This behavior of the data is commonly interpreted as linear discriminability of objects classes. A threshold of 0.75 has been used to rank the values of attributes and to select five most significant secondary attributes. Consequently, the set of secondary attributes reflecting corrosion damage color characteristics can be reduced from 15 to 5 elements (2, 4, 1, 15, 14). This set has the following parameters: mean H value; mean S value; median S value; skews S distribution; skews I distribution. 3.2. Texture and shape characteristics of corrosion defects Corrosion process produces a certain texture or a typical rough surface structure on the metal. This surface texture features are distinct for various types of corrosion damage. It is important to obtain a quantitative system of rating reflecting the visual perception of various textures of the objects under analysis. With this consideration in mind the texture analysis should be performed by the brightness parameters of rough surface images relating to the visual perception characteristics rather than to the sizes of projections. To describe the texture features of corrosion damage we use the method disclosed in [33–35]. According to this method, the term ‘‘texture’’ implies the result of three-dimensional relations between brightness degrees in the rough surface image [36]. The characteristics of these relations are represented by co-occurrence matrix: M ¼ ka; qk
ð8Þ
Each element of the matrix (8) is equal to the number of pairs of texture elements with the azimuth difference a and the spacing q between them (Fig. 3). The routine of calculating the matrix of mutual incidence comprises several steps. First, the azimuth angle a of each element of the digital image is calculated. Then the
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Fig. 3. Diagram of description of corrosion damage texture.
difference between the coordinates of texture elements is calculated in pairs. To reduce calculation time and to save resources the range of possible a values is quantified into 10 levels. The spacing q is calculated in pixels. The maximum spacing of 10 has been selected to make the texture elements discernible. Hence, calculations are made in the sliding window 11 11. Co-occurrence matrix elements values are determined by calculating the numbers of pairs with relevant combinations of the a and q values Mði; jÞ ¼ #pði; jÞ
ð9Þ
The routine is competed by matrix normalization: Mði; jÞ mði; jÞ ¼ P i;j Mði; jÞ
ð10Þ
Images texture properties are characterized by the following set of attributes [37]: X X lx ¼ i mði; jÞ ly ¼ r2x ¼
i
j
j
i
X X j mði; jÞ X
ði lx Þ
2
i
r2y ¼
X
X
ði ly Þ2
X
j
I¼
mði; jÞ
i
XX i
mði; jÞ
j
j
2
ði jÞ mði; jÞ
ð11Þ
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The set comprising (11) attribute of flat object shape recommended in [38] is used to describe corrosion damage morphology. The set includes the following characteristics: area, perimeter, length, shape factor, dimension of the maximum axis, dimension of the minimal axis, ratio between the axes, the mean radius, the maximum radius, the minimal radius, the ratio between the radiuses.
4. Classification of corrosion damage 4.1. Model of the space of attributes To classify the descriptions of color, objects texture and morphology are represented as an ordered sequence of numerical values. In relation to our specific case, to identify image surface corrosion damage, the image under analysis is represented by a vector of 18 elements (5 color, 2 texture and 11 morphological shape attributes): Fs ¼ ½f1 ; f2 ; . . . ; f18
ð12Þ
Prior to the analysis the vector of the attributes of all the objects in the test sample is integrated into a single table and normalized. To check if the parameters meet the criterion of non-homogeneity r2 > 0 [39], integrity parameters are analyzed. If this condition is satisfied, object attributes description parameters can be treated as the coordinates of some n-dimensional space. Resting on this approach, the object under analysis can be represented by a point on the n-dimensional space. The closer the distance between the attributes (point) of an object on the space are, the more is the similarity of the objects. On the same token, the farther the distances between the attributes are, the less alike they are in terms of the attributes. In accordance with this, clusters are formed on the space of attributes. The task of classification is to determine the ranges of the clusters corresponding to various objects and to set the rules being the functions of the attributes, which are used to divide the objects into classes. The function of calculating the measure of distance in some abstract space should satisfy the following four axioms [40]: (1) (2) (3) (4)
Identity: qðF1 ; F2 Þ ¼ 0jF1 ¼ F2 . Symmetry: qðF1 ; F2 Þ ¼ qðF2 ; F1 Þ. Positiveness: qðF1 ; F2 Þ P 0. Triangular inequality: qðF1 ; F3 Þ 6 qðF1 ; F2 Þ þ qðF2 ; F3 Þ.
The function satisfying these conditions is termed a metric space. It allows us to use the attributes with different physical sense or content. For example, one dimension can characterize color, another dimension––size, still another can present the characteristics of the environment at the moment the object is being analyzed. It is possible, because the location of a point as some mathematical abstraction has its own attribute; meanwhile the distance is meaningful only as its difference from another point.
