1. Introduction

Hydrides in the cladding of spent nuclear fuels are of significant interest in the field of radioactive waste. Its precipitation in cladding increases the probability of cladding failure by degrading its mechanical properties [1-2]. In particular, radial hydrides significantly reduce the mechanical strength of highly brittle claddings [3-4]. Therefore, preventing nuclear-related leakage and proliferation accidents through accurate hydride monitoring is essential [5]. Recently, with the development of various imaging devices, image segmentation has attracted attention as a promising technique for tracking and detecting the orientation and distribution of hydrides in real time [6-9].

Image segmentation is a technique that identifies and separates objects in pixel units to facilitate image analysis [10]. This technique has been used in various fields. Particularly, hydride segmentation from cladding images is a representative example of its application in the field of radioactive waste [6-9]. Regarding segmentation, numerous techniques have been proposed, such as thresholding [11], clustering [12], watershed [13], and k-means [14]. Among them, the Otsu algorithm [15] is the most popular among threshold techniques such as entropy [16] and local [17] due to its simplicity and speed. Especially, it is possible to predict the optimal threshold value through mathematical techniques. However, the Otsu algorithm has a limitation in segmentation accuracy according to preprocessing [18]. For example, segmentation quality cannot be guaranteed when the shape of the object to be distinguished is not clear. Therefore, preprocessing for the Otsu algorithm is necessary for the successful segmentation of the cladding image.

Preprocessing is well-known as useful for image quality improvement, specific feature enhancement, and noise reduction [19]. Owing to these advantages, it has been used in various images. Preprocessing can be broadly classified into methods based on morphological operations [20], edge extraction [21], and noise removal [22]. In particular, morphological operations are excellent for emphasizing the morphological characteristics of objects. For example, this operation is effective for enhancing hydrides with small sizes in cladding images [23]. However, there is a problem in that preprocessing results vary depending on the specific operation used because morphological operations consist of various types. Therefore, it is necessary to identify how the morphological characteristics of hydrides change according to the specific morphological operation applied.

This study aims to analyze the segmentation performance of the Otsu algorithm based on morphological operations on spent nuclear fuel cladding images. To achieve this purpose, this study consisted of four steps: extraction of the region of interest, preprocessing using morphological operations, segmentation based on the Otsu algorithm, and performance comparison (Fig. 1). For performance comparison, this study analyzed the difference in histograms, variance between classes, and radial hydride fraction (RHF) of segmented images with and without morphological operations applied.

Fig. 1

Schematic procedure of spent nuclear fuel cladding image for segmentation performance analysis.

2. Methodology

2.1 Step 1: Extraction of the Region of Interest

This study used four cladding images from previous studies [24] to capture the Zr–Nb alloy specimens using an optical microscope (Nikon LV150N). The images show different hydride reorientations, radial hydride fractions, and hydrogen concentrations (Fig. 2). The image in which radial hydride reorientation occurred is shown for Case 1. The other images contained only circumferential hydrides. The Radial hydride fraction (RHF) was the highest in Case 1 (19.5%), and the RHF values corresponding to Cases 2–4 were 2.9%, 1.7%, and 0.3%. The hydrogen concentrations in Cases 1–4 were 674.4, 668.2, 228.7, and 228.7 wppm, respectively.

Fig. 2

Image data from spent nuclear fuel cladding [24].

The image used in this study consists of a cladding containing a hydride and a background. Cladding is important information used as an input during preprocessing. However, the background provides unnecessary information and can be mistaken for a cladding or hydride when calculating the morphology. Therefore, for an accurate hydride analysis, the background must be removed. Hence, this study extracted the cladding as the region of interest by removing the background and not the cladding.

To extract the region of interest, this study first selected two points (P₁ and P₂) at the end of the border of the background to remove the background of the lower region. Subsequently, using the selected pixels, an equation for a straight line passing through two points was deduced. Finally, the values of the pixels below the generated straight line were changed to zero (black). This process was repeated to remove the background from the top of the area. Notably, the pixels above the equation for the straight line created by points P₃ and P₄ on the boundary line were changed to zero. Therefore, only the cladding and hydride were considered in this study.

