Electrical trees are characterized as either of three distinctive forms, apparent by their similarity to botanical trees, which are branch, bush or a mix of both types [9]. Branch-type trees have limited branched structures with fine filamentary channels steming out only from those branches while bush-type trees possess many overlapped branches that are densely packed together appearing as a solid bush-shaped mass. Treeing growth model has been established by Dissado as a three-stage phenomenon: Stage 1: Inception, Stage 2: Propagation and Stage 3: Runaway and breakdown [10], as depicted in Fig. 1. The initiation of the electrical tree is the event where electric trees first emerge from regions with contaminants or voids, generating an electric field higher than the dielectric strength of XLPE insulation. This shift in the dielectric constant inside the material contributes to the increase of the electrical field as well as the ionization of the gas within the void, resulting in the formation of PD. Afterwards, the electrical tree will continue to grow and propagate towards the opposite electrode in the form of a branch, bush or bush-branch structure. As the tree propagates, the field at its tip will increase. At a certain moment the growth speed will begin to increase, creating a runaway of treeing just before the irreversible breakdown is triggered in the insulation material.

Over the years, electrical trees have been measured using several quantitative measurement parameters such as tree length, L, defined as the Euclidean distance from the tree initiation to the furthest tree tip in the 2D projected treeing image in the direction of the electric field and tree width, D, which represent the extent of spread of the tree channels as they grow in the 2D projected image perpendicular to the electric field [11–13] as shown in Fig. 2. Other known parameters include growth rate, dL/dt, and fractal dimension, Df, which measures the average length change rate over time and quantifies the relative space occupied by the tree, respectively. However, an electrical tree needs to be observed in a controlled HV environment and captured digitally using a standard image acquisition system to perform analysis using these parameters.

Due to the inaccessible nature of tree occurrences inside HV cable during the load operation, the electrical tree is developed artificially under a controlled HV laboratory environment for analysis. A typical treeing image acquisition setup consists of a high-voltage circuit, a charge-coupled device (CCD) camera, and a microscope system with digital recording, allowing real-time observation of the tree, which is necessary for growth analysis [14,15]. Insulation samples were designed in needle-to-plane geometry to allow electrical tree propagation from the HV source towards the other end of the electrode within the boundary of the specimen. Note that treeing activity will be monitored in real-time. The recording will later be parsed and segmented for measurement and analysis using image processing. Image analysis has been a progressive research area for years, albeit only a few publications are available regarding their application to electrical tree images. Therefore, this research presents a concise overview of the segmentation methods available, which is one of the vital stages in image processing.

The main aim of segmentation is to search for local features or regions of interest (ROI) in an image that allows them to be distinguished from other objects or backgrounds compared to the ground truth images, representing the best approximation of the ROI. For instance, in a 2D treeing image mostly comprised of two subjects, the propagation tree region and the insulation region, segmentation is performed to identify the tree region apart from its insulation background. The outcome of segmentation is a pixel-based classification performance in which performance is evaluated by various detection performance metrics such as accuracy, sensitivity, specificity, Matthew’s correlation coefficient (MCC) and more. Table 1 shows the mathematical expression for the extensively used metrics in measuring segmentation performance. Note that True Positive (TP) signifies the number of pixels or instances correctly identified as foreground, while True Negative (TN) represents positively identified background pixels. False Positive (FP) indicates the number of background pixels misclassified as foreground, while False Negative (FN) denotes the number of foreground pixels misclassified as background pixels.

Accuracy measures the proportion of correct classification, while precision metric computes the proportion of correct classification over all foreground classification. Sensitivity or recall represents the correct classified foreground pixels to the total number of foreground pixels. Specificity rate indicates the ratio of the correctly classified background pixels to the overall number of backgrounds pixels. In addition, Dice coefficient which represents the harmonic mean of precision and sensitivity, is also considered to be the most conventional standard for measuring segmentation performance. Meanwhile, MCC is said to provide much more accurate segmentation performance results unaffected by imbalanced data [16]. MCC returns the value in the range of −1 to +1, where coefficient +1 represents a perfect classification while −1 implies total misclassification.

