ResUNet: Application of Deep Learning in Quantitative Characterization of 3D Structures in Iron Ore Pellets

Abstract

With the depletion of high-grade iron ore resources, the efficient utilization of low-grade iron ore has become a critical demand in the steel industry. Due to its uniform particle size and chemical composition, pelletized iron ore significantly enhances both the utilization rate of iron ore and the efficiency of metallurgical processes. This paper presents a deep learning model based on ResUNet, which integrates three-dimensional CT images obtained through industrial computed tomography (ICT) to precisely segment hematite, liquid phase, and porosity. By incorporating residual connections and batch normalization, the model enhances both robustness and segmentation accuracy, achieving F1 scores of 98.37%, 95.10%, and 83.87% for the hematite, pores, and liquid phase, respectively, on the test set. Through 3D reconstruction and quantitative analysis, the volume fractions and fractal dimensions of each component were computed, revealing the impact of the spatial distribution of different components on the physical properties of the pellets. Systematic evaluation of model robustness demonstrated varying sensitivity to different CT artifacts, with the strongest resistance to beam hardening and highest sensitivity to Gaussian noise. Multi-scale resolution analysis revealed that segmentation quality and fractal dimension estimates exhibit phase-dependent responses to resolution changes, with the liquid phase being the most sensitive. Despite these dependencies, the relative complexity relationships among phases remained consistent across resolutions, supporting the reliability of our qualitative conclusions. The study demonstrates that the deep learning-based image segmentation method effectively captures microstructural details, reduces human error, and enhances automation, providing a scientific foundation for optimizing pellet quality and improving metallurgical performance. It holds considerable potential for industrial applications.

1. Introduction

Pellets play a crucial role in the modern iron and steel industry, especially in blast furnaces and direct reduction processes. With the gradual depletion of high-grade iron ore resources and the subsequent decline in ore grades, the processing of low-grade iron ore has become increasingly important, and pellets have become an indispensable raw material for improving the efficiency of iron ore utilization and meeting steel production demands [1]. Due to their uniform size and chemical composition, pellets significantly outperform other forms of iron ore in direct reduction furnaces, making them an ideal choice for sponge iron production [2]. Furthermore, the high mechanical strength of pellets ensures their stability during transport and handling, minimizing negative impacts on downstream production processes [3].

To further enhance the production efficiency and quality of pellets, the precise analysis of their microstructure is a critical step. In this regard, deep learning algorithms have made remarkable advancements in the field of image segmentation in recent years, particularly in mineral phase segmentation, where they have shown exceptional results. Latif et al. achieved high-precision segmentation of mineral particles using ResNet, demonstrating the advantages of deep learning in automatically extracting complex image features, as well as improving segmentation accuracy and robustness [4]. Wang Yingda et al. combined the U-Net and ResNet architectures to achieve segmentation accuracies exceeding 99% in micro-CT images while effectively addressing issues such as noise interference and sample imbalance [5,6]. Additionally, Filippo et al. significantly improved the accuracy of mineral boundary segmentation by using the DeepLabv3+ model [7], and Li et al. demonstrated that applying U-Net to SEM-EDS images significantly reduces the impact of noise on classification results [8].

These advanced image segmentation techniques provide a powerful tool for the precise analysis of pellet composition. Accurate segmentation of pellet composition plays a crucial role in enhancing pellet performance and optimizing metallurgical processes. Studies have demonstrated that automated image analysis is critical for understanding the microstructure of iron pellets (e.g., porosity and oxidation degree), which directly influences macroscopic properties such as structural integrity and reduction characteristics [9]. The content of aluminum in silicate melts and hematite, along with factors like porosity and pore density, significantly affect the resistance degradation index (RDI) of the pellets. Precise control of the distribution of these various components is vital for optimizing pellet quality and improving degradation resistance [10]. Furthermore, 3D reconstruction and image segmentation techniques offer deeper insights into the spatial distribution of pellet components. Research has shown that the morphology and spatial arrangement of different components (e.g., hematite, magnetite, and silicates) within the pellet substantially influence its physical properties and compressive strength. This accurate spatial distribution analysis provides a scientific basis for further optimizing pellet performance.

2. Summary of Previous Research

The development of ore phase segmentation technology in iron ore pellets has evolved from early 2D imaging to modern 3D reconstruction and machine learning methods. Nellros and Thurley [9] first employed the Otsu thresholding method for the automated segmentation of hematite, magnetite, and pores in iron ore pellets, achieving basic mineral phase identification but still constrained by the resolution of microscopic imaging. Graça et al. [11] enhanced the precision of mineral morphology and pore characteristic identification by using electron backscatter diffraction (EBSD) to identify mineral phases and quantify microstructures. Donskoi et al. [12] proposed optical image analysis (OIA) to automate the identification of different mineral phases and their morphologies, reducing the subjectivity of manual labeling and improving efficiency.