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There is one more essential factor relating to the features of the metrical space. It has been demonstrated [41] that linear transformations of the space coordinates in no way alter the topological structure of arbitrarily arranged points within it. In particular, it is impossible to alter the mutual arrangement of objects in the space using affined transformations of the type xi ¼ a0i þ a1i f1 þ þ ani fn
ð13Þ
where 1 6 i < n, ani is the matrix of transformation coefficients specifying the operations of displacement, rotation, scale or shear alterations. This conclusion has an essential practical significance in the problems of classification, since no transformation is capable to alter the discriminability of classes. In order to avoid this problem, the metric of Minkovskii method is the most suitable. This metric space is specified in the following form with Euclidean measure [42]: " #1=2 d X 2 qE ðk; mÞ ¼ ðfik fim Þ ð14Þ i¼1
This measure is the most frequently used for the problems of classification, primarily because it gives the values intuitively understandable and easy to interpret. Hence, a multidimensional space of attributes has been selected as a model to formalize the presentation of corrosion damage image data. 4.2. Clustering in the space of attributes At present the multidimensional scaling for clustering is the most common approach in visualizing the multidimensional data [43]. Shepard–Kruskal method of projecting and minimizing discrepancies is used for this purpose [44]. This method is effective in determining the projection coordinates by solving the equations, which are describing the mutual arrangement of points on the plane. The discrepancy function has been calculated as: w¼
n1 X n X
ðoÞ
ðqkl qkl Þ
2
ð15Þ
k¼1 l¼kþ1 ðoÞ
where qkl , qkl are the distances between the points in the original multidimensional space and on the projection plane, respectively. In order to obtain the solution the discrepancy w is specified as 10% of the original sum of distances between objects. Fig. 4 presents the results of multidimensional scaling of objects of the exercise sample corresponding to the objects affected and unaffected by corrosion and the clustering of various types of corrosion defects. This graph corresponds to the division of the regions under analysis into two classes, i.e., those affected and those unaffected by corrosion. Presented data analysis allows the following conclusion: six clusters can be identified on the classification plane, which is conventionally divided into two parts. Region ‘‘A’’ has the cluster corresponding to the specimens unaffected by corrosion. The region ‘‘B’’ has the groups with different types of corrosion damage.
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Fig. 4. Multidimensional scaling results: division of objects into two classes damaged or undamaged by corrosion (Papvepyocnm D1 ¼ Dimension D1, Papvepyocnm D2 ¼ Dimension D2).
4.3. Classification of corrosion defects In order to obtain the functional relationship between objects coordinates on the classification plane and their coordinates (attributes) in the original multidimensional space, linear regression model has been selected: X Dj ¼ a0 þ ai Fi ; fj ¼ 1; 2g ð16Þ i
where a0 ; a are the required coefficients of the model, Fi is the ith attribute of the objects in the exercise sample. In general, the boundaries between two arbitrary classes can be determined in the following way: D2 ¼ b0 þ b1 D1
ð17Þ
where b0 , b1 are the coefficients of linear interpolation. This line divides the classification plane into two semi-spaces, and validates the following condition: 1jd < D12 c¼ ð18Þ 2jd > D12 where D12 is the coordinates of the interclass boundary, and d is the coordinates of the analyzed object. This approach can be expanded to cover the case of n linearly distinguishable classes: c ¼ ijDi1;i < d < Di;iþ1 ;
i ¼ 1; . . . n;
D0;i ¼ 1;
Dn;nþ1 ¼ þ1
ð19Þ
The lines of the relevant boundaries of the classes and clusterization of corrosion damage by calculation of the space of attributes are shown in Fig. 5. This graph is shown to classify the clusters according to the corrosion damage types within a class and reflects a detailed analysis of the region B shown in Fig. 4.
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Fig. 5. (a) Boundaries of corrosion damage classes: ab, crevice corrosion and all other corrosion damage classes; cd, uniform corrosion/fretting; ce, fretting/pitting; fg, pitting/intergranular. (b) Clusterization of corrosion damaged objects according to types: 1, crevice corrosion; 2, intergranular; 3, pitting; 4, fretting; 5, uniform corrosion.
4.4. Evaluation of the probability and accuracy of classification results In order to achieve the probabilistic classification, objects distribution density within clusters is calculated. Corrosion damage tested sample coordinates serve as parameters. For this purpose the histograms of distributions are approximated along the curves of normal distribution. To facilitate the problem a map of classes has been calculated as a matrix with each element corresponding to a certain region of the classification plane, the value of the element is the probability of matching the class. Fig. 6 shows the map of classes for the problem in question. A test sample of 100 images serves to evaluate the accuracy of classification of corrosion defects using the above-mentioned methods. Tests results are summarized in Table 1. The sum of the elements in each line is equal to the number of particles of a relevant class analyzed in the test. In other words, the values in ði; jÞth cells of the table at i 6¼ j are equal to the number of particles classified erroneously.
0.6
6
0.4 0.2
5
0
4 1
-0.2 -0.4
3
-0.6
2
-0.8
-1
-0.5
0
0.5
1
1.5
Fig. 6. Bidimensional map of probabilities of corrosion damage classification: 1, non-corroded specimen; 2, crevice corrosion; 3, intergranular; 4, pitting; 5, fretting; 6, uniform corrosion.
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Table 1 Results of testing of method 1
2
17 2
3 13 2
1 2 3 4 5 6
3 1 13 1
4
5
1 12 3
3 13
6
1 15
Legend: 1, non-corroded specimen; 2, crevice corrosion; 3, intergranular corrosion; 4, pitting; 5, fretting corrosion; 6, uniform corrosion.
All test images have been verified by experts. The degree of agreement between the experts’ views is rated resting upon the method of consensus [45]. The obtained consensus factor equals 0.91. We can conclude that the experts’ views did not differ significantly. The presented data prove that the objects have been classified quite accurately (85%). Hence, the accuracy of the new method of classification is actually the maximum achievable for the class of objects in question.
5. Conclusions Morphological attributes analysis resulted in the formulation and validation of the optimum set of attributes. It will allow us to perform the probabilistic identification of surface corrosion damages using their images. Applicability of pattern recognition theory for automated classification of surface corrosion damage has been developed. Our results have shown, that apart from electrochemical method, corrosion can be evaluated by digital image processing in morphology: color, texture, and shape. Machine vision methods are applied to the analysis of corrosion surface damage for the first time. The analysis of corrosion damage by digital image processing is an important step in the promising direction in corrosion diagnostics.
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