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- Open Access

# Micro-crack detection of multicrystalline solar cells featuring an improved anisotropic diffusion filter and image segmentation technique

- Said Amirul Anwar
^{1}and - Mohd Zaid Abdullah
^{1}Email author

**2014**:15

https://doi.org/10.1186/1687-5281-2014-15

© Anwar and Abdullah; licensee Springer. 2014

**Received:**23 April 2013**Accepted:**3 March 2014**Published:**21 March 2014

## Abstract

This paper presents an algorithm for the detection of micro-crack defects in the multicrystalline solar cells. This detection goal is very challenging due to the presence of various types of image anomalies like dislocation clusters, grain boundaries, and other artifacts due to the spurious discontinuities in the gray levels. In this work, an algorithm featuring an improved anisotropic diffusion filter and advanced image segmentation technique is proposed. The methods and procedures are assessed using 600 electroluminescence images, comprising 313 intact and 287 defected samples. Results indicate that the methods and procedures can accurately detect micro-crack in solar cells with sensitivity, specificity, and accuracy averaging at 97%, 80%, and 88%, respectively.

## Keywords

- Micro-crack detection
- Multicrystalline solar cell
- Image segmentation
- Anisotropic diffusion
- Angular radial transform
- Support vector machine

## 1. Introduction

The increasing demand for solar electrical energy has multiplied the need for photovoltaic (PV) arrays. As the major component of the PV array, the demand for solar cells has also increased. This demand has translated into an increased production of solar cells in recent years. Depending on the materials used in manufacturing, solar cells can be divided into two major types. They are (i) monocrystalline and (ii) multicrystalline silicones. Due to low manufacturing and processing cost of the multicrystalline silicon, this material is generally more preferred in the production of the solar wafer or PV module. There is great potential for the automation in solar cell industry because millions of solar cells are manufactured daily worldwide. According to recent statistics, the growth rate of the solar PV module reached a record high in 2011, generating more than US$93 billion in revenue with multicrystalline cells constituting more than 50% of the world production [1]. Although many operations in the PV industry have been automated, the inspection and grading processes continue to be based on manual or semi-manual efforts.

Finished solar cells are occasionally found to be defective or faulty. The defects fall into two groups: (i) intrinsic and (ii) extrinsic. Grain boundaries are an example of intrinsic defect, while micro-cracks belong to the second category. The former type of defects diminish the short-circuit current of the cell, and this leads to loss in the efficiency. The latter defects form a class of cracks that are entirely invisible to the naked eye. With dimensions smaller than 30 μm [2], this type of defect can only be visualized electronically like using the electroluminescence (EL) technique and high-resolution cameras.

In practice, there are various shapes and sizes of micro-cracks in a solar cell depending on how they are formed. For example a line-shaped micro-crack is caused by scratches, and it generally occurs during cell fabrication [3]. This type of defect can also be due to wafer sawing or laser cutting, which propagates and causes the detachment or internal breakage of the grainy materials within the solar cells [4]. In contrast, star-shaped micro-crack is formed due to a sharp point impact which induces several line cracks with a tendency to cross each other [5]. There are other types of micro-crack defects, but these two are the most commonly found in solar cell production. Köntges et al. [6] reported that there may be a risk of failure for PV modules containing cells that have micro-cracks or other types of defects. Hence, it is important to have high-quality, defect-free cells in the production of PV modules.

To date, few studies have highlighted the benefit of computer inspection for defect detection in EL images of solar cells. For example, multicrystalline solar cell images have been categorized into three distinct classes based on the features extracted from texture analysis [7]. An evaluation of crack formation in the PV module before and after mechanical load testing using EL images has been presented by Kajari-Schröder et al. [8]. Recently, a defect detection scheme based on Fourier image reconstruction has also been reported [9]. These authors presented a successful detection of a micro-crack which is geometrically simple like straight lines. A micro-crack detection scheme for a solar wafer based on an anisotropic diffusion filter has also been documented [10]. As reported by these authors, this filter is very efficient in preserving important edges in the image while smoothing other less important and connected regions. However, correct implementation of this technique depends crucially on the choice of an edge stopping threshold. In most cases, this value has to be determined interactively, frequently through trail-and-error method. Only under very unusual circumstances can anisotropic diffusion filtering be successful using a single threshold since images are likely to be gray level variations in objects and background due to non-uniform lighting and other factors. Clearly, a more robust approach is needed in order to increase the efficiency of this filtering strategy. In this paper, an enhanced version of the anisotropic diffusion filter featuring an adaptive thresholding via a sigmoid transformation function is presented. Meanwhile, pattern classification is established using support vector machines (SVMs) with supervised learning [11]. The methods and procedures are tested using intact and defected solar cells, and results are compared with other filters and artificial classifiers.

