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The discrete-time Fourier transform has essentially the same properties as the continuous-time Fourier transform, and these properties pla. The discrete-time Fourier transform has essentially the same properties as the continuous-time Fourier transform, and these properties play parallel roles in continuous time and discrete time.
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.
Micro-crack detection in the monocrystalline cell is relatively straightforward because this type of cell is characterized by a uniform background. However, this is not the case for the multicrystalline cell, which contains crystal grains as well as dark areas formed from intrinsic structures like dislocation clusters and grain boundaries. Distinguishing micro-crack pixels from the background (i.e., the multicrystalline grains) is a very challenging procedure because the gray scale values of these two areas are not significantly different. The presence of other defects, such as the dark area, darker grains, and broken fingers, complicates the problem.
In spite of these difficulties, the identification is still possible because the micro-cracks tend to appear in the form of strong lines with a low intensity and a high gradient. Figure a (i) shows an example EL image of a defected solar cell, and its close-up view of the region containing the micro-crack is displayed in Figure a (ii).
For comparison, the EL image of a good solar cell is presented in Figure b (i), and its close-up view is shown in Figure b (ii). Meanwhile, the scan-line profile of gray level and gradient of the solar cell defected with a micro-crack is shown in Figure b,c, respectively. These figures highlight the unique textural characteristics of the micro-crack pixels. All EL images used in this study including those shown in Figure are 8-bit gray scale measuring 1,178 × 1,178 pixels in size. Other examples of defected solar cells containing various types and shapes of micro-cracks are shown in Figure. The micro-crack pixels appear in the form of a line or an intersection of lines forming a star-like artifact as depicted in Figure a.
For comparison, Figure b shows examples of good solar cells highlighting the presence of dark regions having arbitrary shapes and sizes. They are formed by an aggregate of dislocation clusters or grainy materials, resembling dark shaped areas when visualized under the EL illumination. As seen from this figure, the presence of many dark areas or regions in both good and defected samples makes a micro-crack inspection an extremely difficult process.
However, a close examination of Figure a reveals that micro-crack pixels exhibit unique shapes or patterns compared to dark regions even though they have the same gray scale values. Thus, some form of image analysis is needed in order to facilitate accurate detection and efficient classification. Figure 3 Examples of micro-cracks and dark regions. (a) Solar cells with various types and shapes of micro-cracks. (b) Good samples showing the formation of dark regions.
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 and, 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 a (i) and Figure b (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.
Let I O be the original EL image of size m × n, and I ^ O u, v 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. Parameters w, d, and σ in Equation are chosen experimentally. The filtering is performed by pixel-to-pixel multiplication between I ^ O u, v and V ^ u, v to produce I ^ e u, v as shown in Figure a. 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 c,d,e. It can be seen from these figures that the fingers have been successfully removed and the background inhomogeneity is reduced.
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Also, the micro-crack pixels are not affected by this filtering operation as evident from Figure d (ii). Therefore, this local processing approach preserves the details in the image while attenuating the slow varying components such as the background irregularities. Figure 4 Pre-processing by filtering in the frequency domain. (a) Original EL image.
(b) Fourier spectrum after filtering with w = 6, d = 10, and σ = 12. (c) Filtered image after inverse Fourier transformation. (d- e) Results after pre-processing corresponding to images in Figure. 2.3 Anisotropic diffusion filtering This subsection presents an implementation of anisotropic diffusion filtering for image enhancement. As can be seen in Figure d (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. (5) 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 and 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.
Most of the approach reported in the literature used trial-and-error experiments in determining 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. Figure 6 Plot of diffusion coefficient with different values of s and g. As seen in Figure, 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 is used. This resulted in different threshold values for different pixels depending on their gray scale values through a mapping process. The proposed anisotropic diffusion method described above was tested using a synthetic image of size 256 × 256 pixels. As shown in Figure a, this image simulates a gradient profile comprising 16 discrete steps. Figure b shows the horizontal line scan of Figure a. The diffused image using the standard diffusion filter is shown in Figure c, while Figure d shows the result using the proposed algorithm. Clearly, image processing using standard diffusion filter produced a very blurred image, resulting in incomplete or missing edges.
