Identification of Rock Fragments after Blasting by Using Deep Learning-Based Segment Anything Model

Abstract

Rock fragmentation is an important evaluation indicator for field blasting operations. This paper applies a deep learning-based method, the Segment Anything Model (SAM), to automatically segment rock fragments. To review the SAM’s segmentation performance, 83 images of rock fragment collected from the mine site were used as the test dataset. Pixel-level accuracy (PA), intersection over union (IOU), and dice coefficient (Dice) were employed to evaluate the model pixel-level segmentation performance. The results showed that the SAM exhibited excellent segmentation performance on the test data (PA = 94.5%, IOU = 94.4%, Dice = 95.4%). The coefficient of determination (R²) values for the 50% and 80% passing sizes (X₅₀ and X₈₀) were 0.970 and 0.991, respectively, which demonstrated that the SAM could achieve high precision measurement of rock fragmentation. Additionally, the effectiveness of the SAM was further evaluated by comparing it to commercial software, and the generalizability of the SAM was verified on two other datasets. The findings revealed that the SAM not only outperformed the Split-Desktop V 4.0 on the test dataset but also achieved comparable accuracy to previous studies on the two other datasets. The SAM could be regarded as a useful tool to provide fast and accurate feedback for field blasting.

1. Introduction

Blasting technology is widely used in mining engineering for rock breaking. The size of rock fragments after blasting directly affects subsequent operations, such as shoveling, transportation, and crushing [1,2,3,4]. Maintaining appropriate rock fragment sizes can reduce blasting costs and enhance mining productivity. More importantly, it mitigates the need for a secondary blast, thereby effectively ensuring the safety of operators. The accurate measurement of a rock fragment size is crucial for achieving high efficiency, cost effectiveness, and safety in mining operations.

As an earlier attempt, empirical models were widely accepted for rock fragment prediction, and the most well-known empirical method is the Kuz–Ram model [5]. After that, several modified methods, such as the crush zone model (CZM) [6], two-component model (TCM) [7], Kuznetsov–Cunningham–Ouchterlony model (KCO) [8], and Kou–Rustan model [9], were proposed. However, these empirical models are presented in different mathematic formulas and are difficult to generalize to other datasets. An extensive review of previous studies, including WipFrag [10], Split Desktop [11], FragScan [12], Fragalyst [13], PowerSieve [14], and GoldSize [15], indicates that the image analysis methods provide more simplicity, efficiency, and accuracy compared to traditional empirical approaches. Because of this, many scholars have developed various digital image-based methods for rock fragment segmentation. For example, Amankwah and Aldrich [16] developed a modified watershed method for rock fragment segmentation. The proposed method outperformed the original watershed method in finer particles’ prediction. Sereshki et al. [17] achieved precise rock fragmentation prediction in laboratory scale by integrating filter algorithms, image binarization, edge detection, and image morphology methods. The obtained results were proven to be more accurate than Split Desktop and GoldSize software. Guo et al. [18] created an improved watershed algorithm for rock fragment segmentation using a novel seed point marking strategy. The obtained results were comparable to manual measurements. Yang et al. [19] proposed a superpixel image segmentation method combining the wavelet transform and nonlocal multiscale fractional differentiation method, achieving over 90% accuracy in particle size distribution prediction. Traditional image segmentation methods often involve cumbersome steps to achieve satisfactory results on specific data. It is challenging for them to deal with images with different brightness, shading, and surface texture characteristics. Therefore, it cannot be widely applied and promoted in engineering [19,20,21].