## 2. Methodology

### 2.1 Electroluminescence image

In this study, a series of image processing procedures are performed, capitalizing the unique textural properties and multicrystalline grain inhomogeneity of the solar cell. The details are described in the next section.

### 2.2 Image pre-processing

As seen in Figures 1 and 3, the EL images of the solar cell contain various features, such as fingers (horizontal lines) that are periodic in nature and perpendicular to the bus-bar (thicker vertical lines in Figure 1a (i) and Figure 1b (i)). A close inspection of these figures revealed that the intensity distribution is not uniform both within the cell and among the cells. The presence of the broken fingers and non-uniform background luminescence directly affects the micro-crack analysis, especially if a simple image segmentation technique is used. The solutions to these problems are to remove the periodic interruption of fingers and minimize the effect on background inhomogeneity on image processing. This can be done by filtering in the frequency domain.

*I*

_{O}be the original EL image of size

*m*×

*n*, and ${\widehat{\mathit{I}}}_{\mathit{O}}\left(\mathit{u},\mathit{v}\right)$ is its Fourier transform representation. Due to the orthogonal properties, the fingers in the spatial domain appear as a straight vertical line located at the center of a spectrum. This line is dominated by high-frequency components because the contrast between fingers and background is relatively higher compared to other inhomogeneities. Meanwhile, the low-frequency regions contain other important components such as the grain boundaries, dislocation clusters, and micro-cracks. Hence, only the high-frequency components located around the vertical line needs to be removed while retaining the low-frequency components. Therefore, a custom-made filter is constructed to remove these artifacts. The filter function is given below:

*w*,

*d*, and

*σ*in Equation 1 are chosen experimentally. The filtering is performed by pixel-to-pixel multiplication between ${\widehat{\mathit{I}}}_{\mathit{O}}\left(\mathit{u},\mathit{v}\right)$ and $\widehat{\mathit{V}}\left(\mathit{u},\mathit{v}\right)$ to produce ${\widehat{\mathit{I}}}_{\mathit{e}}\left(\mathit{u},\mathit{v}\right)$ as shown in Figure 4a. The resulting image is inverse Fourier transform, yielding

*I*

_{ e }(

*x*,

*y*) in spatial space. To minimize the error resulting from the inconsistency of the gray level between cells,

*I*

_{ e }(

*x*,

*y*) is normalized to 128. This filtered image is shown in Figure 4c,d,e. It can be seen from these figures that the fingers have been successfully removed and the background inhomogeneity is reduced. Also, the micro-crack pixels are not affected by this filtering operation as evident from Figure 4d (ii). Therefore, this local processing approach preserves the details in the image while attenuating the slow varying components such as the background irregularities.

### 2.3 Anisotropic diffusion filtering

This subsection presents an implementation of anisotropic diffusion filtering for image enhancement. As can be seen in Figure 4d (ii), the micro-crack pixels are characterized with low gray scale values but high gradients. The convolution of *I*_{
e
}(*x*, *y*) with a simple edge detector (e.g., Sobel kernel) will yield high and low gradients at the edges and micro-crack pixels, respectively. Consequently, the result is that the produced image contains two lines, corresponding to regions with high and low intensity gradients. This will give rise to the difficulty in the detection leading to many false negatives. We solved this problem by means of the anisotropic diffusion filtering, which produces equal response to any pixels, including the micro-crack areas. In order to achieve this, the diffusion filter is programmed to take into account not only the intensity of the gradient but also the intensity of the gray level of each pixel. The details are explained below.

