Abstract
Lithology identification is a crucial step in geological research. In recent years, the development of artificial intelligence technologies has provided new insights into solving problems associated with subjectivity and labor intensity of traditional manual identification. However, when rocks are identified in situ, existing algorithms cannot accurately identify them if the image features of different types of rocks are similar or the rock textures are varied. In this regard, the study of lithology identification for the rock images captured from the field was carried out. First, the object detection algorithm of single shot multibox detector was improved by adding residual net and adaptive moment estimation, and a lithology identification model was constructed. Second, based on the above improved algorithm, the technologies of database and geographic information system were combined to develop an integrated identification method. Third, the proposed methods were applied to 12 types of rocks in Xingcheng area, China, for testing their validity, and feasibility in field geological surveys. Finally, the effects of learning rate and batch size on the identification were discussed, as the epoch number was increased. We found that the average accuracies of the improved single shot multibox detector and integrated method were 89.4% and 98.4%, respectively. The maximum accuracy could even reach 100%. The identification results were evaluated based on accuracy, precision, recall, F1-score, and mean average precision. It was demonstrated that the integrated method has a strong identification ability compared with other neural network methods. Generally, a small learning rate can lead to low loss and high accuracy, whereas a small batch size can lead to high loss and high accuracy. Moreover, the newly proposed methods helped to improve the lithology identification accuracy in the field and support the study of intelligent in situ identification for rock images.
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Introduction
Lithology identification and classification always play important roles in regional geological surveys, geotechnical engineering, and resource exploration (Pour et al., 2018; Kumar et al., 2019; Xu et al., 2021). Lithology identification can be implemented through the visual observation of rock specimens and thin or polished sections. Methodologies associated with geophysics (Bosch and McGaughey, 2001; Asfahani et al., 2015) and geochemistry (Han et al., 2018; Gleeson et al., 2020; Cheng et al., 2022) can also be used for lithology identification. However, specialized geological knowledge and experience are indispensable for traditional identification. When the number of rock samples is large, the accuracy is inevitably decreased due to human subjectivity. Hence, the study of automated and intelligent methods is important for effective lithology identification and classification. This study also makes it more convenient for scholars and technicians without petrology background to conduct lithology identification.
Artificial intelligence (AI) has developed rapidly in recent years. Image recognition technologies using artificial neural network (ANN) are among the hotspots in AI and they have been applied widely in various fields, such as monitoring cultivated land changes (Song et al., 2018), biological image classification (Qin et al., 2020), three-dimensional face recognition (Li et al., 2022), and skin attribute detection (Nguyen et al., 2022). In this regard, some studies on intelligent lithology identification have been conducted. For instance, Marmo et al. (2005) used a multi-layer perceptron neural network to develop a textural identification method for carbonate rocks. Singh and Rao (2005) implemented ore sorting and classification using a radial basis neural network. Singh et al. (2010) proposed an approach to identify textures of basaltic rock based on image processing and neural network. Chatterjee (2013) applied a multi-class support vector machine for rock-type classification of limestone, and an accuracy of 96.2% was obtained. Młynarczuk et al. (2013) conducted automatic classification of microscopic images for nine types of rocks with four pattern recognition methods. Izadi et al. (2017) proposed an intelligent system for mineral identification in thin sections based on ANN. Sun et al. (2019) optimized the logging method while drilling using machine learning algorithms for rapid lithology identification. Xie et al. (2021) developed a coarse-to-fine approach with extremely randomized trees for logging lithology identification. Xu et al. (2022) proposed an on-site identification method of rock images and elemental data using deep learning. Among the above studies, some methods successfully implemented lithology identification using rock images; however, methods for in situ lithology identification in the field are few and have yet to be improved. Moreover, as deep learning has great ability in object detection and identification, methods using deep learning show potential for rapid and accurate lithology identification.