In recent years, deep learning-based convolutional neural networks (CNNs) have demonstrated remarkable performance across various domains of computer vision, achieving human-comparable accuracy in tasks such as image classification [22,23,24,25], object detection [26,27,28,29], and image segmentation [30,31,32]. Specifically in rock fragment segmentation, CNN-based methods have shown significant advantages over traditional image segmentation methods [21,33,34,35,36]. Guo et al. [21] proposed a network for rock fragment segmentation based on multiple CNN structures. A total of 14,628 labeled image patches, extracted from the entire blast rock pile images using data augmentation methods, were used for model development. The model performed quite well on two test images, achieving a higher R² value of 0.9989. In another study, Bamford et al. [37] collected 61,853 images of 512 × 512 size from 3301 sets of images using data augmentation methods and proposed a deep neural network (DNN) model; the size prediction error of the trained model on coarse blocks (X₅₀, X₈₀, X_max) was within ±25%, with half of the results being within ±10%. Wang et al. [20] created a multi-task CNN structure for ore segmentation, which included a boundary detection subnetwork and a mask segmentation network. The proposed model achieved robust results. Additionally, Li et al. [38] used the state-of-the-art edge detection model DexiNed network [39] and image morphology techniques to measure particle size on the conveyor belt in an aggregate crushing plant. The proposed method demonstrated its excellent capability to recognize rock edge features and successfully separated coarse fragments from fine contiguous areas. Among CNN architectures, the U-Net proposed by Ronneberger et al. [30] has become the most practical method for rock fragment segmentation due to its remarkable performance. Various extended versions have been proposed and applied in rock fragmentation prediction [40,41,42,43]. Despite their successes, these deep learning approaches heavily rely on large-scale datasets, which often necessitate tedious, time-consuming, and costly data preparation and manual labeling processes. To resolve these defects, this paper adopts the Segment Anything Model (SAM) [44], a deep learning-based image segmentation fundamental model, for automatic rock fragments’ segmentation. Unlike other deep learning models that require numerous labeled datasets for training, the SAM achieves zero-shot segmentation of rock fragments without the need for pre-prepared training data, significantly reducing manual labor costs and enhancing efficiency.

The main contents of this paper are as follows: (1) an overview of the SAM; (2) test data preparation including image acquisition, image quality analysis, and classification; (3) evaluation of the SAM’s zero-shot segmentation performance on test dataset; (4) analysis and discussion of the effectiveness and generalizability of the SAM; and (5) conclusions and perspectives.

2. Segment Anything Model

Pretrained fundamental models such as BERT [45] and GPT series models [46,47] have shown powerful application value in recent years. These large models stemmed from the emergence of big data and the advancements in computing technology. By utilizing the pretrained knowledge of these fundamental models along with appropriate prompts, they can achieve promising results on new tasks with minimal costs. Like large models in the natural language processing (NLP) field, a fundamental image segmentation model, the SAM, was first proposed in the computer vision field [44].

Most deep learning-based image segmentation models are designed for specific tasks (e.g., image semantic segmentation or instance segmentation) and are trained with the specific dataset. However, when the task changes, new datasets need to be collected and labeled to retrain or fine-tune the model to ensure good model performance. To address this limitation, the SAM, a fully automated pixel-level image segmentation fundamental model, was proposed. It was trained on more than 10 billion masks in 11 million images. The SAM achieved outstanding zero-shot segmentation performance on different image tasks without human intervention and provided an important and generalized basic framework for image segmentation within the field of computer vision. Figure 1 shows the zero-shot segmentation capabilities of the SAM on a large dataset.

The SAM consists of three modules: an image encoder, a prompt encoder, and a mask decoder. The image encoder is responsible for understanding and processing the input data, the prompt encoder aims to address the promptable information, and the mask decoder is responsible for generating the valid mask. The image encoder in the SAM employs a vision transformer (ViT-H/16) [48] pretrained using masked autoencoders (MAE) [49]. The ViT-H/16 has been adapted to handle high-resolution inputs with 14 × 14 windowed attention and four equally spaced global attention blocks. This component consists of approximately 632 million parameters and includes 32 transformer layers. The prompt encoder processes various types of prompts, categorized into sparse and dense prompts. Sparse prompts include points, represented as the sum of a positional encoding and a learned embedding indicating foreground or background, and boxes, represented by an embedding pair that includes the positional encoding of the top-left and bottom-right corners summed with learned embeddings representing these corners. For text prompts, the prompt encoder utilizes the text encoder from Contrastive Language-Image Pretraining (CLIP) to embed free-form text. Dense prompts, such as masks, are input at a 4× lower resolution than the input image and further downscaled using two 2 × 2, stride-2 convolutions followed by a 1 × 1 convolution, all separated by GELU activations and layer normalization. The mask decoder integrates the image embedding and prompt embeddings to predict the output mask. It employs a modified transformer decoder block with prompt self-attention and cross-attention (prompt-to-image and image-to-prompt) followed by a dynamic mask prediction head. This head uses a multi-layer perceptron (MLP) to map the output token to a dynamic linear classifier, computing the mask foreground probability at each image location. The mask decoder consists of two transformer decoder layers, each incorporating self-attention and cross-attention mechanisms. The entire SAM model comprises approximately 1 billion parameters, distributed across the image encoder, prompt encoder, and mask decoder. The overall structure of the SAM is shown in Figure 2. More detailed information can be found in the original paper [44] and the following website: https://github.com/facebookresearch/segment-anything (accessed on 5 April 2023).

