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Application of gradient-based Hough transform to the detection of corrosion pits in optical images
Applied Surface Science 366 (2016) 9–18
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Application of gradient-based Hough transform to the detection of corrosion pits in optical images Yafei Wang, Guangxu Cheng ∗ School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
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Article history: Received 17 October 2015 Received in revised form 10 December 2015 Accepted 27 December 2015 Available online 30 December 2015 Keywords: Pitting corrosion Image recognition Hough transform Statistics
a b s t r a c t In this paper, we introduce a circle detection technique named Hough transform to automatically recognize the corrosion pits in microscopic images. All the points in the input image are transformed into a parameter space, which is represented by a two-dimensional accumulative array with the same size of the original image. Local extreme values in the accumulative array, which represent the candidates of corrosion pits, are located using a maxima searching algorithm. The accuracy of detecting the number, radius and coordinate of pits from simulated images was examined. The results show that more than 95% of pits were successfully detected and the average errors of radius and coordinate are less than 10%, while these errors have negligible effect on the pit size distribution. The introduced method can also differentiate pits from scratches or inclusions, as indicated by the 100% accuracy of pit detection, from the simulated images presented in this study. Therefore, it is believed that the gradient-based Hough transform is a powerful method for the recognition of corrosion pits in microscopic images, making the statistical analysis of pit size and pit locations easier and more efficient. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Despite the intensive research studies of the past decades, the pitting corrosion is not yet fully understood. A large number of pits are usually formed on the steel surface and analysis of a single pit cannot sufficiently contribute to the understanding of the stochastic nature of pitting formations. Therefore, the use of statistical analysis is a necessary step towards the quantitative evaluation of pitting corrosion [1]. However, measuring all pits by employing manual methods can be tedious and time consuming. The difficulty in obtaining the detailed information of corrosion pits (number, sizes, and pit locations) in corrosion images impedes the quantitative evaluation of pitting corrosion. In this paper, an image recognition technique is introduced, which provides an excellent solution in defining this information. Several image processing techniques have previously been applied for the analysis of corrosion images. Those image analysis methods may be used for the classification of the various corrosion types [2–4], approximation of the corrosion rate or weight loss [5,6], coatings and rust assessment [7,8], non-destructive corrosion inspection [9–11], evaluation of pit shape and size [12,13], fractal analysis of corroded surfaces [14,15] or enhancement of corrosion
∗ Corresponding author. Tel./fax: +86 29 83234781. E-mail address: [email protected] (G. Cheng). http://dx.doi.org/10.1016/j.apsusc.2015.12.207 0169-4332/© 2016 Elsevier B.V. All rights reserved.
images [16]. However, the quantitative definition of pit sizes and pit locations, using image recognition technique, has not been widely discussed. The pit depth can be evaluated by using a 3-D measuring technique and Codaro [13] has discussed about the statistical analysis of pit depth measurements, using an image processing method. A 3-D microscope is powerful in depth measurement techniques and 3-D representation of a relatively small number of pits. However, although the 3-D data of all the pits within an image can be simultaneously obtained using confocal laser scanning microscope (CLSM), a user still has to determine the diameter and depth of each pit manually, which, for an image with a relatively large number of pits, measuring the pits manually will take a significant amount of time. In statistical analysis, a large number of pits is usually necessary to guarantee the reliability of the calculations. Also, the spatial point pattern of corrosion pits is also an important issue in the understanding of the nature of pitting corrosion. However, the coordinates of the pit centers cannot be provided by a 3-D microscope or conventional image analysis techniques. In the work of Jarrah [17], a new statistical methodology was proposed, for detecting the pits interactions with each other, based on a two-dimensional spectral analysis, but the method was only validated based on the simulated pits, due to the lack of the experimental coordinates of the pits. The image recognition technique, which is proposed in this paper, can precisely detect the coordinates of a large number of pits. It is believed that the automatic
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recognition of pit locations can assist on resolving the issues, related with the statistical analysis of pitting corrosion in a twodimensional dimensional spectral analysis. In our previous work, regular pits with near-circular shapes were observed in an X80 grade steel, when was tested for its corrosion behavior in NaCl solutions [18]. The observed pit shapes were found to be consistent with the results of stainless steel in a droplet of chloride solution [19] and the Ni-Cr-Mo steel in NaCl solutions under different hydrostatic pressure values [20]. Similar morphologies for pit shapes were also reported in an aluminum alloy [21,22], Zr-based bulk metallic glass [23] and hydrogen-etched graphite [24]. For near-circular pit shapes, the detection of the pit locations becomes a task of circles detection, a widely studied topic in the field of image recognition. A variety of circle detection algorithms have been proposed since the 1990’s [25–27], while there is still an ongoing interest in this area ultil the recent years [28,29]. The circle detection technique has been extensively studied for several applications, such as the soccer game, face recognition or human eye location, while the requirements and issues with the algorithms needed for the different applications may differentiate. For example, in soccer ball detection applications, one of the most challenging issues that need to be overcome is the real-time processing [30], which is however not an issue for the corrosion pit detection applications. In the present paper, a gradient-based Hough transform method is introduced for the detection of corrosion pits in microscopic images. The main difficulties of circle detection for the corrosion images were addressed. The accuracy of the proposed method was evaluated by using simulated images with pre-defined pit parameters and the results of pit detection were demonstrated in optical microscope images.