As classified in Fig. 3, image segmentation methods can be sorted into two main groups, which are region-based and boundary-based. The thresholding method, which is mostly employed in region-based groups, separates the image pixels with respect to their intensity level. The frequently quoted Otsu’s method is one of the techniques that belong to the threshold-based family. Otsu uses global thresholding techniques that use the information of the image’s threshold histogram to form an algorithm, which returns the value of a single threshold that classifies pixels into two regions; foreground and background [17]. While in the year 2000, Sauvola and Pietika introduced a new method of threshold adjustment specifically for different types of text document analysis with various component and degradation types, including illumination and noise [18]. Instead of relying on local or global thresholds like Otsu’s, their technique used rapid image surface analysis for algorithm selection and adaptation according to document contents. It utilized the algorithm selection to compute and propose the threshold value for each pixel. Sauvola claimed to have good adaptation to various degradation types such as illumination, noise and various resolution compared to several other thresholding techniques. The Sauvola method has been employed in several recent studies to perform segmentation on complex imaging conditions [19,20]. In 2015, Tyler Coye developed an advanced variant of the threshold-based segmentation algorithm for segmenting the blood vessel of the fundus image, later known as the Coye Filter [21]. The principal component analysis (PCA) of the weighted LAB color model is used for converting the image into a grayscale. The contrast enhancement is done by adaptive histogram equalization, which excludes the background by subtracting the average filtered image. It has been proved that a variant of the Coye filter achieved the best accuracy compared to the other integrated approaches [22].

Meanwhile, boundary-based segmentation transforms images into boundary profiles by altering the image’s gray value. This can be accomplished either using an edge operator or using machine-learning techniques. Note that Prewitt, Roberts, Canny and Sobel are the most common edge operators [23,24]. In 2019, Yang proposed a method based on double vision sensors by incorporating the Roberts edge filter for measuring dam surface displacement resulting smoother edge marker of the image [25]. The method is claimed to achieve millimeter-level measurement accuracy while having the advantage of a reduced measurement period and being cost-effective. Meanwhile, Venmathi et al. [26] introduced a new detection algorithm for microcalcification clusters in mammograms image using the edge detection method by applying Kirsch’s template, which attains a good balance between suppressing the noise component and keeping edge details in mammograms images. Kirsch’s edge operator consists of 8 convolution kernels, where all 8 masks are applied to each point of the image in rotation to get the best estimation of neighboring edge pixels. In the comparison of over-detected points, closed boundaries and noise reduction, their algorithm outperformed the Canny edge filter. Another complex variation of boundary-based segmentation is the multi-scale line tracking segmentation algorithm (MSLTA), developed by Vlachos & Dermatas, intended for blood vessel segmentation in retinal images [27]. The algorithm is based on a novel seeded multi-scale line-tracking procedure to accurately determine whether the group of pixels belongs to a vessel network map derived from a brightness selection rule. The vessel network is estimated using map quantization, and median filtering is used post-processing to eliminate noise. Other than that, MSLTA boasted a performance accuracy of 92.9%, sensitivity of 74.7% and specificity of 95.5% after being tested with an image from a public database. It is also claimed that MSLTA shows good performance in the presence of noise.