The dataset used to train the SAM was obtained in three phases. First, annotators manually modified masks produced by the pretrained SAM while simultaneously labeling images. Subsequently, the SAM was retrained using these modified datasets. The retrained SAM then automatically generated masks for the images, and the low-confidence parts were then corrected manually, thereby increasing the variety of objects. After that, the SAM was retrained again. Finally, the labeling operation was completed entirely by the SAM, yielding a training dataset consisting of more than 10 billion masks in 11 million images.

The SAM method has been widely used in several fields, including object detection and tracking [50,51], image processing [52,53,54], and medical image analysis [55,56,57]. However, the application of the SAM in geotechnical and mining engineering, particularly in rock fragment segmentation, has not been reported. Consequently, this study comprehensively analyzed the zero-shot performance of the SAM for rock fragment segmentation.

3. Dataset

3.1. Image Acquisition

In this paper, 83 sets of images were collected from the mine site. The dataset consisted of two parts: one set of images was collected from underground and the other part was captured on the surface. A red pen and flashlight were used as size calibrators throughout the photography process, as shown in Figure 3. Notably, to ensure high-quality image acquisition conducive to accurate segmentation and analysis, specific requirements were followed: (1) Shooting Distance: The camera was positioned at a consistent distance of one meter from the rock fragments, ensuring the capture of clear and detailed images without distortion as much as possible. (2) Shooting Angle: Photographs were taken from a top-down, perpendicular angle to the rock surface whenever possible to minimize perspective distortion and accurately capture the contours of the rock fragments, thereby reducing edge deformations. (3) Lighting Conditions: Adequate and uniform lighting was employed to prevent shadows and highlights that could obscure details. Underground images were supplemented with compensating lamps, while surface images utilized natural light.

The filed images showed a diverse distribution of rock size, including fine particles, coarse grains, and a mixture of both. Additionally, the surfaces of the rock blocks obtained from underground often contained more dirt and dust, resulting in more blurred contour lines. Figure 3 shows some examples of the collected images.

3.2. Image Quality Evaluation

It is well known that image quality is closely related to the segmentation results of image analysis methods. Therefore, in this paper, we first quantitively assessed the image quality based on image sharpness and blurriness. The higher the sharpness value was, the better the image quality was. For blurriness, the smaller the value was, the blurrier the image was.

As shown in Figure 4, the sharpness values ranged from 6 to 26 and the blurriness ranged from 100 to 1500, indicating that the image dataset used in this study presented good diversity. In addition, the calculation results of the two metrics showed a similar distribution, which demonstrates that the selected image quality evaluation metrics were reasonable.

3.3. Data Categorization

To evaluate the performance of the SAM, all the images were grouped based on the obtained results of sharpness and blurriness. For this purpose, the K-means method was used for clustering and the sum of squared errors (SSE) was adopted as the loss function. The clustering loss results are shown in Figure 5. In Figure 5, the left y-axis indicates the loss of sharpness while the right y-axis represents the results of blurriness. It could be summarized that the cluster loss obtained based on the sharpness metric was the smallest, and the best K value for clustering could be determined based on the elbow method (K = 2).

As shown in Figure 6, both the sharpness and blurriness results were well categorized into two classes based on the clustering labels of the sharpness metric. This indicates that the selected sharpness metric in this paper was a better benchmark for rock image quality assessment. Then, all the testing images were ultimately divided into two groups, ranked from high-quality images to poor-quality images, with quantities of 53 and 30, respectively. In addition, no training data needed to be prepared for the SAM; therefore, all captured images were considered as test data.