2.2. Hough transform Hough [31] proposed an interesting and computationally efficient procedure (Hough transform, HT) for detecting lines in images, which has become the theoretical foundation of most algorithms that were developed in the past decades for detecting different shapes (line, circle, rectangle, etc.) in images. Ito [32] used the circular Hough transform to identify the eyes in facial images, Barinova [33] used the Hough transform to detect multiple object instances, D’Orazio [30] used the circle Hough transform for the ball recognition, Marquez [34] applied the Hough transform in the cloud tracking, while Khalil [35] studied the droplet size distribution. Many previous studies have been focused on improving the accuracy and efficiency of Hough’s proposed method, proposing a number of algorithms, which, as on overall, can be referred to as the HT-based methods. The key concept of the HT is to detect the parameterized curves in images by mapping the edge pixels into the manifolds in the parameter space, and the methods that will define the peaks in the parameter space can also be used to detect the image curves [36]. As presented in Fig. 1, the equation of a line in a k-y plane is Eq. (1), and every line in the k-y plane corresponds to a unique point in the − plane, hence: x cos + y sin = (1)
2. Material and methods 2.1. Pitting morphology A high-strength, X80 pipeline steel was used for the experimental procedure. Each specimen was ground gradually with 400–1200-grit waterproof abrasive paper and cleaned with distilled water and acetone. Then the specimens were immersed in a 3.5 wt% NaCl solution for 1 h. The pitting morphology was observed using a confocal laser scanning microscope (LEXT OLS4000).
Fig. 1. The normal parameters for a line.
Table 1 Parameters of the simulated pit diameters. Number
20 3.0 0.4
40 3.0 0.4
60 2.6 0.3
70 2.4 0.3
80 2.2 0.3
Fig. 2. Flowchart of the pit recognition process.
(1)
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Fig. 3. Illustration of the determination of circle center: (a) original image, (b) accumulation array after the voting by two gradient vectors, (c) the 3-D colormap of the accumulation array and (d) the signature curve.
Regarding the identification of a circle, if a circle in the picture plane is described as 2
(x − a)2 + (y − b) = c 2
(2)
Then, an arbitrary point (xi ,yi ) in the picture plane will be transformed into a circular cone in the (a,b,c) parameter space. The cones corresponding to all the figure points in a circle will intersect at a single point (a,b,c), and this circle can be defined by those three parameters. A multi-dimensional array of accumulators is used to represent the three-parameter space, in order to make the detection process more efficient than the analytical transformation does [36]. The main drawbacks of the HT are the large software memory size required and the essential time consuming computations. However, this is not a big concern for the detection of corrosion pits, since it does not need to be real-time. For the analysis of a microscopic image of 1024 × 1024 pixels, a computer with a minimum memory of 2 GB would be needed to run the HT program. In this paper, the Matlab 2014b software was employed, in a computer with a memory of 32 GB. 2.3. Accuracy verification The accuracy of the introduced algorithm in the simulated images is verified with pre-defined pit parameters. In the simulated images, both the horizontal and vertical coordinates of the pits
are random numbers. The spatial randomization of the simulated pit coordinates was confirmed with the assistance of the spatstat package software, programmed in the R language [37]. Five groups of different pit diameters were simulated and the data were generated utilizing the “lognrand” function in Matlab software, which creates random numbers that follow the lognormal distribution. The parameters of the pit diameters are shown in Table 1. Each group is repeated three times. 3. Results and discussion There are several public HT-based algorithms for circles detection, among which the Peng’s algorithm [38] has excellent performance in the recognition of pits from optical images. There is a wide variety of other advanced algorithms that could serve the same purpose, HT-based or non-HT-based, which were published in the area of image processing, most of which are not available online. Those who are interested in applying these methods to their own study may have to acquire good knowledge of image recognition and program writing. For the circles detection in corrosion images there are three main issues that have to be managed, i.e., the large number, the wide radius range and the high background noise. For a relatively low magnification image, one hundred or more pits were able to be observed. The pit diameter can range anywhere between several micrometers to several hundred micrometers. Also, there are
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Fig. 5. (a) 2D and (b) 3D colormap of the accumulation array.
Fig. 4. (a) A simulated image with determined number and diameters; (b) recognized pits in the simulated image.