2.2 Step 2: Preprocessing Using Morphological Operations

A morphological operation is a method for distinguishing and highlighting key object shapes in an input image [20]. However, each morphological operation uses a different calculation method, so the output results are different. Therefore, appropriate processes must be selected to improve the morphological properties of hydrides. In this study, the cladding was preprocessed by applying four types of morphological operations to the grayscale images: erosion, dilation, opening, and closing. These operations used small matrices called structuring element (SE). SE is used to perform operations around each pixel of the input image. The study used SE of size 3 × 3 to capture the essential patterns of the target object while minimizing computational complexity [25-26]. Fig. 3 shows the pixels for four morphological operations by an example. The characteristics and formulas for the four types of morphological operations are as follows [27]:

Fig. 3

Results of morphology operations for a grayscale simple image.

First, the erosion operation reduces the bright areas in the grayscale image. This operation reduces the overall brightness of the image and expanding the dark areas. The erosion operation scans each pixel of the input image and finds the minimum pixel value in the area covered by the SE. This value is assigned to the pixel in the output image. This process is applied to every pixel of the input image. The erosion equation is as follows:

where ⊖ denotes the symbol representing the erosion operation. F(x,y) denotes the pixel value at coordinates x,y in the input image F, and B(m,n) denotes the pixel value at coordinates m,n in the SE B. (x + m, y + m) denotes the coordinates of the overlapping region of the SE in the input image, and it indicates the process of finding the minimum value as the SE moves.

Second, the dilation operation expands the bright areas in the grayscale images. This operation increases the overall brightness of the image and expands the bright areas. The dilation operation scans each pixel of the input image and finds the maximum pixel value in the area covered by the SE. This value is assigned to the pixel in the output image. This process is applied to every pixel of the input image. The dilation equation is as follows:

where ⊕ denotes the symbol representing the dilation operation. F(x,y) denotes the pixel value at coordinates x,y in the input image F, and B(m,n) denotes the pixel value at coordinates m,n in the SE B. (x − m, y − m) denotes the coordinates of the overlapping region of the SE in the input image, and it indicates the process of finding the maximum value as the SE moves.

Third, the opening operation applies dilation to the grayscale image after erosion. In this operation, the erosion operation reduces the bright areas, and the subsequent dilation operation restores the original shape and size of the target object. Opening darkens objects and removes bright noise. Thus, the opening removes the bright noise and emphasizes the edges of the dark areas. The formula for opening is as follows:

where∘denotes the symbol representing the opening operation. F denotes the input image and B denotes the SE, ⊖ denotes the erosion, and ⊕ denotes the dilation.

Finally, the closing operation applies erosion to the grayscale image after dilation. In this operation, the dilation operation expands the bright areas, and the subsequent erosion operation restores the original shape and size of the target object. Closing brightens objects and removes dark noise. Thus, closing removes the dark noise and emphasizes the edges of the bright areas. The closing formula is as follows:

where • denotes the symbol representing the closing operation. F denotes the input image and B denotes the SE, ⊕ denotes the dilation, and ⊖ denotes the erosion.

2.3 Step 3: Segmentation Based on the Otsu Algorithm

The Otsu algorithm is an image segmentation technique that automatically calculates the optimal threshold to distinguish objects (target objects) from the background (non-target objects) within an image. It has been used to segment hydrides and cladding in spent nuclear fuel cladding images (Fig. 1). The Otsu algorithm analyzes the histogram of pixel intensities in a grayscale image. Then, it determines the optimal threshold, which serves as the criterion for classifying each pixel as either an object (hydride) or background (cladding). The threshold is determined within the range of 0 to 255, maximizing between-class variance to clearly separate the object from the background. The between-class variance of the Otsu algorithm for determining the optimal threshold is as follows [15] :

where k is the threshold value, σ B 2 is the between-class variance, μT is the average of all pixel values, ω(k) is the proportion of pixels below k, and μ(k) is the average intensity of pixels below k.