However, traditional image processing methods, though widely applied in mineral phase segmentation, exhibit significant limitations when dealing with complex mineral phases. In recent years, the integration of industrial computed tomography (CT) and deep learning techniques has provided new solutions for the accurate segmentation of complex mineral phases [4,13]. Industrial CT can produce high-resolution 3D images of mineral samples, revealing their internal structures, which is crucial for understanding the morphology and spatial distribution of minerals. Nevertheless, traditional thresholding methods face substantial user bias and limitations in processing such data, making it difficult to handle complex mineral phase distributions. In contrast, deep learning, particularly convolutional neural networks (CNNs), has shown remarkable potential in improving segmentation accuracy and automation. CNNs extract image features layer by layer, effectively capturing complex spatial information and thus enabling accurate pixel-level segmentation [14]. Specifically, the U-Net network architecture, originally designed for biomedical images and other tasks requiring high-resolution segmentation, adopts a symmetric encoder–decoder structure. Skip connections between corresponding layers of the encoder and decoder help preserve fine-grained spatial features and achieve high-precision feature reconstruction. The key advantage of this architecture lies in its effective utilization of contextual information, enabling it to achieve ideal segmentation results even with limited training data [15].

A variety of methods combining machine learning and deep learning, such as hybrid U-Net and ResNet network architectures, have been shown to achieve high voxel accuracy and physical precision when segmenting micro-CT images of rocks [5]. In particular, in industrial CT applications, deep learning-based automatic segmentation techniques have demonstrated significant potential for reducing human error and improving the efficiency of data collection and processing [16]. One study proposed an improved U-Net network structure for mineral phase segmentation, which achieved remarkable results, particularly in addressing dolomite minerals with adhesion and unclear boundaries. The enhanced U-Net model incorporates residual blocks and introduces multi-scale parallel convolutions, which improves segmentation quality and enables accurate analysis of the content of each component of dolomite [17].

The aforementioned research confirms that image segmentation methods based on U-Net and its derivative network architectures can indeed yield accurate segmentation results in specific cases. To obtain ideal mineral phase segmentation results, this paper utilizes an improved version of the U-Net architecture, ResUNet, for mineral segmentation. This model introduces a residual connection module on top of the standard U-Net. Compared to the traditional U-Net, these improvements significantly enhance the model’s robustness, enabling it to achieve high segmentation accuracy even with a small training dataset. The flexibility of this architecture and its powerful feature-learning capacity make it particularly well-suited for the accurate segmentation of industrial mineral compositions.

3. Materials and Methods

3.1. Data Preparation

Industrial computed tomography (ICT) is a high-precision, non-destructive testing technique widely used in fields such as materials science, manufacturing, and metallurgy. ICT scans a sample from multiple angles using X-rays or other high-energy beams to acquire a series of 2D projection images, which are then processed using reconstruction algorithms to generate a 3D model of the internal structure of the sample. This technology enables high-resolution imaging of the internal microstructure of complex geometries and multi-phase materials without damaging the object’s structure. The resolution can typically reach the micron scale and is not limited by the properties of the object being tested, making it ideal for precise analysis of subtle defects, pore distribution, and phase composition [18,19].

In this experiment, pellet preparation followed a comprehensive industrial process consisting of several distinct phases. The material processing phase involved pre-proportioning of raw materials, including four types of iron concentrate (33% iron concentrate 1, 18% iron concentrate 2, 14% iron concentrate 3, and 35% iron concentrate 4), plus 5.05% lime and 0.73% bentonite. The subsequent phases included a mixing system (ensuring uniform material blending for compositional consistency), a pelletizing system (forming the mixed materials into green pellets), and a roasting system (controlled thermal treatment of green pellets in a belt calciner). The thermal treatment process was divided into multiple stages: drying (100–500 °C with 100 °C temperature gradients for 5–15 min), preheating (500–1100 °C with 200 °C temperature gradients for 5–15 min), roasting (at temperatures of 1150 °C, 1200 °C, 1220 °C, 1240 °C, 1260 °C, or 1280 °C for 7–20 min), and a soaking phase for temperature homogenization. After production, the pellets were collected, classified, and scanned using a Phoenix V|tome|x M300 industrial CT system (Waygate Technologies, Belgium) at 8 µm resolution to obtain high-resolution cross-sectional images for subsequent analysis. The industrial CT system operated at a source voltage of 110 kV and a source current of 110 µA. Figure 1 illustrates the workflow for obtaining the pellet slice data.

To effectively train the deep learning model and ensure its generalization ability in the mineral phase segmentation task for iron ore pellets, the initial data selection is crucial. Since the performance of deep learning models typically improves with an increasing amount of data [20], high-resolution CT images require careful frame-by-frame processing to ensure accurate identification and differentiation of different components, making data annotation both time-consuming and labor-intensive. In this study, we selected 16 representative CT slices from six different pellet samples as input data for the model. These slices encompass the common components and feature distributions found in iron ore pellets. The specific data annotation process is as follows.