4. Evaluation of the SAM

As mentioned above, all test data were categorized into two groups: high-quality images and poor-quality images. Then, the ground truth for all test images was created through manual annotations. Based on these well-labeled images, the performance of the SAM in rock fragment segmentation was analyzed in detail in terms of pixel-level segmentation accuracy and size distribution results.

4.1. Performance of the SAM on High-Quality Images

(1)

Pixel-level segmentation results

High-quality images, as defined before, were images with a sharpness value greater than 14 and less than 27. Figure 7 shows the segmentation results of four high-quality test images. As can be seen from Figure 7, different colors indicate different rock blocks, the rock block masks generated by the SAM were consistent with the manual labeling results for both large and small blocks.

The widely used image segmentation evaluation metrics, such as pixel-level accuracy ($PA$), mean intersection over union ($mIOU$), and $Dicecoefficient$, were utilized to quantitatively evaluate the pixel-level segmentation performance of the SAM, and the formulas were as follows:

$$PA=\frac{{\sum }_{i=1}^n{p}_{ii}}{{\sum }_{i=1}^n{\sum }_{j=1}^n{p}_{ij}}$$

(1)

$$mIOU=\frac{1}{n+1}\sum _{i=1}^n\frac{p_{ii}}{{\sum }_{j=1}^n{p}_{ij}+{\sum }_{j=1}^n{p}_{ji}-p_{ii}}$$

(2)

$$DiceCoefficent=\frac{2\times \left|X\cap Y\right|}{\left|X\right|+\left|Y\right|}$$

(3)

where n is the number of pixel classes in the labeled image (only the fragments and the background were considered in this study, so $n=2$), $p_{ii}$ denotes the number of pixel points for which i is predicted to be i, $p_{ij}$ represents the number of pixel points for which i is predicted to be j, and $p_{ji}$ reflects the quantity of pixel points for which j is predicted to be i. The Dice coefficient is defined as two times the intersection of the predicted segmentation (X) and the true segmentation (Y) divided by the sizes of X and Y.

Table 1. Quantitative evaluation of SAM pixel-level segmentation performance on high-quality images.

	Evaluation Metrics
SAM	PA	mIOU	Dice Coefficient
	0.955	0.953	0.960

shows the evaluation results of the SAM on all high-quality images. The scores of three evaluation indicators were 0.955, 0.953, and 0.960, respectively, indicating that the SAM exhibited excellent pixel-level segmentation capabilities when applied to high-quality data.

(2)

Block size distribution results

Additionally, the size distribution of the rock blocks was calculated. First, each segmented mask obtained by the SAM was calibrated using a size calibrator (the red marker pen was 13.7 cm × 1.8 cm in length and diameter, and the flashlight was 16 cm × 2.6 cm). Then, the fragment size was further calculated using the equivalent circle diameter as shown in Equation (4) [42]. Finally, the real-world size of the segmented blocks was obtained. The size distributions of the segmented blocks in the four test images were shown in Figure 8.

$$D=2\times \sqrt{\frac{S}{\pi }}$$

(4)

where $S$ indicates the segmentation area and $D$ is the diameter of the equivalent circle.

Based on the obtained block size distribution results, the accumulated passing percentage curve could be calculated using the Rosin–Rammler function [5], as follows:

$$R\left(x\right)=1-e^{-{\left(\raisebox{1ex}{$X$}\!\left/ \!\raisebox{-1ex}{$X_c$}\right.\right)}^n}$$

(5)

where $R\left(x\right)$ represents the proportion of material that passes through the screen, $X$ denotes the screen size in cm, $X_c$ is the characteristic size that 63.21% of the particles pass (cm), and $n$ is the uniformity index.

According to Equation (5), the characteristic size $X_c$ could be expressed as:

$$X_c=\frac{X}{\sqrt[n]{-\mathrm{l}\mathrm{n}(1-R(x\left)\right)}}$$

(6)

Furthermore, as mentioned in [5], when $X$=$X_m$, Equation (6) could also be rewritten as follows:

$$X_c=\frac{X_m}{\sqrt[n]{0.693}}$$

(7)

where $X_m$ is the mean fragment size and the value of $R\left(x\right)$ equals 0.5 when $X$=$X_m$.