Specifically, in electrical tree applications, Watson and Barber carried out electrical tree image segmentation using the thresholding method on treeing images acquired to Pascal-based VAX image processing system (VIPS) developed by their research team to study treeing in polymethylmethacrylate (PMMA) material [28]. The resulting threshold image is then converted into a single-pixel-width skeleton tree through the thinning process using the VIPS to measure tree branch lengths and fork angles. However, since manual thresholding and the thinning process were used, some tree regions were compromised, especially fainter tree branches. Furthermore, this method was unsuitable for trees with overlapped branches like bush-shaped or mixed-shaped trees. In 2009, an electrical tree fractal dimension study on XLPE was performed using the same thresholding method based on an intensity histogram by Chen and Tham, albeit with a different image processing system, a software-based imaging system, KS400 [15]. Nevertheless, since the study depended on processed tree images from the KS400 system, the image segmentation details have not been discussed further. Hence, there is inconclusive data to assess the performance. Meanwhile, Bahadoorsingh et al. [29] proposed using contrast stretching and Gaussian filtering to segment electrical images for structural characterization. The image subtraction method separated the tree region from the rest of the background. Note that the comparison with the precalculated measurement shows a percentage error of less than 3.5%. Other electrical studies that utilized image processing technique was either software-dependent or simulation-based [30,31].

It can be summarized that in recent years, classification study of electrical tree using image processing method is very limited and inadequate. In fact, most of the treeing classification studies were simulation-based where original treeing data have been heavily manipulated by the simulation algorithm to generate electrical tree structures. Therefore, utilizing image processing techniques is a step in the right direction to evaluate the segmentation algorithm's accuracy in classifying the electrical tree region from its insulation background. Since electrical tree can manifest in different growth pattern, existing literature focusing on implementing image segmentation of 2D treeing image to classify the pattern is scarce. For this reason, our proposed h-MSLTA adopted a multi-scale line tracking algorithm with the integration of batch processing method, to classify electrical tree structures in 2D images to provide a low-cost alternative in characterization of electrical trees.

The study was initiated by preparing the insulation sample for the HV treeing experiment. The XLPE material necessary for the treeing acquisition was produced in the chemical laboratory (FTKM7) in Universiti Malaysia Perlis (UniMAP), Malaysia. Samples of XLPE were prepared under heat treatment using XLPE granules of 0.922 g/cm³ density to produce thin translucent sheets of 15mm×25mm×2mm in dimension. Ogura® needle of 1 mm diameter with a tip radius of 5 ± 1 µm and tip angle of 30° was used as HV voltage electrodes, with a gap to the planar ground of 2 ± 0.5 mm. Subsequently, the aluminum tape was used as the planar ground to complete the planar-to-ground geometry specimen, as in Fig. 4. Afterwards, XLPE specimens were examined and placed in a special test chamber that connected to the HV source. As illustrated in Fig. 5, the experiment setup consists of a variable transformer, a 50 Hz 240 V/100 kV HV transformer, a 10 MΩ limiting resistor and a 1000:1 capacitive divider. A real-time digital micro-imaging system consisting of a Leica M60 stereo microscope and a charge-coupled device (CCD) camera, Leica MC170HD, which is connected to a monitoring station, was used for observation of the treeing activity. The real-time treeing observation was conducted in an electrical power laboratory at University Sains Malaysia (USM), Malaysia.

A step-by-step alternating current (AC) voltage of 1 kV with a step duration of 60 s was applied until electrical tree inception voltage (TIV) was observed. The voltage was kept fixed for the whole duration of the experiment, and the tree growth was observed until it reached ±1 mm in length as a precaution to prevent the insulation breakdown. Apart from that, the treeing activity was recorded in real-time in full high-definition (HD) resolution, which was later sampled into batches of treeing images for classification. Fig. 6 shows the XLPE sample subjected to 30 min of the treeing experiment. The electrical tree propagated in the form of bush-type tree where a dense overlapped tree branches emerged from the needle tip towards the other end of electrode can be observed.