First, the slice data were imported into the segmentation workspace in Avizo, and a label image was created. Then, under the guidance of an expert, the mineral compositions were annotated using the Brush tool in combination with the masking function. Initially, the masking threshold was set according to expert recommendations to segment voxels within a specific grayscale range, enabling the rough extraction of the region of interest (ROI). Subsequently, the brush tool was employed for manual adjustment of the annotation details, refining the boundaries of each component through human-computer interaction, thereby ensuring the accuracy of the annotation. The data annotation process for the iron ore pellet is shown in Figure 2. The main annotated components include hematite, liquid phase, and pores. In the annotation, dark blue represents pores, light blue represents hematite, and red represents the liquid phase. The same color scheme is maintained throughout the following sections. In this study, the term ‘liquid phase’ refers to the glassy or semi-crystalline binding material formed during the pellet roasting process. This phase primarily consists of silicate melts that form during the high-temperature roasting stage (1150–1280 °C for 7–20 min in our production process) when fluxing agents (such as the 5.05% slaked lime and 0.73% bentonite used in our experiments) react with siliceous gangue minerals [21]. Chemically, this phase is enriched with Si, Al, Ca, and Fe oxides, with its precise composition varying according to the specific fluxing agents and gangue minerals present in the raw materials. The liquid phase plays a crucial role in pellet strength development by forming bridges between hematite particles and filling interparticle voids, thereby significantly enhancing the mechanical integrity and metallurgical performance of the pellets.

3.2. ResUNet Network Structure

The model for pellet phase segmentation, based on the ResUNet network architecture designed in this paper, can achieve accurate semantic segmentation results with a minimal number of training images. The entire model architecture consists of three main components: the encoder, the bridge, and the decoder. The encoder extracts multi-level features from the image through layer-by-layer convolution and pooling operations, compressing the high-dimensional information in the input image into a more abstract representation. This provides a rich feature foundation for the subsequent decoder. The connection between the encoder and decoder ensures smooth transmission of information from the lower to the higher layers, which helps enhance feature expression and improve the network’s training efficiency. The decoder’s role is two-fold: it upscales and reconstructs the high-level features extracted by the encoder, gradually restoring the image resolution, and combines these with the lower-level features from the encoder to generate an accurate segmented image [15]. This encoding–decoding structure ensures an efficient connection between feature extraction and image reconstruction, which is the core design principle of many semantic segmentation models.

3.2.1. Encoder

In deep learning networks, as the network depth increases, issues such as gradient vanishing or explosion are commonly encountered. These problems can hinder the convergence of the training process and degrade model performance. To address these issues, this paper incorporates batch normalization (BN) into the encoder. The purpose of this integration is to mitigate the problems of vanishing and exploding gradients. Ioffe and Szegedy’s research shows that BN effectively reduces internal covariate shifts in deep networks, thus enhancing the training efficiency and robustness of the network [22].

To address model degradation, He Kaiming and others proposed a residual learning structure, which simplifies the training of deep networks by introducing shortcut connections between network layers, forming residual units [23]. The fundamental idea behind residual units is to learn the residuals between the input and output rather than learning the complete mapping directly, as illustrated in the following example:

$$y_l=h\left(x_l\right)+F(x_l,W_l),$$

(1)

$$x_{l+1}=f\left(y_l\right).$$

(2)

In this context, $x_l$ and $x_{l+1}$ denote the input and output of the l-th residual unit, respectively, $F(·)$ is the residual function, $W_l$ is the convolution function, $h\left(x_l\right)$ is the identity mapping function, and $f\left(y_l\right)$ is the activation function.

The proposed network architecture facilitates the efficient transmission of gradients, alleviates the training degradation problem associated with increased depth, and enhances feature representation. The encoder designed in this study consists of four downsampling units.

As shown in Figure 3a, each unit includes a max pooling layer, two 3 × 3 convolutional layers, two batch normalization (BN) layers, two ReLU activation layers, and residual mapping, which itself includes a 3 × 3 convolutional layer. The output of each downsampling unit is obtained by element-wise summing the feature map and the residual mapping, followed by processing through the BN layer and the ReLU activation layer. The output of each unit is then fed as the input to the subsequent unit, thus forming a feature channel for the decoder.

3.2.2. Bridge

The bridge module contains a downsampling unit where the max pooling layer is replaced by a dropout layer. Research by Garbin et al. indicates that when both dropout and batch normalization are used in convolutional neural networks (CNNs), careful handling is required [24]. Specifically, adjusting the dropout rate can enhance the effectiveness of batch normalization when training with larger batch sizes.

3.2.3. Decoder

The decoder consists of four upsampling units, as shown in Figure 3b. Each unit includes an upsampling layer, a 2 × 2 convolutional layer, two 3 × 3 convolutional layers, three BN layers, three ReLU activation layers, and a residual mapping, which includes a 3 × 3 convolutional layer. In addition, each upsampling unit incorporates a skip connection, which concatenates the feature map from the corresponding encoder path with the feature map from the current unit. This integration of high- and low-level features improves the representational capacity of the network. Before generating the final output, a 4-channel 1 × 1 convolution layer is applied for pixel-wise linear transformation, resulting in multi-channel prediction outputs. The softmax activation function is then used to normalize the output, ensuring that the sum of the output values for each pixel across all channels equals 1, which is suitable for multi-class segmentation tasks. For more details on the ResUNet architecture, refer to Figure 3 and

Table 1. ResUNet network structure.