The optimal threshold k* is given by:

2.4 Step 4: Performance Comparison

This study analyzed the impact of morphological operations on segmentation performance. The histogram, between-class variance and RHF values of each segmented image were calculated and compared (Fig. 1). In the histogram, the peaks and valleys of the segmented images were analyzed according to the morphological operations. In terms of between-class variance, the separation between two classes was examined by considering the maximum and slope of the graph. RHF represents the ratio of radial hydrides. It was used to evaluate the effect of morphological operations on the quantitative disparities in hydrides and to analyze changes in the hydride distribution by comparing them with and without morphological operations. The definition of RHF is as follows [6]:

where L_i is the length of the i^th hydride. f_i is the weight according to the angle of the i^th hydride, which is as follows:

where θ = 0° denotes the circumferential hydride and θ = 90° denotes radial hydride. Therefore, a weight of 0.0 indicates circumferential, 0.5 indicates mixed, and 1.0 indicates radial.

3. Results

This study aimed to analyze the segmentation performance of the Otsu algorithm after applying four types of morphological operations: erosion, dilation, opening, and closing. For analysis, this study identified the effect of each morphological operation on the cladding and segmented images in terms of image features, hydride concentration, and RHF. In addition, this study quantitatively compared segmentation performance in terms of histogram, betweenclass variance, and RHF.

The results reveal that the morphological operation had a distinct effect on the four cladding images. As shown in Fig 4, the dilation operation removed small dark noise by expanding the bright area. However, this operation expanded the cladding (bright area) and reduced the hydride (dark area). This resulted in low local concentrations (blue circle) and made it difficult to identify the form of the hydride. Similarly, the closing operation removed dark noise. Unlike in the dilation operation, the shape and size of the hydrides were relatively maintained, but they still could not adequately emphasize their shape. This operation did not significantly reduce the local concentration compared to the dilation operation, but it is still lower than that of the original image.

Fig. 4

Comparison of the morphological operation results in Case 3, where red and blue circles represent dark noise and hydride, respectively.

The erosion increased the size of the hydride by shrinking the bright areas. This can improve the morphological characteristics of hydrides but expand the dark noise and reduce the image quality. For this reason, erosion operation resulted in a high local concentration. The opening operation reduced dark noise while maintaining the shape and size of the hydride. This implies that it functioned effectively by emphasizing the shape of the hydride and reducing the dark noise. Dilation and erosion operations only increase the size of the cladding or hydride and do not handle the noise in the image. Furthermore, the opening and closing operations are the result of a combination of dilation and erosion; thus, the shape of the hydride is relatively preserved and noise can be removed.

Table 1 shows the RHF according to the morphological operations in Case 3. The Dilation and Closing operations expanded the bright area and did not properly emphasize the shape of the hydride. As a result, the RHF was 0.4% and 0.5%, respectively, which were low values because most of the radial hydrides were not recognized. On the other hand, the Erosion and Opening operations reduced the bright areas and emphasized the shape of the hydrides. Consequently, the RHF was 1.9% and 1.7%, respectively, which were about 4 times higher than Dilation and Closing operations. The erosion operation expanded the dark noise along with the size of the hydride. As a result, the dark noise was recognized as radial hydrides, increasing the RHF. According to a previous study [24], the RHF of the Case 3 was 1.7%. The Opening operation showed an RHF consistent with the previous study. Therefore, the Opening operation showed the highest accuracy among the morphological operations in Case 3.

This study compared the impact of morphological operations on the shape, local concentration, and RHF of hydrides. Hydrides can degrade the mechanical properties of the spent nuclear fuel cladding and cause cracks, depending on their orientation and distribution [3]. For this reason, it is important to analyze the morphological characteristics of hydrides according to the morphological operations.

This study also identified the effects of morphological operations on cladding image segmentation. Image segmentation without preprocessing results in several problems, as shown in Fig. 5. For example, the segmentation incorrectly separated one hydride into multiple hydrides owing to low contrast (Case 1) and misrecognized the distributed dark noise as a hydride (Cases 2 and 4). Moreover, the segmentation did not implement a pale hydride with low pixel intensity (Case 3). By contrast, image segmentation with morphological operations showed a significantly improved performance. The opening operation overcame the problems in Cases 1 and 3 by emphasizing the shape of the hydride. The closing operation reduces misrecognition by removing dark noise in Cases 2 and 4. However, this study confirmed that operations can induce the opposite effect. The opening and closing operations degraded the segmentation performance by increasing the dark noise in Cases 2 and 4 and by decreasing the hydrides in Cases 1 and 3. These results emphasize the importance of appropriate morphological operations by considering the characteristics of the cladding image to improve segmentation performance. This further highlights the need for cladding image preprocessing. Also, this study is the first to reveal that applying morphological operations to images can significantly impact their quality and potentially induce errors. Notably, this study excluded the effect of dilation and erosion operations on image segmentation, which removed hydrides and expanded dark noise.