In contrast, the proposed technique affects low gray scale edges only, while the high gray scale edges remain relatively intact. Processing the micro-crack using the proposed technique would result in blurred response in the diffused image since this type of defect is characterized by low gray scale and high gradient. Theoretically, subtracting this image from the original undiffused background would enhance the defect by removing some of the background components.
Figure 7 Image filtering comparing conventional and proposed anisotropic diffusion filters. (a) Synthetic image. (b) Horizontal scan line of (a). (c) Diffused image using Equation with K = 2 and t = 100; (d) Diffused image using Equation with b = 0.1, ϵ = 128, and t = 100. 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 to produce the edge stopping threshold matrix, g( x, y), which in turn is used to calculate the diffusion coefficient function given by Equation.
Third, Equation 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. The resulting diffused image has a blurred response due to the low-pass filtering effect of the diffusion process. The smoothing effect varies between pixels, and the extent of this depends on the edge stopping threshold value in 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 illustrates the images produced by these enhancement procedures using Figure d (ii) and Figure e (ii) as input images. Referring to Figure a (iii), the micro-crack line is enhanced and clearly visible after subtraction.
Figure 9 Results after image segmentation using double thresholding technique. (a) Defected sample and (b) good sample: (i) B S with α S = 0, (ii) B T with α T = -4, and (iii) B F. 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.
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This procedure helps to improve the feature extraction because it significantly reduces the number of shapes. For each binary shape 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 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 S 1, S 2, S N F 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 using Figure a (iii) as an input image. In this example, the number of shapes is reduced from 3 to 1. The image processing procedures described in the above paragraph have successfully enhanced micro-cracks as well as other objects while suppressing most of the noise pixels. As seen from previous section, the resulted binary image contains several binary connected components that represent crack and other artifacts. Codejock xtreme suite pro activex v16 crack cocaine.
Figure displays some of the objects detected by the algorithm. From this figure, the pixels that represent micro-crack can be distinguished from other artifacts because the former is characterized by some unique shapes and sizes. Therefore, shape analysis is used in order to distinguish between micro-cracks and other objects. This analysis produced features from shape descriptors which are later used in machine learning and classification.
In performing shape analysis, the region-based descriptor known as angular radial transform (ART) is investigated. The standard number of orders of ART is used to represent all binary shapes. The transform has 36 coefficients, and they are used as shape descriptors. Figure shows examples of the ART spectrum for the micro-crack and arbitrary shapes. As seen in Figure, a normalized ART spectrum for the micro-crack shape has more distinct fluctuation compared to the arbitrary shape. This translated into an increased average distance between the two spectrums and will result to a better discrimination of the shapes. The features extracted are used to train the artificial classifier.
In this study, support vector machines (SVMs) are used in machine learning and artificial intelligence. It is a supervised learning algorithm originally developed for two-class classification problems. Therefore, this classifier is suitable for this type of application. Micro-crack shape features are assigned as positive class, while arbitrary shape features are assigned as negative class.
Preliminary experiment suggested that the number of micro-crack shapes is far less than that of arbitrary shapes. Due to the unbalanced number of shapes between classes, the SVM classification may result in a bias toward the class having the most number of samples. This problem is addressed by utilizing a soft margin or penalty parameter which was set to different values for each class. This approach is similar to the implementation of a fuzzy membership associated with the penalty parameter. In this case, the optimal values of the penalty parameter for the positive and the negative classes are chosen experimentally. Also in this study, the SVM is trained using a kernel based on the Gaussian radial basis function (RBF).
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In summary, the methods and procedures implemented for micro-crack detection of solar cells are summarized in a block diagram shown in Figure. Examples of the segmentation results for defected and good cells are shown in Figure. It can be seen from Figure a (i-iv) and the corresponding segmented images in Figure a (v-viii) that the integrity of the binary connected components (shapes) that represent the micro-crack pixels is well preserved.
Referring to these figures, the micro-crack shapes can be easily distinguished from the arbitrary shapes visually. For comparison, the segmentation results of good or intact cells are shown in Figure b (v-viii). For the thoroughness of analysis, the proposed segmentation technique is compared with standard methods such as Otsu's thresholding, the Canny hysteresis, the Sobel edge detector, and the Laplacian of Gaussian (LoG) filter. In addition, a recent method based on Fourier image reconstruction (FIR) is also implemented. 4ukey – password manager 1 0 1 2013.