	Block	Conv Layer	Filter	Output Size
Input				512 × 512 × 1
Encoder	Block1	Conv1–3	[3 × 3, 64]	256 × 256 × 64
	Block2	Conv4–6	[3 × 3, 128]	128 × 128 × 128
	Block3	Conv7–9	[3 × 3, 256]	64 × 64 × 256
	Block4	Conv10–12	[3 × 3, 512]	32 × 32 × 512
Bridge	Block5	Conv13–15	[3 × 3, 1024]	32 × 32 × 1024
Decoder	Block6	Conv16–19	[2 × 2, 512]	64 × 64 × 512
			[3 × 3, 512]
	Block7	Conv20–23	[2 × 2, 256]	128 × 128 × 256
			[3 × 3, 256]
	Block8	Conv24–27	[2 × 2, 128]	256 × 256 × 128
			[3 × 3, 128]
	Block9	Conv28–31	[2 × 2, 64]	512 × 512 × 64
			[3 × 3, 64]
Output		Conv32	[1 × 1, 4]	512 × 512 × 4

.

3.3. Image Augmentation

The training data consist of 16 images, each with dimensions of 1419 × 1065 pixels. Theoretically, our network is capable of accepting images of any size as input; however, processing larger images requires significant GPU memory for storing feature maps. Therefore, this paper adopts fixed-size training images (512 × 512 pixels, as described in Table 1) to train the network. The dataset is split such that 75% of the data are used for training to adjust the model weights, while the remaining 25% are used as a validation set to evaluate model performance and generalization ability. During training, data augmentation techniques are applied to prevent the model from becoming overly adapted to images with specific proportions, orientations, or noise types. These techniques include random horizontal and vertical flipping, random rotation (angle $\in [-{30}^{\circ },{30}^{\circ }]$), random scaling (value $\in [90\%,110\%]$), and random shearing (angle $\in [-{10}^{\circ },{10}^{\circ }]$). Additionally, to increase the diversity of the training samples, a random cropping method is employed in each iteration to process the images into 128 × 128 pixel patches.

3.4. Image Normalization

In this study, we employed the Scatter|correct technology of the Phoenix v|tome|x m300CT device for preliminary artifact suppression. This technology significantly reduces scatter artifacts in high-atomic-number material scans by measuring sample scatter and applying voxel-by-voxel compensation. Building upon this, we processed the input data using standardized normalization:

$$x^{\prime }={\displaystyle \frac{x-\mu }{\sigma }},$$

(3)

where $\mu$ and $\sigma$ represent the mean and standard deviation of the image, respectively. This normalization strategy effectively mitigates common CT imaging artifacts, such as beam hardening and ring artifacts, ensuring grayscale value comparability across different slices.

3.5. Experimental Details

The convolutional neural network development in this paper is implemented using the Keras interface with a TensorFlow backend, and the network is trained on an NVIDIA GeForce RTX 4090(NVIDIA Corporation, Santa Clara, CA, USA). The main training parameters are summarized in

Table 2. Main parameters for model training.

Hyperparameter	Value
Epoch	1500
BatchSize	24
Learning Rate	0.001

.

3.6. Evaluation Metrics

The model is evaluated using the following metrics: recall, precision, F1, and intersection over union (IoU). Their exact definitions are provided in Equations (4)–(7).

$$\mathrm{Recall}={\displaystyle \frac{TP}{TP+FN}},$$

(4)

$$\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}},$$

(5)

$$F1={\displaystyle \frac{2\times \mathrm{Recall}\times \mathrm{Precision}}{\mathrm{Recall}+\mathrm{Precision}}},$$

(6)

$$\mathrm{IoU}={\displaystyle \frac{TP}{TP+FP+FN}}.$$

(7)

True positives (TP) are indicative of the number of correctly predicted positive pixels, while false positives (FP) denote the number of incorrectly predicted positive pixels. In contrast, false negatives (FN) refer to the number of incorrectly predicted negative pixels.

4. Results

4.1. Model Evaluation

Following the conclusion of the training phase, the model is applied to the test set in order to evaluate its performance. The values of each evaluation metric for the model on the test set and the phase segmentation result map are shown in

Table 3. Model evaluation parameters.

	Recall	Precision	F1	IoU
Pores	0.9415	0.9607	0.9510	0.9065
Liquid phase	0.7497	0.9519	0.8387	0.7718
Hematite	0.9701	0.9977	0.9837	0.9679

and Figure 4, respectively. In Figure 4, blue markers represent pores, red markers represent liquid phases, and white markers represent hematite.

To assess the stability and generalization capability of the ResUNet model across different data partitions, we conducted a five-fold cross-validation experiment. Specifically, all 16 annotated images were randomly divided into five groups, with each group serving sequentially as the validation set while the remaining four groups constituted the training set. The low standard deviations of the segmentation metrics (±0.021 for hematite F1 score, ±0.034 for pores, and ±0.047 for liquid phase) demonstrate the model’s robust performance across different data splits. Notably, the slightly higher standard deviation for liquid phase segmentation aligns with the feature ambiguity of this component discussed in subsequent sections.