Fig. 5

Comparison of image segmentation results according to the morphological operation.

Fig. 6 shows the numerical analysis of the segmentation results using a histogram, between-class variance, and RHF. As previously mentioned, the morphological operation shows the shape of the hydrides and reinforces the connectivity between the hydrides in the segmented image. This result can be explained by using a histogram. The valley of the histogram for the segmented image with preprocessing had a deeper and clearer shape than that of the image without preprocessing. The Otsu algorithm provides high segmentation performance when there is a deep and clear valley between two peaks in the histogram [26]. Without a morphological operation, the histogram shows an unclear distinction between the valleys. This resulted in a decreased segmentation performance owing to the lack of a threshold value that could clearly distinguish between the two classes (hydride and cladding). However, with the morphological operation, the valley appeared relatively deep and clear in the same x-axis range. This is because the morphological operation emphasizes the morphological characteristics of the hydride, and a threshold value is selected to distinguish the two classes during the segmentation process.

Fig. 6

Comparison of the histogram, between-class variance, and RHF for the segmented images for Case 3 with and without morphological operation.

The valley of the previously analyzed histogram plays an important role in calculating between-class variance. A deep valley indicates a large difference between the two classes. The difference between the two classes was increased through morphological operations, which increased the value of the between-class variance. Therefore, the deeper the valley, the larger the between-class variance. Consequently, the maximum value for the graph with the morphological operation was 1,344.5, an increase of 10.8% compared to the previous value (1,214.8). Additionally, the slope of the graph increased steeply after the morphological operation. This implies that as the difference between the two classes increases, better segmentation results can be achieved with morphological operations at most threshold values. Therefore, the morphological operation increases the difference between the two classes, making the valley of the histogram deep and clear. Valley changes maximize the between-class variance, which increases image segmentation performance.

The improved performance is also evident in the difference of RHF values. As shown in Fig. 6, the blue line represents circumferential hydrides, while the red line represents mixed hydrides with both circumferential and radial orientations. The image without morphological operation shows RHF of 1.0%, whereas the image with morphological operation shows RHF of 1.7%. This corresponds with previously reported findings of 1.7%, highlighting the significant role of morphological operations in enhancing data reliability. This study objectively demonstrated the effects of morphological operations. As a result, morphological operations improved the accuracy of image segmentation and provided information similar to that of specimens.

Thus, this study analyzed the performance of the Otsu algorithm by evaluating four morphological operations. As mentioned earlier, morphological operations have a significant impact on images. It was found that a suitable combination of morphological operations can enhance segmentation performance.

Despite these strengths, this study had some limitations. First, this study considered only the segmentation results when morphological operations were performed only once. The segmentation results varied depending on the number of applications of morphological operations. Notably, this may affect the analysis results, depending on the researcher’s judgment. Second, this study did not investigate the effects of a combination of various preprocessing methods. Although morphological operations are the most popular preprocessing methods, different preprocessing methods, such as edge extraction, noise removal, and blurring images are necessary to determine whether they can contribute to the improvement in segmentation performance. Finally, four cladding images with unique characteristics are used. Additional research using various images is required to disseminate the results of this study. If further studies are conducted based on these limitations, they could contribute to the development of image analysis research on radioactive waste disposal.

4. Conclusion

This study aimed to analyze the segmentation performance of Otsu algorithm by applying preprocessing using morphological operations to spent nuclear fuel cladding images. For quantitative analysis, this paper investigated the effect of operations in terms of feature differences, histograms, and between-class variance among the segmented images. The following conclusions were drawn from this study: