In the field of mathematical morphology, the dilation regions in an image by moving the dilation process expands the bright regions in an image by moving a structuring element (SE) and selecting the maximum values; conversely, the erosion process reduces these regions by choosing the minimum values. Opening involves first eroding the image and then dilating it on the basis of the erosion; while closing involves first dilating followed by erosion. These two operations provide crucial functions for image processing. Here are the specific definitions of opening and closing [16]: (1)(f∘S)=(fΘS)⊕S (2)(f⋅S)=(f⊕S)ΘSwhere, Θ,⊕,∘and⋅ represent erosion, dilation, opening, and closing operations, respectively; S is the SE; f are the original images.

The top-hat transform is a technique used to extract image details by utilizing basic morphological operations such as erosion, dilation, opening, and closing. In morphological processing, the white top-hat transform extracts bright details by calculating the difference between the original image and the image processed by the opening operation. Conversely, the black top-hat transform extracts dark details by subtracting the image processed by the closing operation from the original image. The combination of these two transforms effectively captures fine features in the image. The following formula represents the enhancement operator [17]: (3)fe=f+(f−f∘S)−(f⋅S−f)where, fe is the enhanced image. Researches by Kang et al. and He et al. [17,18] have shown that as the scale of the structuring element increases, traditional enhancement operators can cause excessive enhancement in images. To address this issue, a differential-scale morphological enhancement operator was proposed. Based on the definitions of white and black top-hat transforms, the following differential top-hat transform is obtained: (4)ft(i+k)=f−(fΘSi)⊕Si+k (5)fb(i+k)=(f⊕Si+k)ΘSi−fwhere, ft(i+k) represents the differential white top-hat transform, fb(i+k) represents the differential black top-hat transform, Si denotes the circular structuring element of scale i, and Si+k denotes the circular structuring element of scale i+k. The differential multi-scale morphological enhancement operator is as follows: (6)fe=f+(ft(i+k)Θg−fb(i+k)Θg)where, g is a 3 × 3 structural element.

In this section, the author discusses how to select an appropriate scale for structural elements to achieve optimal image enhancement. Different scales of morphological enhancement operators need further optimization to ensure the selection of the appropriate scale size. In the research on one-dimensional signal operating, References [19–23] provided a thorough discussion on the performance of structural elements with different sizes in extracting signal features. The findings indicate that as the size of these structural elements increases, their ability to extract signal characteristics initially improves and then gradually declines.

Román et al. [24] conducted a study in the field of two-dimensional image processing, exploring the application of entropy ‘E’ in multi-scale morphological image enhancement. They proposed E as a metric to evaluate the capability of image feature extraction. This paper selected infrared images of laboratory-manufactured bubble defects and infrared thermal images of damaged WTBs as test subjects to verify the applicability of entropy in this study of enhancing defect images. Fig. 1 illustrates the trend of changes in E.

Fig. 1a,b respectively shows the normal image and infrared thermal image of a premade bubble defect, while Fig. 1d,e respectively displays the normal image and infrared thermal image of a blade crack defect. As demonstrated in Fig. 1, images captured using traditional camera techniques exhibit certain limitations in revealing defects, with defect characteristics being notably obscure. This may impact subsequent analysis and judgment processes. In light of this, the present study employs infrared acquisition as a supplementary method. Infrared imaging technology, with its sensitivity to temperature and thermal variations, effectively detects defects that are not easily identifiable in the visible spectrum. The application of this method significantly enhances the accuracy and reliability of defect detection, particularly when diagnosing surface and sub-surface damage in materials, where its advantages are even more pronounced. Fig. 1c,f shows the fitted curves of entropy variations as the structural elements gradually increase. The experimental results indicate that the trend of entropy is similar to the trend of signal feature extraction capability. As the structural elements increase, the image feature extraction capability first increases and then decreases, with an optimal scale range existing.

Entropy, as a metric to gauge the richness of information in an image, is employed here as the objective function for the adaptive differential multi-scale morphological enhancement algorithm. Its core aim is to control the termination conditions of the iterative image enhancement process by quantifying the amount of information in the image. This method leverages the characteristics of entropy to adjust the degree of image enhancement, with the goal of optimizing image quality and the readability of the information. High entropy values typically indicate that an image contains more details and information, while low entropy values suggest that the image content is relatively uniform, with less information. During the image enhancement process, by monitoring and controlling the entropy of the image, the iteration can be effectively guided, ensuring that the image maintains detail integrity and avoids noise amplification due to over-enhancement. Thus, entropy, as an objective function, provides a precise control mechanism for image enhancement, aiming to achieve the best possible image quality and information readability. Therefore, this paper proposes an iterative thresholding method based on entropy to select the appropriate scale. Entropy is a measure used to quantify the degree of disorder or complexity in an image. It is determined by calculating the histogram distribution of the image to find the probability of occurrence for each pixel intensity value. The formula is as follows [25]: (7)E(f)=−∑k=0L−1P(k)log2⁡(P(k))where, f represents the original image, k represents the pixel value in the image, and P(k) represents the probability of that pixel value occurring in the image. When the input image is a grayscale image, L=2b (where b is typically 8). The higher the value of entropy, the richer the details and information content in the image; conversely, lower entropy indicates relatively fewer details and less information content in the image.

The experimental results indicate that determining the scale i value solely based on the maximum value may lead to over-enhancement of the image. Therefore, we introduce a stopping criterion to limit the number of iterations of the enhancement algorithm. At each step, by calculating the absolute difference between the current and previous enhanced images E and dividing it by the absolute value of the current iteration E, we obtain EI to measure the degree of contrast enhancement. The calculation formula is as follows: (8)EI=|Ecurrent−Eprevious||Ecurrent|

When the measure of contrast enhancement EI exceeds a user-defined constant ζ, the iterative process is stopped. The index at this point corresponds to the most suitable structural element scale.

The method proposed in this paper enhances image detail features by iteratively adjusting the threshold of the objective function E to obtain the optimal scale interval. The specific process are as follows:

Note: The selection of the constant ζ follows these principles: Keeping the difference scale k constant, gradually adjust the scale i of the structural elements and calculate the EI values at each scale. The average of these EI values, EIA is obtained and set twice as a cut-off constant. If the EI value for a scale exceeds this cut-off constant, then that value i is selected as the optimal scale. After determining the best scale i and keeping it unchanged, the value of the differential scale k is then selected in the same way. After selecting the optimal scale i, keep it constant and repeating the selection of the value of the difference scale k. Usually, the largest EI value is chosen as the truncation constant when selecting the difference scale k because the difference scale k tends to be smaller.

To better adapt to the defect detection algorithm, the enhanced image needs to undergo grayscale inversion. The preprocessed image is shown in Fig. 2.

From Fig. 2b, it can be seen that morphological processing not only enhances the image contrast but also improves the detail features, making the edge features of defects more prominent. Additionally, grayscale inversion further optimizes the image quality, providing more suitable conditions for subsequent threshold segmentation.

The Otsu method is a technique used to separate the target and background in an image. It finds an optimal threshold by calculating the method that maximizes the between-class variance, effectively separating the target and background pixels. During the segmentation process, the Otsu method can automatically select the optimal threshold, thereby achieving image segmentation and detection processing. The between-class variance is represented as [26]: (9)σ2=ω1×μ12+ω2×μ22where ω₁ and ω₂ are the weights of the target defect pixels and background pixels, respectively. μ₁ are μ₂ the mean gray levels of the target pixels and background pixels, respectively.

If the between-class variance reaches its peak, the corresponding gray level is the threshold T determined by the Otsu method. The specific mathematical expression is as follows [26]: (10)T=arg⁡max0<t<Lσ2

When detecting defects in infrared images of WTBs, the original Otsu thresholding method has significant limitations. Due to the non-uniform brightness in the captured infrared images, the Otsu method, which is based on grayscale contrast, struggles to accurately segment the defect areas from the background on the blades. The segmentation result using the original Otsu algorithm is shown in Fig. 3.