Then, Equation (5) could be updated as follows:

$$R\left(x\right)=1-e^{-{0.693\left(\frac{X}{X_m}\right)}^n}$$

(8)

The value of parameter $n$ could be calculated based on the well-established formulas in the Kuz–Ram model [5]. However, another calculation method was also recommended [58,59]:

$$n=\frac{0.842}{ln{k}_{80}-ln{k}_{50}}$$

(9)

where $k_{80}$ and $k_{50}$ are the sieve sizes at 50% and 80% particle passage (cm), respectively.

Figure 9 shows the comparison results of the accumulated passing percentage obtained from the SAM and manual segmentation results on the four testing samples. The dotted lines indicate the SAM method, and the solid line represents the manual segmentation result. It can be seen that the percentage passing curves of the SAM method were very close to the manual segmentation results on the four testing images. Furthermore, the values of 10 characteristic sizes ($X_{10}$, $X_{20}$, $\dots$, $X_{100}$) of the four test images obtained by the SAM were compared with the results obtained from manual segmentation, as shown in

Table 2. Comparison results of 10 characteristic sizes obtained by the SAM and manual segmentation results of four testing images.

		Characteristic Size Parameters (mm)
		${\mathit{X}}_{10}$	${\mathit{X}}_{20}$	${\mathit{X}}_{30}$	${\mathit{X}}_{40}$	${\mathit{X}}_{50}$	${\mathit{X}}_{60}$	${\mathit{X}}_{70}$	${\mathit{X}}_{80}$	${\mathit{X}}_{90}$	${\mathit{X}}_{100}$
Image 1	True value	8.30	13.20	17.65	22.05	26.64	31.67	37.50	44.89	56.04	72.74
	SAM	7.68	12.46	16.87	21.26	25.89	31.00	36.96	44.57	56.15	67.5
Image 2	True value	13.35	19.33	24.36	29.09	33.81	38.80	44.40	51.23	61.13	111.29
	SAM	13.41	19.26	24.14	28.71	33.26	38.05	43.40	49.92	59.33	108.52
Image 3	True value	9.08	13.47	17.24	20.82	24.44	28.31	32.68	38.07	45.96	69.23
	SAM	8.98	13.05	16.50	19.75	23.00	26.44	30.30	35.02	41.88	68.08
Image 4	True value	9.38	13.73	17.42	20.91	24.41	28.13	32.32	37.45	44.92	93.16
	SAM	8.45	12.55	16.05	19.39	22.77	26.37	30.44	35.46	42.81	91.31

where $X_{10}$, $X_{20}$, $X_{30}$, $X_{40}$, $X_{50}$, $X_{60}$, $X_{70}$, $X_{80}$, $X_{90}$, and $X_{100}$ represent the size of the fragments that pass through the sieve at 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%, respectively.

. The mean absolute error (MAE), root mean square error (RMSE), and the coefficient of determination (R²) were used to quantitatively assess the SAM performance. The average results for the three evaluation indicators on the four test images were 0.04, 1.25, and 0.98, respectively.

As mentioned in Section 3.3, there were a total of 53 sets of high-quality images. Therefore, the block size distributions for all high-quality samples obtained by the SAM and the manual segmentation were summarized, as shown in Figure 10. The results of characteristic sizes $X_{10}$, $X_{20}$, $X_{30}$, $X_{40}$, and $X_{50}$ obtained by the SAM were slightly different compared to the manual segmentation results. The differences were primarily because a few images contained finer blocks. During manual labeling, these finer blocks may have been distinguished by the naked eye, while the SAM may not have been able to segment them. Moreover, overlaps or shading between small blocks may also cause the SAM to generate a larger block mask during segmentation. Except for the five characteristic sizes mentioned above, the results for the rest of the characteristic sizes ($X_{60}$, $X_{70}$, $X_{80}$, $X_{90}$, and $X_{100}$) were highly consistent with the manual segmentation results, as shown in Figure 10. Figure 11 displays the evaluation results for the obtained 10 characteristic sizes. The R² values for all the characteristic sizes except $X_{10}$ and $X_{20}$ were higher than 0.95, and the RMSE and MAE values were less than 0.1, which indicates that the SAM could provide accurate measurements of rock fragment size.