usually many scratches, or other irregular inclusions or defects, on the surface of the steel, which have to be differentiated from the pits. However, the gradient-based HT method is proved to be powerful in handling these difficulties. The recognition process of the pits in an optical image, using the gradient-based HT, includes several steps, as shown in Fig. 2. The microscopic image, with a size of 1024 × 2014 pixels, was imported and converted to a grayscale image. Prior to initiating the main function, a filter is usually necessary to be applied to the image for de-noising, which will significantly improve the accuracy of the recognition. Then the HT is implemented in the way described by Eq. (3), where, “accum”, is the result accumulation array from the circular Hough transform (CHT), which has the same dimensions as the input image, “circen”, are the coordinates of the center of pits detected, “cirrad”, is the radii of the pits detected, “img”, is the input image file, Rmin and Rmax , are the possible minimum and maximum
radii of pits to be searched, g, is the gradient magnitude threshold, which is performed before the voting process of the circular HT, in order to remove the ‘uniform intensity’ of the image background from the voting process, Rf , is the radius of the filter used in the search of local maxima in the accumulation array and m, is the tolerance factor of multiple pits detected at the same coordinate. [accum, circen, cirrad] = CircularHough Grd(img, [Rmin Rmax ], g, Rf , m)
(3)
The CHT consists of three steps, i.e. to compute the gradient field of the input image, to transform the gradient field to an accumulation array and, finally, to find the peaks in the accumulation array. The gradient-based method was firstly proposed by Illingworth [39] and was later modified by Peng [40] and was used to detect circular patterns. The values of all points in a grayscale image fluctuate within the range of 0 and 1 (black to white), which are defined as the image intensities. The gradient field of image intensity can be calculated using the Eq. (4), where, (i,j), are the pixel indices, I(i,j), is the image intensity for a specific pixel, with (i,j) indices, and ∇ I (i, j), is the gradient vector at pixel with (i,j) indices.
∇ I (i, j) = Vx , Vy |(i,j) = (I (i, j) − I (i, j − 1) , (i, j) − I (i − 1, j) , ) (4)
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Fig. 7. Accuracy of the recognition of the number of pits.
defined by the vector ∇ I (i, j). The accumulation array is constructed by collecting the votes from all nonzero gradient vectors. Therefore, the maximum intensity in the accumulation array represents the center of a pit, as shown in Fig. 3c. For the determination of circle radius, a signature curve is defined by the Eq. (5), where, r, is the distance to the circle center, ∇ (i, j) is the gradient vector, q (i, j) is the radial vector from the circle center (ic , jc ) to the pixel (i, j), f (r) is averaged dot product of the gradient vector and the radial vector. The summation is over all the (i, j) picels that satisfy the conditions of Eq. (6), where, r, is the interval between adjacent r values.
∇ (i,j)·q(i,j)
q(i,j)
(i,j)
f (r) =
(i,j)
Fig. 6. Deviation between the recognized radii and the actual values.
This algorithm capitalizes the feature of the nonzero gradient vectors, which, in the gradient, they are either pointing toward or away from the center of a circle. A voting process is utilized in order to transform the gradient field into an accumulation array, as shown in Fig. 3a and b. A weight value (marked in gray in Fig. 3b) is added to the pixels in the accumulation array, which lies on the line segment,
| q (i, j) − r| <
1
r 2
(5)
(6)
For a solid circle, as shown in Fig. 3a, the estimated radius is defined as the coordinate of the extreme, of the signature curve, as shown in Fig. 3d. The signature curve of a hollow circle is more complicated to define, and the readers may refer to reference [40], for further information.
Fig. 8. Error of the radii and coordinates of detected pits, with symbols representing the average values and error bars the standard deviation. Rtrue and Rrecog represent the real radius and recognized radius, respectively; Er shows the error of radius. Ctrue and Crecog represent the coordinates of the real pit center and recognized pit center, respectively; Ec shows the error of the coordinates.
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Fig. 9. Comparison of the probability distributions of the simulated and recognized radii.
3.1. Recognition accuracy The recognition results, which were taken from an example image with 70 pits, are presented in Figs. 4, 5 and 6. The radii of pits follow the lognormal distribution, with a location parameter of 2.4 and a scaling parameter of 0.3. The simulated image and the corresponding pits, recognized using the HT method, are presented in Fig. 4a and b, respectively. It is clear that the radii and coordinates of all pits can be successfully detected. The accumulation arrays in two-dimensions and three-dimensions are presented in Fig. 5a and b, respectively. Each local maximum value in the accumulation array corresponds to a circle candidate. A maximum searching algorithm selects the real circle from the potential candidates, based on some pre-defined criteria. Fig. 6 shows the deviation of the recognized radii from the true values, of the image presented in Fig. 4a. It can be seen that the recognition error for the pit radius is less than 11%. The results of the repeated tests are presented in Figs. 7 and 8. As presented in Fig. 7, the detection accuracy of the number of the pits is higher than 95%. Fig. 8 shows the error deviations of the radii and coordinates. The average error value of the radii is approximately 5%, with a standard deviation smaller than 5. The error of coordinates is defined as the distance between the detected center and the real center, divided by the real radius. The average error of coordinates is less than 10%, with a standard deviation smaller than 4. Furthermore, the detection accuracy is not affected by the increase of the number of pits. The difference between the real distribution and the recognized distribution of the radii is presented in Fig. 9. Both the probability density function and the cumulative distribution function of the recognized circles fit well with the actual ones. The highest pit radius (∼50 pixels) is approximately 10 times of that of the lowest pit radius (about 5 pixels), therefore, this method can be considered as being non-dependent on the radius range, making it suitable for the detection of corrosion pits in optical images.
Fig. 10. (a) A simulated image with irregular shapes, with the error of detected radii shown in (b) and (c).