Convolutional neural network (CNN) is an important and widely used part of deep learning. At present, CNN types used commonly in object detection include region-based CNN (R-CNN) (Girshick et al., 2014), fast R-CNN (Girshick, 2015), faster R-CNN (Ren et al., 2015), you only look once (YOLO) (Redmon et al., 2016), and single shot multibox detector (SSD) (Liu et al., 2016). Fast R-CNN and faster R-CNN were developed based on R-CNN, and R-CNN-based methods can make accurate but slow identification. Meanwhile, the methods using YOLO are fast; however, their accuracy needs to be improved. SSD combines the ideas of the grid in YOLO and the anchor in faster R-CNN; moreover, it is faster and more accurate than YOLO and faster R-CNN. SSD has thus been applied for electronic component recognition (Sun et al., 2020), remote sensing (Lu et al., 2021), and automatic driving (Chen et al., 2022). Hence, SSD can help improve the accuracy of lithology identification in the field.
In this study, SSD was improved first and an intelligent lithology identification method based on improved SSD for rock images was proposed. Then, database (DB) and geographic information science (GIS) technologies were introduced to construct an integrated identification method. The proposed methods were applied to the rocks in Xingcheng area, China. Finally, the influencing factors of the identification results were discussed.
Methods
Aiming at the problem associated with low in situ lithology identification accuracy for rocks in the field caused by complicated image features, two methods are proposed in this section: improved SSD and integrated method based on DB, GIS, and improved SSD (DGS).
Building Datasets
The prerequisite for intelligent lithology identification is building datasets, which is important for training models. During training, large amounts of labeled samples are provided to improve the accuracy and generalization ability of a network. However, limited by the manual capturing of photographs, the number of rock images from the field cannot meet the training demands. Hence, the image number is increased through data augmentation. The method of building datasets is as follows.
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Data acquisition: All photos of rock outcrops were captured from the field, and this method was different from a study that utilized images of rock samples (Xu et al., 2022); meanwhile, only one lithology was shot in one image to reduce the effect of non-rock objects, such as vegetation, and water.
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Preprocessing: The parts with contents irrelevant to the rock, such as references in the images, were removed.
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Labeling: The images captured from the field were labeled (Fig. 1) according to the features of the rock images, and the files with the suffix “.xml” were saved in the format of PASCAL Visual Object Classes.
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Augmentation: The files with the suffix “.xml” and images were augmented through (horizontal or vertical) flipping, changing the brightness (increasing to 120–150% of the original image), random fuzzification, translation, scaling, and rotation (Fig. 2). More images were obtained through augmentation. Moreover, the robustness of the model and the accuracy of the results can be improved by augmentation.
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Filtering: The augmented images were filtered by removing images that had very few or even no target rocks so that the features could be more accurately captured and extracted.
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Dividing: 80% of the filtered images were used to build a training dataset, and the remaining 20% served as the testing dataset.
Improved SSD
Network Structure
In SSD, visual geometry group network with 16 weight layers (VGG16) (Simonyan and Zisserman, 2014) is used commonly to extract image features. However, the vanishing gradient problem is caused by the increased depth of VGG16. Residual net (ResNet) helps solve this problem using the residual function (He et al., 2016). Thus, ResNet with 50 layers (ResNet50) was applied as a basic network instead of VGG16.
There were three parts in the structure of improved SSD (Fig. 3): ResNet50, extra feature layers, and prediction layer. ResNet50 was used for feature extraction. Each feature map had default boxes in different sizes. Among these default boxes, the highest layer had a scale of 0.85, the lowest layer had a scale of 0.10, and the layers in between had scales of 0.25, 0.40, 0.55, and 0.70. Extra feature layers were added to the end of ResNet50 for predictions at multiple scales, and the sizes of the layers decreased progressively. Prediction layer was used to obtain the location, confidence, and classification of the bounding boxes.
Loss Function
During identification, the loss function loss was used to indicate the difference between prediction and ground truth. The higher the value of loss, the lower the precision. The equation for loss (Liu et al., 2016) is:
where N is the number of positives, Lconf is the confidence loss, Lloc is the localization loss, and α is a weight factor, which was set to 1. The equation for Lconf is:
where Pos represents positives, which are samples belonging to the target lithology; Neg represents negatives, which are samples that do not belong to the target; \(x_{ij}^{p}\) is the indicator for matching the ith default box to the jth ground truth box of category p; and \(c_{i}^{p}\) is the confidence of lithology p for the ith default box.
The equations for Lloc are:
where l is the predicted box, g is the ground truth box; (cx, cy) is the center coordinate of the default box d; w and h are the width and height of d, respectively; \(l_{i}^{m}\), \(g_{j}^{m}\), and \(d_{i}^{m}\) are the parameters m of the ith predicted box, the jth ground truth box, and the ith default box, respectively; \(g_{o,j}^{m}\) is the offset of \(g_{j}^{m}\); \({\text{smooth}}_{{L_{1} }}\) is the robust L1 loss function (Girshick, 2015); xi and yi are the values of the target and output, respectively; and β specifies the threshold at which to change between L1 and L2 loss, which is a constant set to 1 in this study.
Optimization Strategy
The adaptive moment estimation (Adam) algorithm (Kingma and Ba, 2014) was adopted instead of stochastic gradient descent as the optimization strategy. Adam combines the advantages of adaptive gradient (Duchi et al., 2011) and root mean square propagation (Tieleman and Hinton, 2012). Hence, it can deal with sparse gradients and non-stationary objects. The equations of Adam are as follows:
where gt is the gradient of loss function f with respect to parameter θ at time step t; mt is the biased first moment estimate at time step t; vt is the biased second raw moment estimate at time step t; \(\hat{m}_{t}\) and \(\hat{v}_{t}\) are the bias-corrected first moment estimate, and bias-corrected second raw moment estimate, respectively; α is the step size; β1 and β2 are the exponential decay rates for the moment estimates; and ε is a small positive number to avoid generating a singular value.
Integrated Identification Method
DGS, a method based on improved SSD, and using the constraint provided by DB and GIS, is proposed to further improve lithology identification in the field.
Rocks of different lithology can have similar appearances. Therefore, identification using only rock images can lead to misclassifications. In most cases, historical work can provide rock information, such as location and lithology, which can be the basis for identification. Once imported into the database, the known rock information provides constraints for in situ identification for further improved accuracy. Specifically, after the preliminary identification using improved SSD, the lithology with maximum confidence was not output as an identification result. Instead, a set of lithology candidates was output as the preliminary result. According to rock location, the known lithology information in the area was obtained from the database, which was regarded as a constraint to compare with the preliminary identification result. Based on this comparison, the lithology candidate that was not in the set of known lithology was removed from the preliminary result. Then, the lithology with maximum confidence in the rest was considered the final result. If the lithology in the constraints were quite different from the candidates, only improved SSD was used and the constraints did not affect the lithology identification. Information on newly identified rocks could be imported into the database to provide the constraints for future works. In DGS, the DB technique was used to provide the constraints, the GIS technique was used to provide spatial information, and the improved SSD was used for identification. The combination of DB, GIS, and improved SSD contributed to high-accuracy in situ identification.
It should be noted that there is a prerequisite for this integrated method: the historical work has been performed in the study area (i.e., the geological background, including the lithology, is known). If no geological information was collected, only improved SSD was used. It could be inferred from the above that DGS could be adopted in many application scenarios of lithology identification. For example, exposed rocks can be identified in situ using DGS during mine production, so that the ore body can be distinguished from the surroundings and a database of lithology distribution could be built, supporting high-efficiency mining.
Compared with the improved SSD, DGS apparently helped obtain optimal identification, build the lithology database, and provide new insights into the in situ identification in the field. The steps of DGS are as follows (Fig. 4):
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Build the database for known lithology using MySQL.
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Import rock information, including location and lithology, collected from different ways into the database.
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Capture images of the rocks in the field and obtain the coordinates using a positioning tool, such as, the GPS module in cameras or smartphones.
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Import the rock images into improved SSD and simultaneously search the lithology information from the database according to the coordinates.
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Implement lithology identification using improved SSD to produce candidates and the constraints are provided by the database.
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Obtain the final result by integrating the information of the candidates and constraints and import it into the database.
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Evaluate the results with the metrics after identification (for details, see section of Assessment Methodology).
Tests and Results
The proposed methods were applied to rock images obtained from Xingcheng area, China. The tests were implemented to verify the effectiveness and feasibility of the methods.
Geological Setting and Rock Images
Xingcheng area is in the southwestern part of Liaoning Province. In terms of regional geomorphology, it is located in a coastal hilly area on the eastern margin of Heishan Hills in the West Liaoning Mountainous Region. In terms of regional tectonics, it is located north of the North China Craton. In this area, the strata are well-developed, with various types of rocks (Liang et al., 2015).
The rock images were captured from Diaoyutai, Jiashan, Longhuitou, Heiyugou, and Taili in Xingcheng area. Well-exposed rocks with distinguishing lithologic features were considered typical rocks and used for identification. Among the rock images (Fig. 5), those of biotite monzonitic granite, monzonitic granite, quartz syenite, amphibolite, diabase, and granite pegmatite were captured from Diaoyutai, those of conglomeratic feldspathic quartz sandstone and quartz conglomerate were captured from Jiashan, those of polymictic conglomerate, quartz sandstone, quartz conglomerate, and diabase were captured from Longhuitou, those of oolitic limestone were captured from Heiyugou, and those of granite pegmatite, diabase, and mylonite were captured from Taili.
In total, 1187 raw images were captured from the field using the smartphone OnePlus 6, and one target lithology was captured in one image. The location information of the rocks was acquired using the smartphone’s GPS synchronously when the photographs were captured. According to the section Building Datasets, 11870 images were finally obtained after preprocessing, labeling, augmentation, and filtering. Of these images, 80% were used to build a training dataset, and 20% served as the testing dataset.
Lithology Identification Tests
In the tests, all of the codes were written in Python language. Python tool boxes were used, including LabelImg for labeling the images, imgaug and PIL for data augmentation, and PyTorch for designing the network and calling graphics processing unit (GPU). The tests were implemented on the GPU node of the supercomputer TianHe HPC4. The node had 2 × Intel Xeon Gold 6354 18-core processors with 3.00 GHz, 2 × NVIDIA HGX A100 GPU, and 256 GB memory. The operating system was RedHat Enterprise Linux 8.4.
The built dataset was adopted to test the trained improved SSD, and the constraints were introduced by DB and GIS. The results obtained from improved SSD and DGS were compared. In Figure 6, polymictic conglomerate, quartz conglomerate, and mylonite were taken as examples to show the identification results of DGS. When the epoch number was 200, learning rate was 1 × 10−4, and batch size was 4. The identification accuracies of the improved SSD and DGS were recorded (Table 1).
As shown in Table 1, the average accuracies of the improved SSD and DGS were 89.4% and 98.4%, respectively. After introducing the constraints, the lithology candidates were removed, that might have had high confidence but did not exist in the area where the target rock was located. Hence, the accuracy could be improved and could even reach 100% for some types of rocks. Compared with the improved SSD, DGS resulted in varying degrees of accuracy improvement. However, the accuracies for biotite monzonitic granite, diabase, granite pegmatite, and polymictic conglomerate were not improved by DGS. Moreover, the accuracies for these four rocks were more than 90%. This shows that, in most cases, DGS can improve the accuracy for rocks exposed in only one area; for widely distributed rocks, the accuracy may not be improved considerably by DGS; however, DGS at least does not produce negative effects. This indicates that the proposed methods are effective and feasible. The identification ability of the improved SSD was proven to be unaffected by location, but that of DGS was related to the lithology distribution.
Discussions
As DB and GIS only provided the constraints, and the basis of DGS was the improved SSD, analyzing the factors that impact on training was important to DGS as well as the improved SSD. The identification results obtained through the training with different parameters are discussed in the following tests. The effects of parameter variations on the identification performance are analyzed.