*I*

_{ d }(

*x*,

*y*,

*t*) at iteration

*t*[12]. Mathematically,

*c*is a diffusion coefficient that is a non-negative function of the magnitude of the gradient of four Laplacian neighbors,

*i*= {1, 2,…, 4}. Letting

*s*= |∇

*I*

_{ d }|, then the diffusion coefficient in Equation 3 is given as

These diffusion coefficients exhibit a low value at high gradient purposely to preserve the corresponding edges. On the other hand, these coefficients produce high value at low gradient indicating a strong smoothing effect on the pixels involved. Thus, the anisotropic diffusion filtering will produce a smoothed image while the important edges are preserved. Parameter *K* appearing in Equations 4 and 5 is an edge stopping threshold, and it needs to be correctly specified in order to ensure a successful application of this filtering strategy. If *K* is too small, then the diffusion process will be terminated earlier, resulting in *I*_{
d
}(*x*, *y*, *t*) which is approximately equal to *I*_{
d
}(*x*, *y*, 0). In contrast, fixing *K* too large will significantly diffuse the image, resulting in image blurring. Therefore, the choice of the parameter *K* is important for producing a diffused image that retains the important edges while smoothing the other regions of the image.

*K*. In contrast, this study used a diffusion coefficient function that eliminates the need to use this parameter. Referring to the micro-crack pixels defined in the previous section, we are interested in every pixel with a high gradient but a low intensity value. For this reason, the gradient threshold does not have to be rigidly fixed. In order to achieve this, parameter,

*K*is replaced with the function that adaptively generates a unique threshold for each pixel using the input image gray values. The proposed diffusion coefficient is as follows:

*g*is a mapping of the image intensity of

*I*

_{ d }(

*x*,

*y*, 0) through the sigmoid transfer function given by

*b*determines the gradient of ramp in the transfer function and

*ϵ*is a threshold value where the intensity of

*I*

_{ d }(

*x*,

*y*, 0) is mapped to the center of the gray scale range. Equation 8 is defined as an edge stopping threshold matrix, and it has the same dimension as

*I*

_{ e }(

*x*,

*y*). Every element in

*g*(

*x*,

*y*) is the edge stopping threshold value for the corresponding pixel in

*I*

_{ e }(

*x*,

*y*). Equation 7 is plotted for different

*s*and

*g*values, and the result is graphically shown in Figure 6.

As seen in Figure 6, the response of the diffusion coefficient varies with the different threshold values. The response is more sensitive when the threshold value is low with respect to the same gradient *s*. High value of the coefficient yields a high diffusivity for the corresponding pixel in the image which leads to blurring effect. As mentioned earlier, existing techniques only used a single edge stopping threshold value for the whole image. In this study, an adaptive edge stopping threshold function given in Equation 8 is used. This resulted in different threshold values for different pixels depending on their gray scale values through a mapping process.

In this study, the proposed anisotropic diffusion filtering is performed in three steps. First, the filtered image, *I*_{
e
}(*x*, *y*), is smoothed using a 2-D Gaussian filter of size 5 × 5 yielding *I*_{
d
}(*x*, *y*, 0). Second, the smoothed image is then processed using Equation 8 to produce the edge stopping threshold matrix, *g*(*x*, *y*), which in turn is used to calculate the diffusion coefficient function given by Equation 7. Third, Equation 3 is invoked and the calculation is terminated after a few iterations. In this case, the iteration number is determined heuristically and is usually less than 10 in most cases.

*g*(

*x*,

*y*). For a pixel with a low threshold value, the smoothing is significant and yields a very blurred response. In contrast, this image processing technique produces image which is approximately equal to the original image if the smoothing effect is weak. As previously explained, the resulting image is obtained by subtracting

*I*

_{ d }(

*x*,

*y*,

*t*) from

*I*

_{ d }(

*x*,

*y*, 0) to produce the new, enhanced image denoted as

*I*

_{ Δ }(

*x*,

*y*). Figure 8 illustrates the images produced by these enhancement procedures using Figure 4d (ii) and Figure 4e (ii) as input images. Referring to Figure 8a (iii), the micro-crack line is enhanced and clearly visible after subtraction.

### 2.4 Post-processing

*I*

_{ Δ }(

*x*,

*y*). It consists of two thresholding stages: (i) binary image reconstruction using double thresholding and (ii) the intensity tracing and thresholding. All threshold values are calculated using an adaptive thresholding technique [13]. The general expression of adaptive thresholding is given by

where *μ* and *σ* are the mean and the standard deviation of the gray level intensity of the input image, respectively, and *α* is a scaling factor.