Figure shows the close-up view of the results of these different segmentation techniques using images in Figure a (i-iv) as input images. In this case, the ground truth images are plotted manually by an expert human inspector.
Download tuxera ntfs 2018 product key. It can be seen from Figure b that the segmentation using Otsu's global thresholding technique is able to detect micro-crack as well as other pixels. Meanwhile, both the Sobel detector and Canny hysteresis thresholding resulted in incomplete or disjointed micro-crack pixels. On the other hand, the LoG is only effective in detecting a limited number of micro-crack pixels, particularly the large ones as evident from Figure e. In contrast, the FIR method is accurate when detecting well-defined micro-crack pixels especially the ones appearing like straight lines. This method failed to completely detect star-shaped micro-crack pixels as evident from Figure f. In contrast, the results from the proposed segmentation technique are shown in Figure g. Clearly, the proposed method is able to detect all shapes and sizes of micro-crack pixels in the image.
Close examination of this figures revealed that some unwanted pixels also appeared in the segmented images. They are mostly due to the presence of dark regions in the solar cell. Since their appearance are distinctly different from micro-crack pixels, the use of the ART shape descriptor helped reduce the error resulting from misdetection. (12) 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 a (i-iv) are shown in Figure h (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, 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. In this case, the higher the F-measure, the better the image segmentation. The cpt and crt indices calculated from defected cell images in Figure are tabulated in Table. These indices are also calculated for the remaining 110 defected cells which are not shown in this paper.
The average values are listed in the last column of Table. Referring to this table, the completeness of Otsu's method is the highest compared to other algorithms.
But this is not the case for correctness as the crt index for this algorithm is the second lowest. Consequently, Otsu's method reconstructs many micro-crack pixels as well as noise as evident visually in the examples in Figure. As expected, the Sobel edge detection and Canny hysteresis methods produce only average results for both completeness and correctness. The same trend is observed for the FIR method. In contrast, the LoG filter produces the lowest cpt and crt scores, suggesting that this method does not correctly or completely detect micro-crack pixels. Meanwhile, the proposed segmentation technique yields the highest crt and the second highest cpt scores. This result suggests that this method ha.
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Image thresholding is a simple, yet effective, way of partitioning an image into a foreground and background. This image analysis technique is a type of image segmentation that isolates objects by converting grayscale images into binary images. Common image thresholding algorithms include histogram and multi-level thresholding. Image Processing Made Easy. See also: color profile , image analysis , image enhancement , image reconstruction , image segmentation , image transform , digital image processing , image processing and computer vision , Steve on Image Processing , edge detection , image registration , affine transformation , lab color , point cloud , 3D Image Processing. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location.
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Open Mobile Search. Trial software. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Fairuz Husna view profile. Vote 0. Crack detection on concrete. Asked by Fairuz Husna Fairuz Husna view profile. Hi, i have problem in measuring the length and width the crack image. I want the measurement by following the crack pattern. Please help me on this. This will approximately be Detection threshold matlab torrent area divided by the Cierne drevaky na opatku length.
Make it green across the whole image but magenta inside the blob. Cargando imagen gif para. See Also. Walter Roberson view profile. Cancel Copy to Clipboard. Answer by Walter Detection threshold matlab torrent Walter Roberson view profile. Skeletonize and then bwdistgeodesic. Fairuz Husna Fairuz Husna view profile.
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The R-waves can be detected by thresholding We perform peak detection on the smooth signal and use.
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Updated 04 Apr It takes incoming vector then find all parts that above threshold and cut the vector to above threshold parts. It returns cell array of above threshold parts of the vector and two arrays of start-indexes and end-indexes. Learn About Live Editor. Choose a web site to get translated content where available and see local events and offers.
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Image thresholding is a simple, yet effective, way of partitioning an image into a foreground and background. This image analysis technique is a type of image segmentation that isolates objects by converting grayscale images into binary images. Image thresholding is most effective in images with high levels of contrast. Object detection is a computer vision technique for locating instances of objects in images or videos. Object detection algorithms typically leverage machine learning or deep learning to produce meaningful results. When humans look at images or video, we can recognize and locate objects of interest within a matter of moments. Nov 20, 聽路 How to detect peaks above a certain threshold in Learn more about peaks Signal Processing Toolbox.