The original 2D treeing raw video was sampled into treeing images for segmentation. The h-MSLTA algorithm is based on a multi-scale line-tracking process [27] due to the robustness in detecting boundary profiles similar to the nature of electrical tree branches. The original MSLTA belongs to the boundary-based segmentation algorithm, that initiates tracking from a small group of pixels, derived from a brightness selection rule to develop network of classified pixels belong to a path or line. However, the original line tracking algorithm was intended for single image processing at one time for a blood vessel segmentation in retinal images. To study the full nature of electrical tree growth, the propagation is observed over a certain period of time. Hence, the segmentation must also be performed by selecting images with varied time instances of experiment duration. In order to process large image data sets, we proposed the integration of batch image processing to perform pre-processing on the treeing images, as illustrated in Fig. 7. Firstly, the raw video was parsed into several treeing images based on their timestamp duration while retaining the original high-resolution quality. Then, it was stored according to their batch identification based on the acquired treeing samples. Correspondingly, images were batch processed to extract the individual green channel of the original RGB color channel for segmentation. The purpose of using only the green channel for segmentation provides a better image contrast between the tree region and the insulation background for easier classification.

The image histogram is generated from the green channel for pixel brightness estimation. TLOW and THIGH are the estimated threshold range from using the size of possible tree area from the treeing image histogram. THIGH is estimated by the background and tree pixels confidence percentile, while the threshold TLOW is estimated by the percentile of pixels that hold great confidence to belong to the background. The range of histogram area selected for h-MSLTA is approximately 20% and 70% percentile coverage, as depicted in Fig. 8. Since this brightness rule will greatly affect the algorithm’s robustness, these rates are carefully considered after performing segmentation manually on all datasets of treeing images to separate tree pixels from the rest of its background. As discussed in Subsection 2.4, the original MSLTA begins by carefully selecting a group of starting pixels derived from the brightness level range, known as seeds. Given I(x,y) as pixel brightness of the image at position (x,y), a set of starting pixels or seed denoted as Vs, which the algorithm starts tracking for a tree network, is defined as Eq. (1).

(1)Vs={(x,y):TLOW<I(x,y)<THIGH}

Consequently, the line tracking process begins where the confidence of each pixel belonging to a tree line at an odd scale W is assessed and stored in the confidence array, CW and the set of a tracking pixel, Vc are both initially set to zero, as in Eq. (2). The pixels belonging to a tree network will be determined based on a significant entry in the confidence array.

CW(x,y):=0

(2)k:=1,Vc(k):=Vs(t),Cc:={},where Vc is the set of the tracked pixels in the current iteration, t and Cc is the new line tracking pixels set which are the 8 nearest neighbors (N8) of the current tracking pixel, excluding previous Vc pixels as expressed in Eq. (3):

(3)Cc=N8(Vc(k))−Vc

Afterwards, the cross-sectional profile parameter, VI is estimated for all the candidate pixels in the Cc, using Eq. (4).

VI((x,y)),(r,θi))=I(x+[rcosθi−wsinθi],

y+[rsinθi+wcosθi])+I(x+[rcosθi+wsinθi],

y+[rsinθi−wcosθi])−2I(x+[rcosθi],

(4)y+[rsinθi],(x,y)∈Ccandw=w-12, where (r,θi) is the polar coordinate relative to pixel (x, y), while w is the width of the cross-sectional profile. The angle with maximum positive cross-sectional profile parameter, θ0, which exceeds a predefined threshold T, is used to find the new tracking pixel location in Eq. (5).

θ₀ = argmax {V_I ((x,y), (r θ_i)) : = V_I((x,y) (r,θ_i)) > T},

(5)(xc,yc)=(x+rcosθ0,y+rsinθ0)

Lastly, the current tracking pixel is added to Vc and confidence array, CW is updated.

k:=k+1,Vc(k):=(x,y)

(6)CW(x,y):=CW(x,y)+1,(x,y):=(xc,yc)

The tracking procedure for the next candidate pixel is repeated from Eq. (3). The process is executed Ts times (t=1:Ts), where Ts=length(Vs) for the entire pixels in the set of seeds Vs and for all scales, W. However, if VI in Eq. (5) is less than the threshold line, T, the tracking process is restarted for a new starting seed from the process in Eq. (2). By adopting this effective pixel elimination using the positive threshold, T, fault line detection can be reduced in the noisy treeing image. The full stages of h-MSLTA and design specification are depicted in Fig. 9 and Table 2, respectively.