As shown in Fig. 3, the segmentation effect of the original Otsu algorithm is not ideal. The segmentation threshold of this method is located on the right side of the peak in the histogram, while the predicted optimal threshold is at the green line at the bottom left of the histogram. Consequently, this algorithm incorrectly classifies some background pixels as crack targets, failing to accurately separate the cracks.

To improve the accuracy of defect detection and reduce the impact of uneven brightness, this study optimized the Otsu algorithm by increasing the weight of the target pixels. This adjustment makes the threshold closer to the actual grayscale value of the defects, resulting in a more accurate display of the defect locations and contours in the detection results. The calculation method of the inter-class variance for the optimized algorithm is as follows: (11)σ2=k×ω1×μ12+ω2×μ22where k represents the cumulative gradient of the grayscale values.

Cumulative gradient refers to accumulating the histogram of the image to form a cumulative gradient histogram. The peak in the cumulative histogram reflects the prominent features of the original histogram. By examining the cumulative histogram, one can more accurately identify important features in the image, thereby providing a more reliable basis for threshold selection. The calculation process for k is as follows: (12)p(t)=N(t)N (13)u(t)=∣p(t+1)−p(t)∣ (14)k=1−∑i=1tu(i)where, N(t) represents the number of pixels with a grayscale value of t, p(t) denotes the probability of the grayscale value t, and u(t) indicates the gradient value of the probability p(t). The segmentation result of the WTB infrared crack image using the improved Otsu algorithm is shown in Fig. 4.

As shown in Fig. 4, the results processed by the improved algorithm are superior to those of the original algorithm. Fig. 4c demonstrates that the segmentation threshold of the improved algorithm shifts to the left, closer to the optimal threshold. However, due to the low grayscale contrast between cracks and the background in infrared images, as well as the presence of uneven brightness, accurate segmentation of cracks cannot always be achieved. When the threshold is set too high, the detected cracks may merge with the brighter parts of the background. To address this issue, this paper proposes an adaptive threshold segmentation method to reduce the impact of uneven illumination, ensuring perfect separation of the target and background during detection. Adaptive threshold computation is widely used in the field of statistical signal processing, optimizing signal detection performance by dynamically adjusting the threshold [16,17,27]. The main process of the algorithm is as follows:

Step 1: Perform image preprocessing using differential morphological enhancement and grayscale inversion to enhance image detail features and reduce uneven brightness;

Step 2: Optimize the threshold selection process by using the threshold obtained from the improved Otsu algorithm as the initial value, denoted as TS;

Step 3: Divide the infrared defect image into two categories, target and background, based on the threshold T_S, denoted as t and b, respectively;

Step 4: Calculate the average grayscale values of t and b, denoted as At and Ab, respectively, and d use to represent the difference between At and Ab;

Step 5: The formula for the adaptive threshold calculation is as follows: (15)Tf=α×(1−1f(d))×At+(1f(d))×Abwhere, f(d)=log10⁡(10+β×d). The value range of β is [0,10], and its value is positively correlated with the average grayscale value of the image.

Step 6: If TS=Tf, then the final threshold value is T=Tf; otherwise, assign the value of Tf to TS, and repeat steps Step 3 to Step 5 until TS converges.

As observed from Fig. 5, the defect detection rate exhibits a trend with respect to the changes in α and β. An increase in α leads to a decrease in the defect detection rate, while an increase in β results in an enhancement of the defect detection rate. Although a lower value of α may yield marginally improved evaluation metrics, it could also compromise the complete detection of defects in images with low contrast. In order to balance these considerations, this study has opted for an α value of 0.65 and a β value of 10.

By applying the adaptive threshold segmentation using the improved Otsu algorithm, the segmentation effect of the improved algorithm in this paper is shown in Fig. 6.