*I*

_{ Δ }(

*x*,

*y*) to be segmented twice, first using a high threshold value

*τ*

_{ S }and second using a low threshold value

*τ*

_{ T }. Equation 9 is used to compute

*τ*

_{ S }and

*τ*

_{ T }using scaling factors

*α*

_{ S }and

*α*

_{ T }, respectively. This segmentation technique produces two binary images referred herein as the seed image

*B*

_{ S }and the target image

*B*

_{ T }. In this case

*B*

_{ S }consists of mainly incomplete but noise-free edges, whereas

*B*

_{ T }contains complete edges and noise. The next step in the segmentation involves reconstructing the final binary image

*B*

_{ F }from

*B*

_{ S }and

*B*

_{ T }followed by dilation and closing. In this case,

*B*

_{ F }contains {

*S*

_{1},

*S*

_{2},…,

*S*

_{ N }} where

*S*represents the shape in the form of binary connected components and

*N*is the number of shapes following the first stage thresholding step. The resulting binary images are presented in Figure 9 using Figure 8a (iii) and Figure 8b (iii) as input images.

Next, the intensity tracing and thresholding are performed on *B*_{
F
} using *I*_{
e
}(*x*, *y*) as the reference image. The purpose of this procedure is to further reduce the noise or the unwanted shapes, such as scratches, dislocation clusters, or grain boundaries. The gray values of these artifacts are relatively higher compared to those of the micro-crack pixels. This procedure helps to improve the feature extraction because it significantly reduces the number of shapes.

*S*in

*B*

_{ F }, the value of the gray intensity composed of pixels at the same location and bounded by the same contour

*S*is traced and extracted from the normalized image after pre-processing. The mean value of the gray intensity for each extracted pixels group is computed. Any shape that has a mean value which is less than the specific threshold is retained in

*B*

_{ F }. Otherwise, it is treated as noise and hence eliminated. Again, the adaptive thresholding given in Equation 9 is used with

*α*

_{ tr }fixed experimentally while

*μ*and

*σ*are obtained from

*I*

_{ e }(

*x*,

*y*). These procedures generate a new set of shapes $\left\{{\mathit{S}}_{1},{\mathit{S}}_{2},\dots ,{\mathit{S}}_{{\mathit{N}}_{\mathit{F}}}\right\}$ whose number is less than the ones contained in the original set (i.e.,

*N*

_{ F }≤

*N*). An example of the intensity tracing and thresholding is shown in Figure 10 using Figure 9a (iii) as an input image. In this example, the number of shapes is reduced from 3 to 1.

### 2.5 Shape analysis

## 3. Result and discussion

In this section, the experimental results from the methods and procedures described in the above sections are presented. This includes the image segmentation and classification. All experiments are performed on a desktop computer equipped with a dual core 2.80 GHz processor, 2 GB of RAM, and an installed MATLAB software package. The results obtained in this section are based on 600 samples of which 313 are good samples and the remaining are defected or cracked cells.

### 3.1 Image processing

*F*-measure is used [19]. Mathematically,

where *ℓ*_{
GT
} is the number of micro-crack pixels in the corresponding ground truth image, *ℓ*_{
r
} is the number of pixels in the segmented image which matches the ground truth micro-crack pixels, and *ℓ*_{
N
} is the total number of extracted pixels in the segmented image. Examples of ground truth images corresponding to defected cells in Figure 15a (i-iv) are shown in Figure 15h (i-iv), respectively. On the other hand, the cpt index indicates the completeness of the segmentation technique in detecting micro-crack pixels in the defected solar cells. Clearly, from Equation 11, cpt is equal to 1 if *ℓ*_{
r
} = *ℓ*_{
GT
}, indicating the perfect match between the number of micro-crack pixels detected by the algorithm and the ground truth image. In contrast, cpt is equal to 0 if there is no match. Meanwhile, the crt index measures the correctness of the segmented image produced. Similarly, this index is equal to 1 if the segmented image matches the ground truth. Practically, *ℓ*_{
r
} ≤ *ℓ*_{
N
} since micro-crack as well as noise pixels are also detected. Hence crt also ranges from 0 to 1. Calculating cpt and crt enables the *F*-measure to be computed using Equation 10. In this case, the higher the *F*-measure, the better the image segmentation.