4.2. Performance of the SAM on Poor-Quality Images

In this section, the segmentation performance of the SAM on the poor-quality images is discussed. The sharpness values of these images ranged from 6 to 14, and the total number of images was 30. Most of the poor-quality images were obtained under poor environmental conditions, such as poor brightness and contour texture, more dust or dirt, uneven block sizes, and so on. The collected images are shown in Figure 12.

(1)

Pixel-level segmentation results

Figure 13 displays the segmentation results of the SAM on some poor-quality rock block images. It can be seen that the performance of the SAM was affected to some extent. For example, in image 1 and image 2 of Figure 13, the background color of the test samples is darker, which resulted in the fragments in the red box region not being well recognized. In addition, the surfaces of the rock blocks in images 3 to 8 are covered with dirt or dust, making the outlines of the rock blocks in the images unclear. As a result, it was easy to miss or misidentify certain rock blocks, e.g., multiple small blocks may have been merged into a large block, as shown in the green boxed area in Figure 13. For image 9 in Figure 13, the blocks in the boxed area are also not segmented due to the poor lighting condition and contour tracks.

Although the segmentation performance of the SAM was somewhat affected in the poor-quality images, it only performed poorly on a few rock blocks in localized areas. And the values of the three evaluation indicators were 0.936, 0.935, and 0.948, respectively. Compared with the performance on high-quality data, there was only a decrease of 1.9%, 1.8%, and 1.2%, respectively, as shown in

Table 3. Comparison of SAM pixel-level segmentation performance on high- and poor-quality images.

	Performance on High-Quality Images	Performance on Poor-Quality Images	Difference
PA	0.955	0.936	↓ 1.9%
mIOU	0.953	0.935	↓ 1.8%
Dice Coefficient	0.960	0.948	↓ 1.2%

.

(2)

Block size distribution results

In addition, 10 characteristic size values for all poor-quality images were obtained using the SAM, as shown in Figure 14. The characteristic size results from $X_{10}$ to $X_{40}$ showed some differences compared to the manual segmentation results. However, the results for the other characteristic sizes were unaffected, indicating that the image quality had no significant impact on the final results for the primary characteristic sizes, such as $X_{50}$ and $X_{80}$. Furthermore, the 10 characteristic sizes generated from the SAM and manual segmentation results were compared based on the three evaluation indexes, R², RMSE, and MRE, as shown in Figure 15. The R² value of the characteristic size larger than $X_{50}$ exceeded 0.95, and the RMSE and MRE were both less than 0.1. This demonstrated that the SAM method applied in this paper could obtain satisfactory performance even on poor-quality images.

5. Analysis and Discussion

In this section, the effectiveness and the generalizability of the SAM for rock fragmentation segmentation are discussed. First, the effectiveness of the SAM was evaluated by comparing it with commercial software (Split Desktop). Second, the generalizability of the SAM model was verified using two additional datasets collected from the previous literature.

5.1. Comparison with the Split Desktop

Split Desktop is a well-known commercial software for rock block size prediction and analysis. It is frequently utilized in real engineering applications or as an auxiliary tool for theoretical analysis in academic research. Figure 16 and Figure 17 show the segmentation results of the two types of images using the Split Desktop software and the SAM, respectively.

(1)

Comparison of pixel-level segmentation results

As shown in Figure 16, the SAM achieved comparable results to the Split Desktop software for high-quality images. Additionally, it is worth noting that the SAM method even outperformed the Split Desktop software for larger blocks or blocks with sharp contours. For example, in the areas marked by the red boxes in image 1 to image 3, the surface of these blocks is shaded; the Split Desktop software performed under segmentation, making the shadowed regions classified as the finer particles. For image 4 in Figure 16, the two blocks marked by the red boxes have sharp surface contours, and the Split Desktop software mistakenly segmented them into several small blocks, leading to over-segmentation and making the results smaller than the true values. For these cases, however, the SAM method performed extremely robustly, and all the marked blocks were accurately segmented.