The segmentation results and evaluation metrics on the test set show that the model based on the ResUNet architecture exhibits strong performance in the task of segmenting the composition of iron ore pellets. The model demonstrates high segmentation accuracy for hematite and pores. However, the accuracy of liquid phase segmentation is lower compared to other components. This issue can be attributed to the ambiguous grayscale and edge features of the liquid phase in CT images, which make accurate representation difficult. For example, microcrystalline hematite in the pellet contains numerous very small micropores, which are challenging to detect due to the limited spatial resolution of CT scanning. As a result, these micropores are often merged with the surrounding matrix, leading to a decrease in pixel intensity in the synthetic images. This similarity causes errors in identifying the liquid phase in different slices during the data annotation process, and such annotation errors accumulate in the training data, affecting the model’s performance. During the model training phase, since the model relies on pixel-level features, it becomes challenging to extract significant feature differences when the grayscale features of the liquid phase closely resemble those of other components. Furthermore, the irregular and complex shape of the liquid phase imposes greater demands on the model’s ability to extract spatial features, leading to lower segmentation accuracy. Despite this, the model demonstrates remarkable robustness and reliability in identifying and segmenting the components of the iron pellet. Compared to traditional image segmentation methods, the deep learning-based model is more effective in capturing the intricate details of the pellet’s microstructure, reducing human errors, and increasing the automation of the segmentation process.

4.2. Comparative Experiments and Analysis of Segmentation Methods

To comprehensively evaluate the performance advantages of our proposed ResUNet model for iron ore pellet phase segmentation, we implemented the multi-Otsu thresholding method and a basic U-Net architecture for comparison with the proposed ResUNet.

4.2.1. Multi-Otsu Thresholding Method

The original CT images underwent preprocessing for noise reduction and enhancement, applying Gaussian filtering ($\sigma =5$) to eliminate noise and morphological operations (opening and closing) to optimize image quality. Subsequently, a single-threshold Otsu method was used for preliminary image segmentation, combined with contour analysis techniques to precisely extract the pellet body while effectively excluding edge interference elements. For three-phase segmentation, we employed the multi-Otsu thresholding method to segment the non-background region into three distinct phases. This method is based on maximizing between-class variance by solving the following optimization problem:

$$\{{\tau }_1,{\tau }_2\}=arg\underset{{\tau }_1,{\tau }_2}{max}\left\{{\sigma }_B^2({\tau }_1,{\tau }_2)\right\},$$

(8)

where ${\sigma }_B^2$ represents the between-class variance, and ${\tau }_1$ and ${\tau }_2$ are the two thresholds to be determined.

4.2.2. Basic U-Net Architecture

The basic U-Net employs the same encoder–decoder structure as ResUNet but without residual connections. This network maintains the skip connections characteristic of the U-shaped architecture for recovering spatial information lost during the segmentation process but lacks the residual learning mechanism. We trained the basic U-Net using identical training strategies and hyperparameter settings as ResUNet to ensure a fair comparison.

4.2.3. Experimental Results and Analysis

Figure 5 and Figure 6 present the comparative segmentation performance of the three methods on the test set. The results clearly demonstrate that ResUNet outperforms the other two methods across most evaluation metrics.

The experimental results reveal that for hematite, the multi-Otsu method achieved perfect precision (1.0000) but relatively low recall (0.8145), indicating its tendency to misclassify portions of hematite regions as other phases. For liquid phase segmentation, the multi-Otsu method performed poorly (IoU = 0.2836); despite high recall (0.9739), its extremely low precision (0.2853) indicates substantial misclassification of non-liquid regions as liquid phase, primarily due to significant grayscale feature overlap between the liquid phase and other phases.

The basic U-Net provided a more balanced segmentation performance compared to the Otsu method, with notable improvement in liquid phase segmentation (IoU increased from 0.2836 to 0.6123). However, compared to ResUNet, the basic U-Net still demonstrated performance gaps across all metrics. ResUNet achieved superior performance in segmenting all three phases, with particularly pronounced advantages in complex regions such as liquid phases and pores. The residual connection architecture enhanced ResUNet’s ability to learn complex mineral phase features and interface characteristics by mitigating gradient vanishing problems and improving feature propagation.

Although our data are inherently three-dimensional, we opted for a 2D slice-based approach rather than 3D volumetric modeling for several reasons: limited annotated data (only 16 representative slices) are insufficient to meet the substantial training data requirements of 3D architectures (such as 3D U-Net and VoxResNet); significantly higher computational resources and memory demands are required for 3D network training, especially with high-resolution industrial CT images; our experiment found that under current data constraints, the 2D ResUNet architecture effectively captures sufficient spatial information for high-precision segmentation while maintaining computational efficiency and generalization capability. In future work, as the annotated data volume increases and computational resources improve, we plan to explore the potential of 3D architectures for iron ore pellet phase segmentation.

4.3. Model Robustness Analysis

We systematically evaluated the ResUNet model’s performance under Gaussian noise, beam hardening, and ring artifacts. In our experiments, Gaussian noise parameters (0.01, 0.02, and 0.03) represent the standard deviation of added noise, beam hardening parameters (1.0, 0.8, and 0.6) represent gamma values for nonlinear transformation, with smaller values indicating stronger beam hardening effects, and ring artifact parameters (0.06, 0.1, and 0.14) represent relative intensity ratios, with larger values indicating more pronounced artifacts. Figure 7 illustrates examples of these artifacts under selected parameter settings.

Our experimental results revealed varying degrees of model sensitivity to different artifact types. For Gaussian noise, the segmentation performance of all components declined significantly as noise levels increased from 0.01 to 0.03. The liquid phase was most severely affected, with its IoU decreasing from 0.772 to 0.309 (approximately 60% reduction) at the 0.03 noise level, while hematite remained relatively stable but still exhibited an IoU reduction of approximately 10% at high noise levels (0.03).

For beam hardening artifacts, the model demonstrated an interesting nonlinear response. At gamma = 1, the liquid phase was most affected, with IoU decreasing from 0.772 to 0.547 (approximately 29% reduction). However, as gamma values decreased to 0.8 and 0.6, liquid phase segmentation performance unexpectedly improved, with IoU increasing to 0.734 and 0.762, respectively. This non-monotonic trend suggests that moderate beam hardening may actually enhance the contrast between certain components, benefiting the segmentation task. Hematite maintained exceptional segmentation accuracy (IoU > 0.94) across all beam hardening levels, demonstrating superior robustness.

For ring artifacts, model performance declined systematically as artifact intensity increased from 0.06 to 0.14. Under the most severe ring artifact conditions (0.14), the liquid phase IoU decreased from 0.772 to 0.365 (approximately 53% reduction), pore IoU decreased from 0.907 to 0.769 (approximately 15% reduction), and hematite IoU decreased from 0.968 to 0.892 (approximately 8% reduction). The impact of ring artifacts on model performance fell between that of Gaussian noise and beam hardening, likely because ring artifacts incorporate both systematic grayscale variations (similar to beam hardening) and local discontinuities (similar to random noise).

Comparing the impact of all three artifact types, we found that the ResUNet model generally exhibited the strongest robustness to beam hardening, followed by ring artifacts, and was most sensitive to Gaussian noise. This differential response likely stems from the residual connections and batch normalization mechanisms, which enable the model to adapt more effectively to systematic grayscale variations (such as beam hardening) while exhibiting relatively weaker resistance to random noise. Notably, moderate beam hardening even improved segmentation accuracy for certain components (such as the liquid phase), a finding with potential value for optimizing CT image preprocessing strategies.

From a component perspective, the liquid phase exhibited the highest sensitivity under all artifact conditions, primarily because its grayscale values in CT images partially overlap with other components, making classification more susceptible to artifact-induced grayscale changes. In contrast, hematite maintained high segmentation accuracy under all test conditions due to its distinctive grayscale characteristics in CT images. Even under the most severe Gaussian noise (0.03) and ring artifact (0.14) conditions, hematite’s IoU remained above 0.87 and 0.89, respectively.

Figure 8 visually demonstrates the impact of different artifact types and intensities on segmentation performance. The results confirm that despite artifact interference, the ResUNet model consistently maintains high-precision segmentation capability for hematite, while liquid phase segmentation is most sensitive to artifacts, particularly random noise and ring artifacts. Under high noise and strong ring artifact conditions, over-segmentation or under-segmentation of liquid phase regions increases significantly, while pore segmentation performance falls between these extremes.

4.4. Reliability Analysis of Phase Identification

We must acknowledge that the 8 µm CT spatial resolution employed in this study presents certain limitations for mineral phase identification, particularly for precise liquid phase characterization. This resolution constraint inevitably results in incomplete resolution of microstructural features below the detection threshold and may introduce partial volume effects and segmentation errors at phase interfaces. Accurate identification becomes especially challenging when liquid phase structures approach or fall below the 8 µm threshold.

Given these limitations, we systematically evaluated the reliability of liquid phase identification at the current resolution by analyzing the spatial continuity of segmentation results. We quantitatively assessed consistency in the liquid phase distribution between adjacent slices using the Dice similarity coefficient (DSC). The DSC, defined as twice the intersection of liquid phase regions in two slices divided by the sum of their respective areas, reflects the continuity and stability of liquid phase spatial distribution between adjacent slices. This metric is widely employed in medical and materials science image segmentation evaluation [25,26]. Our analysis revealed average spatial continuity exceeding 84% (Figure 9 and

Table 4. Statistics of continuity measures.

Metric	Value
M	84.49%
Mdn	83.32%
SD	3.63%
Skewness	−1.75
Kurtosis	16.01

). This high degree of spatial continuity indicates that the identified liquid phase structures represent genuine material features rather than noise or artifacts, even at the current resolution limit, thus confirming the reliability of our identification results.

Based on this assessment, we maintain that the 8 µm resolution provides sufficient reliability for the objectives of this study. We have accounted for these error margins when interpreting our results, and they do not significantly impact our main conclusions regarding the relationship between phase distribution and pellet characteristics.

4.5. Model Application

4.5.1. Three-Dimensional Reconstruction

The model is applied to automatically segment the entire sequence of slice images of the iron pellet. The segmentation results are then used for 3D reconstruction via direct volume rendering (DVR). DVR uses the scalar field values of the volume data to control the absorption and emission characteristics of light. By defining alpha mapping and colormap, it is possible to effectively highlight the features of different components. In this paper, a hardware-accelerated 3D texture rendering method is employed in Avizo 3D 2022.2 software to visualize the segmentation results in real-time, layer by layer, and from back to front. This approach allows for efficient and precise 3D visualization of the body data. Figure 10 and Figure 11 show the 3D structure of the pellet, pores, liquid phase, and hematite in various representations.

4.5.2. Quantitative Analysis

Volume Fraction

The volume fraction is calculated according to the following formula:

$${\varphi }_p={\displaystyle \frac{V_p}{V_{\mathrm{mask}}}}.$$

(9)

In this equation, ${\varphi }_p$ represents the volume fraction of the target label, $V_p$ represents the volume of the target label, and $V_{\mathrm{mask}}$ represents the total volume of the mask region. The volume of the target label, denoted as $V_p$, is calculated as follows:

$$V_p=\sum _{i,j,k}{I}_p(x_i,y_j,z_k)·V_{\mathrm{voxel}}.$$

(10)

In this equation, $I(x_i,y_j,z_k)$ denotes the voxel label value, which is assigned a value of “1” for voxels belonging to the target label and “0” for all other voxels. $V_{\mathrm{voxel}}$ represents the physical volume of a single voxel, calculated from the imaging resolution $(gx,gy,gz)$.

$$V_{\mathrm{voxel}}=gx·gy·gz.$$

(11)

The calculation of $V_{\mathrm{mask}}$ is performed by statistically counting all non-zero voxels in the segmented image and then aggregating their corresponding voxel volumes. The method used to calculate $V_{\mathrm{mask}}$ is the same as that for $V_p$. The results are shown in

Table 5. Fractional volume of each component of the pellet.

Pores	Liquid Phase	Hematite
9.599%	12.534%	77.867%

.

Fractal Dimension

In fractal geometry, the Hausdorff–Besicovitch dimension is one of the primary methods for calculating the fractal dimension (FD), which is used to quantify an object’s capacity to fill space. However, in many cases, the Hausdorff–Besicovitch dimension can be difficult to compute, and in some instances, its value may not even exist. As an alternative, the box-counting dimension can be used to approximate the Hausdorff–Besicovitch dimension. Extensive experiments have shown that, within a certain scale range, the box-counting dimension provides a reliable approximation of the planar or spatial complexity of an object and is referred to as the fractal parameter [27].

In this paper, the fractal dimension is used as a quantitative metric to analyze the surface complexity and geometric irregularity of the three-dimensional mineral phase model after segmentation. The fractal dimension quantifies the geometric complexity of the target surface using the box-counting method. First, the three-dimensional mineral phase model is converted into a binary image. Non-overlapping boxes of scale $ϵ$ are placed over the target area, and the number of non-empty boxes containing the target voxels, denoted as $N\left(ϵ\right)$, is counted. The fractal dimension D is then calculated using linear regression in a logarithmic coordinate system:

$$logN\left(ϵ\right)=-D·logϵ+C.$$

(12)

Among the parameters considered, D represents the fractal dimension, which reflects the spatial filling capacity of the target surface across multiple scales. A value close to three indicates a complex and rough surface, whereas a value close to two suggests a regular and smooth surface. The calculation results are presented in

Table 6. Three-dimensional fractal dimension of each component of the pellet.

Pores	Liquid Phase	Hematite
2.36	2.45	2.56

.

4.6. Effect of Spatial Resolution on Segmentation Results

Having confirmed the fundamental reliability of liquid phase identification at the current resolution, we further investigated the specific impact of spatial resolution variations on segmentation quality and fractal analysis accuracy. We designed a multi-scale analysis experiment based on downsampling, using the Lanczos algorithm to downsample the original 8 µm resolution CT images to 12 µm (1.5×), 16 µm (2×), 20 µm (2.5×), and 24 µm (3×), as illustrated in Figure 12. We then compared segmentation results and fractal dimension estimates across these different resolutions.

The Lanczos algorithm was selected for its superior preservation of edge features and structural details, providing a more realistic simulation of CT imaging results at varying resolutions.

To ensure a fair comparison of segmentation quality, we upsampled the low-resolution segmentation results to the original 8 µm resolution using nearest-neighbor interpolation and calculated Dice coefficients against the original high-resolution segmentation results. As shown in Figure 13a, decreased resolution led to reduced segmentation quality for all phases, though with varying degrees of impact. When resolution decreased from 8 µm to 12 µm, the Dice similarity coefficients compared to the original segmentation results were 0.97 for hematite, 0.95 for pores, and 0.90 for the liquid phase. A further reduction to 16 µm lowered these values to 0.95, 0.91, and 0.83, respectively. At 20 µm resolution, Dice coefficients further decreased to 0.93 (hematite), 0.89 (pores), and 0.80 (liquid phase), ultimately reaching 0.92, 0.87, and 0.76 at 24 µm resolution.