**Completeness and correctness measures of the segmentation results**

Measure | Method | Figure15a (i) | Figure15a (ii) | Figure15a (iii) | Figure15a (iv) | Overall average |
---|---|---|---|---|---|---|

cpt | Otsu | 0.9747 | 0.9706 | 0.8410 | 0.6304 | 0.8832 |

Sobel | 0.2686 | 0.4029 | 0.2538 | 0.4137 | 0.3703 | |

Canny | 0.1248 | 0.1751 | 0.0275 | 0.1048 | 0.1248 | |

LoG | 0.0316 | 0.0472 | 0 | 0.0520 | 0.0492 | |

FIR | 0.4976 | 0.3668 | 0.3547 | 0.2057 | 0.2952 | |

Proposed | 0.9368 | 0.8873 | 0.8899 | 0.7510 | 0.7185 | |

crt | Otsu | 0.0026 | 0.0089 | 0.0153 | 0.0586 | 0.0078 |

Sobel | 0.0064 | 0.0248 | 0.0061 | 0.0123 | 0.0122 | |

Canny | 0.0086 | 0.0290 | 0.0015 | 0.0151 | 0.0157 | |

LoG | 0.0004 | 0.0016 | 0 | 0.0034 | 0.0014 | |

FIR | 0.0156 | 0.0302 | 0.0110 | 0.0286 | 0.0116 | |

Proposed | 0.0195 | 0.0843 | 0.0258 | 0.0854 | 0.0462 |

*F*-measure are shown graphically in Figure 16. It can be seen from this figure that the

*F*-measure score produced by the proposed segmentation algorithm is consistently higher compared to other techniques. Overall, the proposed algorithm results in

*F*-measure averaging at 0.0821 compared to 0.0216 FIR, 0.0028 LoG, 0.0258 Canny, 0.02288 Sobel, and 0.0153 Otsu. This again proves that the proposed method is more efficient in detecting micro-cracks in solar cells.

*b*and

*ϵ*for the sigmoid mapping function and

*t*which is the number of iterations for anisotropic diffusion. Meanwhile,

*ϵ*corresponds to the average intensity of the input image ${\mathit{\mu}}_{{\mathit{I}}_{\mathit{e}}}$. This simplified the computation of the mapping function as the target micro-crack pixels have the intensity below this average value. Meanwhile, parameter

*b*represents the gradient of the sigmoid mapping function. Higher value of this parameter resulted in steeper gradient for the mapping function. Figure 17 demonstrates the effect of changes in the value of

*b*on

*I*

_{ Δ }(

*x*,

*y*) using Figure 15a as input images. Clearly from this figure, the best result is obtained for

*b*= 1. Hence, this value was used to process all images reported in this paper.

*t*in which the image needs to be diffused. This parameter must be properly chosen to ensure successful enhancement of the micro-crack pixels at a minimal computational cost. The higher the number of the iteration, the longer the computational time. Figure 18 shows the normalized values of cpt, crt, and

*F*-measure for the different numbers of iteration. These indices are averaged from 114 defected cells. As can be seen from Figure 18, the highest value of

*F*-measure occurred at

*t*= 1. However, the cpt index corresponding to first iteration is significantly low, indicating the image that it produces is incomplete. Hence, the image needs to be iterated further in order to improve the cpt index. Close examination of Figure 18 revealed that the second highest

*F*-measure occurs at the fourth iteration. Even though the cpt decreases slightly at this iteration, the image is more complete and less noisy compared to the first iteration. A further increase in the number of iteration would result in the decrease of the

*F*-measure as well as the cpt and crt indices. Therefore, the diffusion process of all images shown in this paper is terminated after the fourth iteration (

*t*= 4).