Figure 17 exhibits the comparison results of the poor-quality samples. As can be seen from images 5 to 10, there were more defective segmentation objects marked in the red boxes, and many of them had low brightness, poor texture features, and dusty or dirty surfaces. The Split Desktop software failed to provide satisfactory segmentation results for such fragments, and it directly segmented them into several smaller blocks. Compared to the Split Desktop software, the SAM could give more accurate segmentation results and displayed stronger generalization capabilities.

(2)

Comparison of block size distribution results

Apart from that, the fragment size distribution results obtained by the Split Desktop and the SAM were compared, as shown in Figure 18 and

Table 4. Comparison results of 10 characteristic sizes obtained by the SAM, Split Desktop, and manual segmentation results of four testing images.

		Characteristic Size Parameters (mm)
		${\mathit{X}}_{10}$	${\mathit{X}}_{20}$	${\mathit{X}}_{30}$	${\mathit{X}}_{40}$	${\mathit{X}}_{50}$	${\mathit{X}}_{60}$	${\mathit{X}}_{70}$	${\mathit{X}}_{80}$	${\mathit{X}}_{90}$	${\mathit{X}}_{100}$
Image 1	True value	8.30	13.20	17.65	22.05	26.64	31.67	37.50	44.89	56.04	72.74
	SAM	7.68	12.46	16.87	21.26	25.89	31.00	36.96	44.57	56.15	67.5
	Split Desktop	5.20	10.21	15.04	19.82	24.81	29.50	34.00	39.14	46.21	70.12
Image 2	True value	13.35	19.33	24.36	29.09	33.81	38.80	44.40	51.23	61.13	111.29
	SAM	13.41	19.26	24.14	28.71	33.26	38.05	43.40	49.92	59.33	108.52
	Split Desktop	5.20	11.08	17.12	23.35	30.00	36.23	42.65	50.00	59.74	89.56
Image 3	True value	9.08	13.47	17.24	20.82	24.44	28.31	32.68	38.07	45.96	69.23
	SAM	8.98	13.05	16.50	19.75	23.00	26.44	30.30	35.02	41.88	68.08
	Split Desktop	3.82	8.05	12.56	17.13	22.18	26.83	31.20	37.84	45.92	75.76
Image 4	True value	9.38	13.73	17.42	20.91	24.41	28.13	32.32	37.45	44.92	93.16
	SAM	8.45	12.55	16.05	19.39	22.77	26.37	30.44	35.46	42.81	91.31
	Split Desktop	4.32	8.72	13.15	17.68	22.21	26.42	30.83	35.84	42.71	80.04

. Figure 18 exhibits the accumulated percent passing results obtained by the Split Desktop on four high-quality test images. Table 4 shows the results for the 10 characteristic sizes. Obviously, the characteristic sizes $X_{10}$, $X_{20}$, $X_{30}$, and $X_{40}$ obtained from the Split Desktop were smaller than the real values. This was mainly due to the under-segmentation of the Split Desktop, which made some blocks not fully segmented. In addition, the difference in the segmentation results between the Split Desktop and the true values tended to increase gradually in characteristic size ranges from $X_{50}$ to $X_{90}$. The main reason for this discrepancy was the over-segmentation of the Split Desktop, i.e., some large blocks were split into smaller ones. Because of this, the number of blocks with characteristic sizes between $X_{50}$ and $X_{90}$ increased, leading to large fluctuations in the corresponding values. At the same time, the value of the characteristic size $X_{100}$ was naturally smaller than the true value due to the incorrect segmentation of some large blocks into small ones. The segmentation performance of the SAM method was quite stable on the four high-quality testing images, as shown in Figure 10 and Figure 11.

The block size distribution comparisons between the Split Desktop and the SAM methods on all the high-quality images and the poor-quality images are summarized in Figure 19. The mean absolute error (MAE) was used to evaluate the accuracy of the segmentation results, as defined in Equation (10):

$$MAE=\frac{1}{M}\sum _{i=1}^M\left|y_i-y_i^{\prime }\right|$$

(10)

where $y_i$ and $y_i^{\prime }$ represent the target values and the segmentation results, respectively. $M$ is the number of testing samples.