As shown in Fig. 6, the improved algorithm not only clearly identifies the cracks but also ensures that the final threshold meets the optimal threshold criteria. Additionally, the algorithm demonstrates strong robustness when processing infrared images under conditions of uneven brightness, significantly enhancing the accuracy of defect detection in WTBs.

The experimental dataset for this study was sourced from on-site collections at wind farms in the Inner Mongolia region, as well as from pre-prepared samples in the laboratory. The dataset encompasses a variety of blade defect types, specifically including cracks, wrinkles, and bubbles. These defect types were captured using high-precision image acquisition devices to facilitate in-depth analysis. This dataset provides detailed information under both practical and controlled conditions for research into wind turbine blade damage detection techniques, thereby aiding in the development and validation of algorithms and detection methods.

Our team has developed and manufactured a continuous thermal excitation infrared non-destructive testing device, which is primarily used for blade inspection in wind farms. The experimental setup consists of the following components:

a. Two halogen lamps (with a power of 1 kW) for providing the necessary thermal energy.

b. A specialized heatproof lamp cover to ensure safety and minimize heat loss.

c. An electronic control system to regulate and manage the operation of the entire device.

d. A small motor to drive any movable parts within the equipment.

e. A computer equipped with an i7 processor for data processing and analysis.

f. An infrared thermal recorder, model NECR300W2, was used to capture thermal images of the inside of the blade.

To evaluate the performance of different algorithms in WTB detection. This study conducted a comparative analysis using the Otsu method, Xiong’s algorithm, Truong’s algorithm and Xie’s algorithm, and the improved algorithm proposed in this paper. The detection results of various methods are shown from Figs. 7–10.

From Fig. 7, it can be observed that due to the low contrast between the cracks and the background as well as the presence of uneven brightness, all three comparison methods resulted in the cracks blending with the background, failing to effectively detect the crack defects. Fig. 7e is particularly inapplicable, completely failing to detect any defects. In contrast, the method proposed in this paper can effectively segment the cracks and avoid the issue of uneven brightness. However, due to the small difference in grayscale values between the upper part of the crack and the background, it is difficult for the algorithm to distinguish effectively. Although this issue affects the performance of the method under specific circumstances, our approach still demonstrates good overall performance in most standard tests.

In Figs. 8 and 9, in scenarios where there is a high contrast between leaf defects and their background, the first three detection methods are all capable of identifying defects. However, these methods retain excessive background pixels in their detection results. Notably, Figs. 8e and 9e still fail to achieve effective defect detection. Compared to the other four detection techniques, the enhanced Otsu algorithm proposed in this study demonstrates superior performance in detecting WTB defects.

In Fig. 10, due to the high brightness of the background area on the left side of the original image, the algorithms in Fig. 10b,d only barely reveal the bubble contours, and their detection performance is extremely poor; the algorithm in Fig. 10e fails to detect the bubble defects. The algorithm in Fig. 10c detected the bubble defects’ contours well but included some false noise points within the red rectangular box compared to our method; the algorithm in Fig. 10f. Our method clearly detected the bubble contours without including noise points.

This study employs the Average Hausdorff Distance (ADH), Defect Segmentation Rate (D_SR), Misclassification Error (M_E) and structural similarity (SSIM) as evaluation metrics to objectively assess the performance of the proposed algorithm. Unlike other metrics based on confusion matrices, the Hausdorff Distance (HD) is a spatial distance-based metric. HD measures the distance between actual and predicted segmentations by focusing on contour similarity. Since HD is sensitive to outliers, most applications use the Average Hausdorff Distance. The defect segmentation rate quantifies the effectiveness of segmenting defect areas, with values ranging from 0 to 1; higher values indicate better detection performance. The higher the misclassification error, the worse the detection performance. If the M_E value is 1, it means that no defects were detected, whereas an M_E value of 0 indicates excellent detection performance. In the table, bold values represent the best metric values.