### 3.2 Shape classification

For comparison purpose, the scattered plots of shape features produced by the well-known methods like (i) the Fourier descriptor (FD) [22], (ii) the generic Fourier descriptor (GFD) [23], and (iii) the projection-based Radon composite features (RCF) [24] are also included in this figure. A close examination of Figure 20 shows that the overlap between micro-crack and other arbitrary shapes is more prominent in Figure 20b,c,d than in Figure 20a. All micro-crack shapes in Figure 20b,c,d occupy the regions that are enclosed within other arbitrary shapes. Clearly, there is no unique demarcation between these two groups in the PCA space. Hence, any attempt to use FD, GFD, or RCF as features in the classification scheme would result in many samples being misclassified. In contrast, the overlap between the groups is less prominent for ART features, as shown in Figure 20a. It can be seen that the other arbitrary shapes are skewed to the right, whereas the micro-crack shapes are skewed to the left. Therefore, it is hypothesized that the features extracted using ART are more separable compared to those extracted using FD, GFD, and RCF.

**Distribution of intact and defected cells in the dataset**

Dataset | Defected | Intact | Total |
---|---|---|---|

Training | 114 | 126 | 240 |

Testing | 173 | 187 | 360 |

*k*-nearest neighbor algorithm (

*k*-NN), from which the results are compared with SVM. Furthermore, the performance of each algorithm is quantitatively evaluated in terms of three measurable metrics: (i) sensitivity, (ii) specificity, and (iii) accuracy. These metrics are based on a simple measure of the true positive TP, the true negative TN, the false positive FP, and the false negative FN. Mathematically, they are defined as follows:

*σ*

_{RBF}= 27,

*C*

^{+}= 390, and

*C*

^{-}= 19. Clearly, from Table 3, the SVM classifier outperformed LDA, QDA, and

*k*-NN in term of sensitivity, accuracy, and

*G*-Mean assessment metrics. Overall, less than 3% of defected cells are misclassified, and more than 80% of good cells are correctly classified. However, the

*k*-NN classifier performed best in the classification of good cells with 88% specificity. Nevertheless, the SVM produces the highest

*G*-Mean, indicating that the error in misclassification of this algorithm is consistently low. Therefore, SVM is overall the best classifier for this type of application.

**The classification results of the testing set**

Classifier | Descriptor | Sensitivity | Specificity | Accuracy | G-Mean |
---|---|---|---|---|---|

LDA | ART | 0.9306 | 0.7594 | 0.8417 | 0.8406 |

QDA | ART | 0.9711 | 0.7166 | 0.8389 | 0.8342 |

| ART | 0.8266 | 0.8824 | 0.8556 | 0.8540 |

SVM | ART | 0.9769 | 0.8021 | 0.8861 | 0.8852 |

FD | 0.9711 | 0.4332 | 0.6917 | 0.6486 | |

GFD | 0.9595 | 0.4973 | 0.7194 | 0.6908 | |

RCF | 0.9653 | 0.5936 | 0.7722 | 0.7570 |

For completeness, SVM experiments were repeated using FD, GFD, and RCF shape descriptors, and the results are also given in Table 3. Clearly, ART outperformed other shape descriptors in all assessment metrics. This again demonstrated that ART gives the best discriminating ability when dealing with this type of shape classification problem compared to other shape descriptors. In addition, the average processing time for each EL image is approximately 4.1 s which is comparable to the semi-manual inspection by a human expert. Meanwhile, the smallest micro-crack detected by the proposed algorithm is 47 pixels in size which physically corresponds to 6.22 mm in length.

## 4. Conclusions

The early detection of micro-cracks in solar cells is important in the production of PV modules. In this study, an image processing scheme composed of segmentation procedures based on anisotropic diffusion and shape classification is presented. The results show that the segmentation procedures can detect and identify micro-crack pixels efficiently in the presence of various forms of noise. The anisotropic diffusion filtering with gray level-based diffusion coefficient proposed in this study produced excellent enhancement and improved segmentation. The advantage of this filtering technique is its ability to enhance the pixels with low gray scale and high gradient such as the micro-crack defects in solar cell. Trained with SVM using 240 samples, this artificial classifier produced a correct classification rate of consistently higher than 88% with average sensitivity and specificity of 97.7% and 80.2%, respectively. These results are very promising as it demonstrates a first attempt of integrated image processing and machine learning platform toward its eventual application of micro-crack inspection of solar cells.

## Declarations

### Acknowledgements

This work is supported by the Malaysia Collaborative Research in Engineering, Science and Technology Centre (CREST) 304/PELECT/6050264/C121.

## Authors’ Affiliations

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