3.2. Effect of irregular shapes In actual optical images, there are usually irregular shapes, such as scratches, inclusions or precipitates. In order to detect the pits accurately in such images, the algorithm should be able to differentiate between the real pits and the irregular shapes. An image with simulated scratches and inclusions is presented in Fig. 10a and the recognition error is shown in Fig. 10b and c. It is clear that the recognition accuracy is not affected by irregular shapes
additions, implying that the suggested method has a strong ability of differentiating pits from scratches and irregular inclusions. 3.3. Recognition of real pits The results of the pits recognition procedure of an actual pit image are presented in Fig. 11. It is demonstrated that all the pits were successfully recognized. The radii and coordinates were
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Fig. 11. Recognition results for a real image: (a) An optical image of corrosion pits, (b) recognized pits, the accumulation array of CHT in (c) two dimensions and (d) three dimensions, (e) overlapped pits, and (f) fitted distributions for the manually measured pits and the recognized pits.
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Fig. 12. Transformation of the corroded area into an equivalent circle.
Equivalent circles
Fig. 13. Recognition of the irregular pits.
written into a two-dimensional array, which provides detailed information (number, diameter and location) of the corrosion pits. The accumulation array of CHT is presented in Fig. 11b and c. As previously discussed, each pit in the original image corresponds to one local extreme value in the accumulation array. And each local extreme value represents a candidate of a recognized pit. A final step of the recognition procedure is a maximum searching process which will determine the real pits among the pit candidates. Even pits with a very low diameter or overlapped pits can be accurately recognized, as demonstrated in Fig. 11e. The actual pit diameters were measured manually, using software for editing photographic images, and the total number of the pits was determined as 50. The HT recognized 47 pits from the image, which gives an accuracy of the recognition procedure of is 94% (47 out of 50). The matching among the lognormal distributions of the manually measured pits and the recognized pits are presented in Fig. 11f, where it can be observed that the recognized data are very accurate in the evaluation of the pit size distribution. The minimum pit diameters that can be detected through HT depend on the magnification of the microscopic image. Generally, pits with a diameter of as small as 5 pixels, within an image with a 1024 × 1024 pixels
image, can be successfully detected. If the pit size is much smaller than this minimum value, it would be necessary to use a larger magnification. This method can detect a large number of pits, at a wide radius range and with high background noises. A wide radius range option important as the pit sizes usually vary in a very wide range (in this case between 10 m and 200 m). The use of algorithms that cannot detect such a wide radius range will lead to a high missdetection rate and low accuracy. The miss-detection of pits is usually attributed to the presence of scratches, defects and overlapped pits in the input image. This issue can be overcome by increasing the contrast between the unrecognized pits and the background, by darkening them manually with a photograph editing software. In this way, the accuracy of this algorithm can be significantly improved. The use of image recognition techniques for pit detection greatly benefits the statistical analysis of corrosion pits, since it can significantly reduce the difficulty of measuring the number, sizes and locations of the pits. Also, the analysis of pit size distribution and the spatial point pattern of pitting corrosion images become very efficient.
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3.4. Other remarks It should be noted that the detected radii must be an integer number (in the unit of pixel), which increases the error of the recognition technique. This limitation may be overcome by making modifications to the original algorithms. The readers that are interested in improving this program in this way might need to change the definition of the signature curve. The algorithm that is presented in the present study is also capable of finding regular circles in other image types, such as cells, hollow spheres or fruits, but is limited in finding regular circles instead of ellipses. For elliptical shapes with high eccentricity, the detection results will be two regular circles centered at the two focus points, respectively. 3.5. Recognition of pits with irregular shapes Both circular and irregular pit shapes can be observed in the actual experiments. Therefore, a simple method, which is based on the concept of equivalent circles, is proposed, in order to recognize the irregular pits in images, as presented in Fig. 12. A corrosion pit with an irregular shape can be converted into an equivalent circle, with the same area of the corroded zone. The coordinates of the center of the circle will be the average values of all the points in the corroded zone. So, both the radius and coordinate can be determined. Therefore, the recognition of the irregular pits can be completed in several steps. First, the image is imported and converted into a grayscale image. Then, the corroded zones are located in the image by setting a threshold value above which the determined points will be considered as corroded. Following that, those corroded zones are separated from each other by finding the adjacent points (comparing the coordinates to each other). Finally, the radius and coordinate of each separated zone are determined by counting the number of points in each zone and building the equivalent circle. The recognition process of pits with irregular shapes is illustrated in Fig. 13. 4. Conclusions The gradient-based Hough transform is introduced to recognize the corrosion pits in microscopic images. The results show that this method is powerful in detecting a large number of pits with a wide radius range and high background noises. Therefore, it is proved to be an excellent tool in the automatic recognition of the diameter and locations of corrosion pits in digital images, which can significantly increase the efficiency of quantitative evaluation of pitting corrosion samples. Statistical analysis of the size and location distribution also becomes simplified, based on the suggested pit detection technique. Acknowledgments The authors would like to gratefully acknowledge the financial support from the National Basic Research Program of China (973 Program, Grant No.2015CB057602). We would also like to thank Mr. Liheng Bian in Tsinghua University for his advice on the circle finding algorithms. References [1] ASTM Standard G46-94, Standard Guide for Examination and Evaluation of Pitting Corrosion, 2005. [2] A.M. Zimer, E.C. Rios, P.D.C.D. Mendes, W.N. Gonc¸alves, O.M. Bruno, E.C. Pereira, L.H. Mascaro, Investigation of AISI 1040 steel corrosion in H2 S solution containing chloride ions by digital image processing coupled with electrochemical techniques, Corros. Sci. 53 (2011) 3193–3201.
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Application of gradient-based Hough transform to the detection of corrosion pits in optical images Yafei Wang, Guangxu Cheng ∗ School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 17 October 2015 Received in revised form 10 December 2015 Accepted 27 December 2015 Available online 30 December 2015 Keywords: Pitting corrosion Image recognition Hough transform Statistics
a b s t r a c t In this paper, we introduce a circle detection technique named Hough transform to automatically recognize the corrosion pits in microscopic images. All the points in the input image are transformed into a parameter space, which is represented by a two-dimensional accumulative array with the same size of the original image. Local extreme values in the accumulative array, which represent the candidates of corrosion pits, are located using a maxima searching algorithm. The accuracy of detecting the number, radius and coordinate of pits from simulated images was examined. The results show that more than 95% of pits were successfully detected and the average errors of radius and coordinate are less than 10%, while these errors have negligible effect on the pit size distribution. The introduced method can also differentiate pits from scratches or inclusions, as indicated by the 100% accuracy of pit detection, from the simulated images presented in this study. Therefore, it is believed that the gradient-based Hough transform is a powerful method for the recognition of corrosion pits in microscopic images, making the statistical analysis of pit size and pit locations easier and more efficient. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Despite the intensive research studies of the past decades, the pitting corrosion is not yet fully understood. A large number of pits are usually formed on the steel surface and analysis of a single pit cannot sufficiently contribute to the understanding of the stochastic nature of pitting formations. Therefore, the use of statistical analysis is a necessary step towards the quantitative evaluation of pitting corrosion [1]. However, measuring all pits by employing manual methods can be tedious and time consuming. The difficulty in obtaining the detailed information of corrosion pits (number, sizes, and pit locations) in corrosion images impedes the quantitative evaluation of pitting corrosion. In this paper, an image recognition technique is introduced, which provides an excellent solution in defining this information. Several image processing techniques have previously been applied for the analysis of corrosion images. Those image analysis methods may be used for the classification of the various corrosion types [2–4], approximation of the corrosion rate or weight loss [5,6], coatings and rust assessment [7,8], non-destructive corrosion inspection [9–11], evaluation of pit shape and size [12,13], fractal analysis of corroded surfaces [14,15] or enhancement of corrosion
∗ Corresponding author. Tel./fax: +86 29 83234781. E-mail address: [email protected] (G. Cheng). http://dx.doi.org/10.1016/j.apsusc.2015.12.207 0169-4332/© 2016 Elsevier B.V. All rights reserved.
images [16]. However, the quantitative definition of pit sizes and pit locations, using image recognition technique, has not been widely discussed. The pit depth can be evaluated by using a 3-D measuring technique and Codaro [13] has discussed about the statistical analysis of pit depth measurements, using an image processing method. A 3-D microscope is powerful in depth measurement techniques and 3-D representation of a relatively small number of pits. However, although the 3-D data of all the pits within an image can be simultaneously obtained using confocal laser scanning microscope (CLSM), a user still has to determine the diameter and depth of each pit manually, which, for an image with a relatively large number of pits, measuring the pits manually will take a significant amount of time. In statistical analysis, a large number of pits is usually necessary to guarantee the reliability of the calculations. Also, the spatial point pattern of corrosion pits is also an important issue in the understanding of the nature of pitting corrosion. However, the coordinates of the pit centers cannot be provided by a 3-D microscope or conventional image analysis techniques. In the work of Jarrah [17], a new statistical methodology was proposed, for detecting the pits interactions with each other, based on a two-dimensional spectral analysis, but the method was only validated based on the simulated pits, due to the lack of the experimental coordinates of the pits. The image recognition technique, which is proposed in this paper, can precisely detect the coordinates of a large number of pits. It is believed that the automatic
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recognition of pit locations can assist on resolving the issues, related with the statistical analysis of pitting corrosion in a twodimensional dimensional spectral analysis. In our previous work, regular pits with near-circular shapes were observed in an X80 grade steel, when was tested for its corrosion behavior in NaCl solutions [18]. The observed pit shapes were found to be consistent with the results of stainless steel in a droplet of chloride solution [19] and the Ni-Cr-Mo steel in NaCl solutions under different hydrostatic pressure values [20]. Similar morphologies for pit shapes were also reported in an aluminum alloy [21,22], Zr-based bulk metallic glass [23] and hydrogen-etched graphite [24]. For near-circular pit shapes, the detection of the pit locations becomes a task of circles detection, a widely studied topic in the field of image recognition. A variety of circle detection algorithms have been proposed since the 1990’s [25–27], while there is still an ongoing interest in this area ultil the recent years [28,29]. The circle detection technique has been extensively studied for several applications, such as the soccer game, face recognition or human eye location, while the requirements and issues with the algorithms needed for the different applications may differentiate. For example, in soccer ball detection applications, one of the most challenging issues that need to be overcome is the real-time processing [30], which is however not an issue for the corrosion pit detection applications. In the present paper, a gradient-based Hough transform method is introduced for the detection of corrosion pits in microscopic images. The main difficulties of circle detection for the corrosion images were addressed. The accuracy of the proposed method was evaluated by using simulated images with pre-defined pit parameters and the results of pit detection were demonstrated in optical microscope images.
2.2. Hough transform Hough [31] proposed an interesting and computationally efficient procedure (Hough transform, HT) for detecting lines in images, which has become the theoretical foundation of most algorithms that were developed in the past decades for detecting different shapes (line, circle, rectangle, etc.) in images. Ito [32] used the circular Hough transform to identify the eyes in facial images, Barinova [33] used the Hough transform to detect multiple object instances, D’Orazio [30] used the circle Hough transform for the ball recognition, Marquez [34] applied the Hough transform in the cloud tracking, while Khalil [35] studied the droplet size distribution. Many previous studies have been focused on improving the accuracy and efficiency of Hough’s proposed method, proposing a number of algorithms, which, as on overall, can be referred to as the HT-based methods. The key concept of the HT is to detect the parameterized curves in images by mapping the edge pixels into the manifolds in the parameter space, and the methods that will define the peaks in the parameter space can also be used to detect the image curves [36]. As presented in Fig. 1, the equation of a line in a k-y plane is Eq. (1), and every line in the k-y plane corresponds to a unique point in the − plane, hence: x cos + y sin = (1)
2. Material and methods 2.1. Pitting morphology A high-strength, X80 pipeline steel was used for the experimental procedure. Each specimen was ground gradually with 400–1200-grit waterproof abrasive paper and cleaned with distilled water and acetone. Then the specimens were immersed in a 3.5 wt% NaCl solution for 1 h. The pitting morphology was observed using a confocal laser scanning microscope (LEXT OLS4000).
Fig. 1. The normal parameters for a line.
Table 1 Parameters of the simulated pit diameters. Number
20 3.0 0.4
40 3.0 0.4
60 2.6 0.3
70 2.4 0.3
80 2.2 0.3
Fig. 2. Flowchart of the pit recognition process.
(1)
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Fig. 3. Illustration of the determination of circle center: (a) original image, (b) accumulation array after the voting by two gradient vectors, (c) the 3-D colormap of the accumulation array and (d) the signature curve.
Regarding the identification of a circle, if a circle in the picture plane is described as 2
(x − a)2 + (y − b) = c 2
(2)
Then, an arbitrary point (xi ,yi ) in the picture plane will be transformed into a circular cone in the (a,b,c) parameter space. The cones corresponding to all the figure points in a circle will intersect at a single point (a,b,c), and this circle can be defined by those three parameters. A multi-dimensional array of accumulators is used to represent the three-parameter space, in order to make the detection process more efficient than the analytical transformation does [36]. The main drawbacks of the HT are the large software memory size required and the essential time consuming computations. However, this is not a big concern for the detection of corrosion pits, since it does not need to be real-time. For the analysis of a microscopic image of 1024 × 1024 pixels, a computer with a minimum memory of 2 GB would be needed to run the HT program. In this paper, the Matlab 2014b software was employed, in a computer with a memory of 32 GB. 2.3. Accuracy verification The accuracy of the introduced algorithm in the simulated images is verified with pre-defined pit parameters. In the simulated images, both the horizontal and vertical coordinates of the pits
are random numbers. The spatial randomization of the simulated pit coordinates was confirmed with the assistance of the spatstat package software, programmed in the R language [37]. Five groups of different pit diameters were simulated and the data were generated utilizing the “lognrand” function in Matlab software, which creates random numbers that follow the lognormal distribution. The parameters of the pit diameters are shown in Table 1. Each group is repeated three times. 3. Results and discussion There are several public HT-based algorithms for circles detection, among which the Peng’s algorithm [38] has excellent performance in the recognition of pits from optical images. There is a wide variety of other advanced algorithms that could serve the same purpose, HT-based or non-HT-based, which were published in the area of image processing, most of which are not available online. Those who are interested in applying these methods to their own study may have to acquire good knowledge of image recognition and program writing. For the circles detection in corrosion images there are three main issues that have to be managed, i.e., the large number, the wide radius range and the high background noise. For a relatively low magnification image, one hundred or more pits were able to be observed. The pit diameter can range anywhere between several micrometers to several hundred micrometers. Also, there are
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Fig. 5. (a) 2D and (b) 3D colormap of the accumulation array.
Fig. 4. (a) A simulated image with determined number and diameters; (b) recognized pits in the simulated image.
usually many scratches, or other irregular inclusions or defects, on the surface of the steel, which have to be differentiated from the pits. However, the gradient-based HT method is proved to be powerful in handling these difficulties. The recognition process of the pits in an optical image, using the gradient-based HT, includes several steps, as shown in Fig. 2. The microscopic image, with a size of 1024 × 2014 pixels, was imported and converted to a grayscale image. Prior to initiating the main function, a filter is usually necessary to be applied to the image for de-noising, which will significantly improve the accuracy of the recognition. Then the HT is implemented in the way described by Eq. (3), where, “accum”, is the result accumulation array from the circular Hough transform (CHT), which has the same dimensions as the input image, “circen”, are the coordinates of the center of pits detected, “cirrad”, is the radii of the pits detected, “img”, is the input image file, Rmin and Rmax , are the possible minimum and maximum
radii of pits to be searched, g, is the gradient magnitude threshold, which is performed before the voting process of the circular HT, in order to remove the ‘uniform intensity’ of the image background from the voting process, Rf , is the radius of the filter used in the search of local maxima in the accumulation array and m, is the tolerance factor of multiple pits detected at the same coordinate. [accum, circen, cirrad] = CircularHough Grd(img, [Rmin Rmax ], g, Rf , m)
(3)
The CHT consists of three steps, i.e. to compute the gradient field of the input image, to transform the gradient field to an accumulation array and, finally, to find the peaks in the accumulation array. The gradient-based method was firstly proposed by Illingworth [39] and was later modified by Peng [40] and was used to detect circular patterns. The values of all points in a grayscale image fluctuate within the range of 0 and 1 (black to white), which are defined as the image intensities. The gradient field of image intensity can be calculated using the Eq. (4), where, (i,j), are the pixel indices, I(i,j), is the image intensity for a specific pixel, with (i,j) indices, and ∇ I (i, j), is the gradient vector at pixel with (i,j) indices.