The bars marked with red asterisks indicate the results obtained from Split Desktop, while the bars without an asterisk represented the results from the SAM. As can be seen in Figure 19, the mean absolute errors of the 10 characteristic sizes obtained by Split Desktop were higher than those obtained by the SAM method for both high-quality and low-quality data. The SAM performed more stably; the average MAE value for all characteristic sizes was less than 1. Additionally, for Split Desktop, the mean absolute errors exhibited a “U” shape from characteristic size $X_{10}$ to $X_{100}$ in both high-quality and poor-quality images, achieving the best result at $X_{50}$. According to Figure 19a,b, the mean absolute errors of all the characteristic sizes were very close to each other on both high-quality and poor-quality images, indicating that Split Desktop was also a well-developed and robust software.

5.2. Performance on Another Dataset

Furthermore, two other datasets presented in previous studies were collected to verify the generalizability of the SAM. In the study of Guo et al. [18], the authors developed an improved watershed algorithm to segment blasted rock images; two test images were used in their study to evaluate the performance of the modified watershed method. As shown in Figure 20, the two test images were also segmented by the SAM method. The developed watershed algorithm segmented almost all of the fragments, from large blocks to very small parts. However, there were some apparent errors in the second test image, as shown in the boxed region of Figure 20. Traditional image segmentation methods involve various image preprocessing steps (such as image binarization, denoising, and morphology process), and the adjusted threshold values only worked for the specified data. In contrast, the SAM applied in this paper achieved superior performance on the two test images.

The second validation test was conducted based on the data used in another study [21]. In that study, they created a deep learning-based approach to measure the size of rock fragments by combining different neural network structures. It is worth noting that the data preparation and image labeling tasks are the most time-consuming and labor-intensive tasks for training deep learning models. Nevertheless, this is an indispensable step. Consequently, a total of 14,628 images with 512 × 512 size were prepared as data in their study, and two images with sizes of 2304 × 2016 and 1408 × 2080 were used as the test data. The two testing images were applied in this paper, and the values of the 10 characteristic sizes were calculated, as shown in Figure 21. The dotted lines with square markers indicate the SAM segmentation results, the dotted lines with triangle markers are the segmentation results of the model developed by other scholars, and the dotted lines with circle markers represent the true values. In addition, Figure 22 shows the segmentation results of the test images obtained using the SAM and the previous study; the results demonstrate that the SAM could achieve comparable accuracy to the method proposed in the previous study. Moreover, the biggest advantage of the SAM is that it did not require training data for final segmentation and exhibited excellent zero-shot segmentation performance.

6. Conclusions

This paper applied a deep learning-based image segmentation fundamental method, namely, the Segment Anything Model (SAM), to achieve the automatic segmentation of rock fragments. The performance of the SAM was analyzed in detail regarding pixel-level segmentation accuracy and size distribution values. The main conclusions are as follows:

(1)

In terms of pixel-level segmentation, the SAM achieved high accuracy on all test data, with average values of 94.5%, 94.4%, and 95.4% for PA, IOU, and Dice, respectively. In addition, the R² values of the measured characteristic sizes X₅₀ and X₈₀ reached 0.97 and 0.99, respectively. The results indicate that the SAM exhibits excellent zero-shot performance on rock fragments’ segmentation.

(2)

The SAM demonstrated strong robustness and outperformed the commercial software (Split Desktop), particularly on blocks with low brightness, poor texture features, and dusty or dirty surfaces. The average MAE values for the SAM and Split Desktop on the test data were 0.936 and 6.154, respectively. Furthermore, on the two other datasets, the SAM achieved comparable accuracy to the traditional image segmentation method and deep learning-based method developed by other scholars.

(3)

Overall, the SAM produced satisfactory results in segmenting rock fragments. Based on these accurate measurements, the rapid evaluation of blasting operations and precise optimization of blasting parameters can be achieved. Moreover, potential applications of the SAM in mining and geotechnical engineering could be explored, such as mineral composition analysis and measurement of rock quality designation (RQD) based on digital images of core holes.

7. Limitations

Although the SAM model demonstrates high precision in rock fragment segmentation, our study has certain limitations. Due to the constraints associated with data collection post-blasting, we assumed that the surface rock sizes provided a representative sample of the overall rock size distribution within the pile. This assumption may not always hold true, particularly in cases of significant variation in rock size distribution within the pile. Future research should explore more comprehensive sampling methods to enhance the reliability of the findings.