To further quantify resolution effects on segmentation quality, we calculated Dice coefficient rates of change between adjacent resolution points (Figure 13b) and percentage changes relative to the original 8 µm resolution (Figure 13c). The rate of change analysis clearly shows that the liquid phase exhibited a 10% Dice coefficient decrease between 8 µm and 12 µm, further accelerating to 7.8% between 12 µm and 16 µm. These rates substantially exceed those of hematite (3% and 2.1%, respectively) and pores (5% and 4.2%, respectively) over the same intervals. Cumulative change analysis relative to the original resolution revealed that at 24 µm resolution, the liquid phase Dice coefficient decreased by 24% overall, while hematite and pores decreased by 8% and 13%, respectively.

Through this systematic resolution sequence evaluation, we observed that segmentation quality degradation was not strictly linear, with the liquid phase demonstrating accelerated degradation in the lower resolution range. These results clearly indicate that the liquid phase, being the finest component, exhibits the highest sensitivity to resolution changes, which explains why its F1 score (83.87%) was lower than other components at the original 8 µm resolution.

For fractal dimension estimation, we observed that spatial resolution effects manifest as complex phase-dependent patterns, as illustrated in Figure 14a. The fractal dimension of the liquid phase exhibited an approximately linear decreasing trend with decreasing resolution, gradually declining from the original 2.45 to 2.44 (12 µm), 2.44 (16 µm), 2.40 (20 µm), and 2.35 (24 µm), representing an overall reduction of approximately 4.0%. Similarly, the pore fractal dimension showed a downward trend, decreasing from 2.36 to 2.33 (12 µm), 2.33 (16 µm), 2.29 (20 µm), and 2.24 (24 µm), with an overall reduction of approximately 5.1%. In contrast, the hematite fractal dimension displayed non-monotonic behavior: initially increasing with decreasing resolution from 2.56 to 2.59 (12 µm) and 2.65 (16 µm), then gradually decreasing to 2.61 (20 µm) and 2.58 (24 µm) at lower resolutions. This differential behavior likely reflects the multi-scale structural characteristics of hematite, where certain mesoscale morphological features are optimally captured at 16 µm resolution.

To further quantify resolution effects on fractal analysis, we calculated the percentage change in fractal dimension relative to the original 8 µm resolution, as shown in Figure 14b. The results indicate that within the studied resolution range (8–24 µm), fractal dimensions of liquid and pore phases can vary by up to 4%–5%, while hematite exhibits relatively smaller, non-linear variations.

Although absolute fractal dimension values vary with the resolution, the relative complexity relationships among phases remained largely consistent throughout our studied resolution range: hematite consistently exhibited the highest complexity, followed by liquid phase and pores. This finding supports the robustness of our study, suggesting that qualitative conclusions regarding phase distribution complexity remain reliable despite resolution dependencies.

5. Conclusions

In this study, the ResUNet model was employed to achieve high-precision segmentation of hematite, the liquid phase, and pores in iron ore pellet slices, yielding an average F1 score of 92.44%. This result demonstrates the effectiveness and robustness of the ResUNet architecture in handling complex multi-phase mineral structures, providing a solid foundation for subsequent 3D reconstruction and quantitative analysis.

The systematic evaluation of spatial resolution effects revealed that the liquid phase exhibited the highest sensitivity to resolution changes, with segmentation quality decreasing by approximately 24% when resolution decreased from 8 µm to 24 µm, compared to 8% for hematite and 13% for pores. Despite these resolution-dependent variations, our spatial continuity analysis confirmed the reliability of phase identification at the current 8 µm resolution, with average Dice similarity coefficients exceeding 84% between adjacent slices.

The 3D reconstruction results show that the volume fractions of pores, liquid phase, and hematite are 9.599%, 12.534%, and 77.867%, respectively. The high hematite content suggests that the pellets have a high iron content, which enhances their metallurgical properties. The presence of the liquid phase improves the binding and fluidity during the smelting process, optimizing thermal efficiency and reduction outcomes. Moreover, a reasonable porosity ensures air permeability and efficient thermal conductivity while maintaining mechanical strength.

The fractal dimensions of the three phases, as determined in 3D, were 2.36 for pores, 2.46 for the liquid phase, and 2.57 for hematite. These values indicate that the hematite phase has the most complex spatial structure, followed by the liquid phase, while the pore structure is relatively simple. Our multi-scale analysis demonstrated that while absolute fractal dimension values exhibit resolution-dependent variations (4%–5% for liquid and pore phases), the relative complexity relationships among phases remained consistent across different resolutions, supporting the robustness of our findings.

The 3D structural data and quantitative parameters obtained provide a scientific basis for optimizing the quality and metallurgical properties of iron ore pellets. High-precision mineral phase segmentation and fractal analysis offer valuable insights into the microstructural characteristics of the pellets and serve as data support for improving preparation processes and optimizing mineral phase compositions. Future research should integrate metallurgical experimental data to explore the influence of varying mineral phase ratios and fractal characteristics on metallurgical properties. This approach will enable the efficient utilization of iron ore pellet resources and the comprehensive optimization of production processes in the iron and steel industry.