∇ I (i, j) = Vx , Vy |(i,j) = (I (i, j) − I (i, j − 1) , (i, j) − I (i − 1, j) , ) (4)
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Fig. 7. Accuracy of the recognition of the number of pits.
defined by the vector ∇ I (i, j). The accumulation array is constructed by collecting the votes from all nonzero gradient vectors. Therefore, the maximum intensity in the accumulation array represents the center of a pit, as shown in Fig. 3c. For the determination of circle radius, a signature curve is defined by the Eq. (5), where, r, is the distance to the circle center, ∇ (i, j) is the gradient vector, q (i, j) is the radial vector from the circle center (ic , jc ) to the pixel (i, j), f (r) is averaged dot product of the gradient vector and the radial vector. The summation is over all the (i, j) picels that satisfy the conditions of Eq. (6), where, r, is the interval between adjacent r values.
∇ (i,j)·q(i,j)
q(i,j)
(i,j)
f (r) =
(i,j)
Fig. 6. Deviation between the recognized radii and the actual values.
This algorithm capitalizes the feature of the nonzero gradient vectors, which, in the gradient, they are either pointing toward or away from the center of a circle. A voting process is utilized in order to transform the gradient field into an accumulation array, as shown in Fig. 3a and b. A weight value (marked in gray in Fig. 3b) is added to the pixels in the accumulation array, which lies on the line segment,
| q (i, j) − r| <
1
r 2
(5)
(6)
For a solid circle, as shown in Fig. 3a, the estimated radius is defined as the coordinate of the extreme, of the signature curve, as shown in Fig. 3d. The signature curve of a hollow circle is more complicated to define, and the readers may refer to reference [40], for further information.
Fig. 8. Error of the radii and coordinates of detected pits, with symbols representing the average values and error bars the standard deviation. Rtrue and Rrecog represent the real radius and recognized radius, respectively; Er shows the error of radius. Ctrue and Crecog represent the coordinates of the real pit center and recognized pit center, respectively; Ec shows the error of the coordinates.
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Fig. 9. Comparison of the probability distributions of the simulated and recognized radii.
3.1. Recognition accuracy The recognition results, which were taken from an example image with 70 pits, are presented in Figs. 4, 5 and 6. The radii of pits follow the lognormal distribution, with a location parameter of 2.4 and a scaling parameter of 0.3. The simulated image and the corresponding pits, recognized using the HT method, are presented in Fig. 4a and b, respectively. It is clear that the radii and coordinates of all pits can be successfully detected. The accumulation arrays in two-dimensions and three-dimensions are presented in Fig. 5a and b, respectively. Each local maximum value in the accumulation array corresponds to a circle candidate. A maximum searching algorithm selects the real circle from the potential candidates, based on some pre-defined criteria. Fig. 6 shows the deviation of the recognized radii from the true values, of the image presented in Fig. 4a. It can be seen that the recognition error for the pit radius is less than 11%. The results of the repeated tests are presented in Figs. 7 and 8. As presented in Fig. 7, the detection accuracy of the number of the pits is higher than 95%. Fig. 8 shows the error deviations of the radii and coordinates. The average error value of the radii is approximately 5%, with a standard deviation smaller than 5. The error of coordinates is defined as the distance between the detected center and the real center, divided by the real radius. The average error of coordinates is less than 10%, with a standard deviation smaller than 4. Furthermore, the detection accuracy is not affected by the increase of the number of pits. The difference between the real distribution and the recognized distribution of the radii is presented in Fig. 9. Both the probability density function and the cumulative distribution function of the recognized circles fit well with the actual ones. The highest pit radius (∼50 pixels) is approximately 10 times of that of the lowest pit radius (about 5 pixels), therefore, this method can be considered as being non-dependent on the radius range, making it suitable for the detection of corrosion pits in optical images.
Fig. 10. (a) A simulated image with irregular shapes, with the error of detected radii shown in (b) and (c).
3.2. Effect of irregular shapes In actual optical images, there are usually irregular shapes, such as scratches, inclusions or precipitates. In order to detect the pits accurately in such images, the algorithm should be able to differentiate between the real pits and the irregular shapes. An image with simulated scratches and inclusions is presented in Fig. 10a and the recognition error is shown in Fig. 10b and c. It is clear that the recognition accuracy is not affected by irregular shapes
additions, implying that the suggested method has a strong ability of differentiating pits from scratches and irregular inclusions. 3.3. Recognition of real pits The results of the pits recognition procedure of an actual pit image are presented in Fig. 11. It is demonstrated that all the pits were successfully recognized. The radii and coordinates were
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Fig. 11. Recognition results for a real image: (a) An optical image of corrosion pits, (b) recognized pits, the accumulation array of CHT in (c) two dimensions and (d) three dimensions, (e) overlapped pits, and (f) fitted distributions for the manually measured pits and the recognized pits.
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Fig. 12. Transformation of the corroded area into an equivalent circle.
Equivalent circles
Fig. 13. Recognition of the irregular pits.
written into a two-dimensional array, which provides detailed information (number, diameter and location) of the corrosion pits. The accumulation array of CHT is presented in Fig. 11b and c. As previously discussed, each pit in the original image corresponds to one local extreme value in the accumulation array. And each local extreme value represents a candidate of a recognized pit. A final step of the recognition procedure is a maximum searching process which will determine the real pits among the pit candidates. Even pits with a very low diameter or overlapped pits can be accurately recognized, as demonstrated in Fig. 11e. The actual pit diameters were measured manually, using software for editing photographic images, and the total number of the pits was determined as 50. The HT recognized 47 pits from the image, which gives an accuracy of the recognition procedure of is 94% (47 out of 50). The matching among the lognormal distributions of the manually measured pits and the recognized pits are presented in Fig. 11f, where it can be observed that the recognized data are very accurate in the evaluation of the pit size distribution. The minimum pit diameters that can be detected through HT depend on the magnification of the microscopic image. Generally, pits with a diameter of as small as 5 pixels, within an image with a 1024 × 1024 pixels
image, can be successfully detected. If the pit size is much smaller than this minimum value, it would be necessary to use a larger magnification. This method can detect a large number of pits, at a wide radius range and with high background noises. A wide radius range option important as the pit sizes usually vary in a very wide range (in this case between 10 m and 200 m). The use of algorithms that cannot detect such a wide radius range will lead to a high missdetection rate and low accuracy. The miss-detection of pits is usually attributed to the presence of scratches, defects and overlapped pits in the input image. This issue can be overcome by increasing the contrast between the unrecognized pits and the background, by darkening them manually with a photograph editing software. In this way, the accuracy of this algorithm can be significantly improved. The use of image recognition techniques for pit detection greatly benefits the statistical analysis of corrosion pits, since it can significantly reduce the difficulty of measuring the number, sizes and locations of the pits. Also, the analysis of pit size distribution and the spatial point pattern of pitting corrosion images become very efficient.
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3.4. Other remarks It should be noted that the detected radii must be an integer number (in the unit of pixel), which increases the error of the recognition technique. This limitation may be overcome by making modifications to the original algorithms. The readers that are interested in improving this program in this way might need to change the definition of the signature curve. The algorithm that is presented in the present study is also capable of finding regular circles in other image types, such as cells, hollow spheres or fruits, but is limited in finding regular circles instead of ellipses. For elliptical shapes with high eccentricity, the detection results will be two regular circles centered at the two focus points, respectively. 3.5. Recognition of pits with irregular shapes Both circular and irregular pit shapes can be observed in the actual experiments. Therefore, a simple method, which is based on the concept of equivalent circles, is proposed, in order to recognize the irregular pits in images, as presented in Fig. 12. A corrosion pit with an irregular shape can be converted into an equivalent circle, with the same area of the corroded zone. The coordinates of the center of the circle will be the average values of all the points in the corroded zone. So, both the radius and coordinate can be determined. Therefore, the recognition of the irregular pits can be completed in several steps. First, the image is imported and converted into a grayscale image. Then, the corroded zones are located in the image by setting a threshold value above which the determined points will be considered as corroded. Following that, those corroded zones are separated from each other by finding the adjacent points (comparing the coordinates to each other). Finally, the radius and coordinate of each separated zone are determined by counting the number of points in each zone and building the equivalent circle. The recognition process of pits with irregular shapes is illustrated in Fig. 13. 4. Conclusions The gradient-based Hough transform is introduced to recognize the corrosion pits in microscopic images. The results show that this method is powerful in detecting a large number of pits with a wide radius range and high background noises. Therefore, it is proved to be an excellent tool in the automatic recognition of the diameter and locations of corrosion pits in digital images, which can significantly increase the efficiency of quantitative evaluation of pitting corrosion samples. Statistical analysis of the size and location distribution also becomes simplified, based on the suggested pit detection technique. Acknowledgments The authors would like to gratefully acknowledge the financial support from the National Basic Research Program of China (973 Program, Grant No.2015CB057602). We would also like to thank Mr. Liheng Bian in Tsinghua University for his advice on the circle finding algorithms. References [1] ASTM Standard G46-94, Standard Guide for Examination and Evaluation of Pitting Corrosion, 2005. [2] A.M. Zimer, E.C. Rios, P.D.C.D. Mendes, W.N. Gonc¸alves, O.M. Bruno, E.C. Pereira, L.H. Mascaro, Investigation of AISI 1040 steel corrosion in H2 S solution containing chloride ions by digital image processing coupled with electrochemical techniques, Corros. Sci. 53 (2011) 3193–3201.
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