Assessment Methodology
Assessments of identification performance were implemented during the tests.
The first was the assessment of the predicted boxes when outputting the identification result of a single image. For each image in the dataset, non-maximum suppression (NMS) was adopted for the filtering (Fig. 7). The maximum confidence of all the predicted boxes was found, and the identification result of the corresponding box was output. Hence, confidence was used as the metric to judge which box to output.
The second one was the assessment with loss for model training. The values of loss during training and testing were used typically as the metric for evaluating the network. However, as this evaluation was conducted only for training during the test, only the values of loss in the training were used.
The third assessment was made for the results of the methods. Based on the section of Building Datasets, only one type of rock was captured in each image when acquiring data. Therefore, for the improved SSD and DGS, the candidate with maximum confidence was considered the prediction result, and accuracy was equal to the ratio of correctly identified image numbers to the total image numbers, which was different from the common way. Accuracy (Acc), precision (Pre), recall (Rec), F1-score (F), and mean average precision (mAP) were used to evaluate the identification. Their equations are, respectively, as follows:
where Nc is the number of images identified correctly, N is the total number of images, mAP is the mean average precision, APi is the average accuracy of lithology i, and K is the total number of lithology.
Performance Analysis
Different learning rates and batch sizes were used for the model training. In the methods, learning rate is the stride in epochs during the training, and batch size is the sample number utilized in one iteration. The effects of parameter variation on identification performance were discussed and analyzed. The epoch number was set to 200.
First, we set batch size to 16 and learning rates to 5 × 10−2, 1 × 10−2, 5 × 10−3, 1 × 10 -3, 5 × 10−4, 1 × 10−4, and 5 × 10−5. The effect of learning rate on identification was discussed. All the other parameters and dataset were the same in the training. The values of loss (Fig. 8) and accuracies (Fig. 9) were recorded during the training with different learning rates. When the learning rate was 5 × 10−2, loss was too high, and its curve had a different shape from those of the others; therefore, it was plotted separately.
In the loss figure (Fig. 8a), as the epoch number increased, the values of loss decreased quickly and tended to stabilize, except when the learning rates were 1 × 10−2 and 5 × 10−3. Based on this test, an extremely large learning rate led to the case where loss could not decrease to a low level, such as when learning rate was 1 × 10−2. Similarly, when the learning rate was 5 × 10−3, loss had a faster convergence and smaller final value than loss obtained when the learning rate was 1 × 10−2; however, this was still unexpected. The final values of loss were 1.445 and 0.370 when the learning rates were 1 × 10−2 and 5 × 10−3, respectively, which were much higher than the values obtained when using other learning rates. When the learning rates were 1 × 10−3, 5 × 10−4, 1 × 10−4, and 5 × 10−5, the final values of loss were 0.023, 0.015, 0.005, and 0.004, respectively. These indicated that the smaller the learning rate, the smaller the values of loss. Moreover, in the first 25 epochs, the smaller the learning rate, the faster the convergence rate. However, the convergence rate was faster when learning rate was 1 × 10−4 than when the learning rate was 5 × 10−5. Figure 8b shows that when the learning rate was 5 × 10−2, loss increased and decreased repeatedly, which could even be larger than the initial value. The value of loss finally reached a large value (33.407). This proved that learning rate had a major effect on the convergence and fitting of loss, and the learning rate should not be larger than 1 × 10−3.
Based on the accuracies of the improved SSD (Fig. 9a), the final accuracies increased to varying degrees compared with the initial values. When the learning rates were 5 × 10−2, 1 × 10−2, 5 × 10−3, 1 × 10−3, 5 × 10−4, 1 × 10−4, and 5 × 10−5, the final accuracies were 9.0%, 11.9%, 27.1%, 30.6%, 24.5%, 38.1%, and 43.5%, respectively. The corresponding final accuracies of DGS were 31.9%, 34.8%, 55.5%, 57.4%, 55.8%, 67.4%, and 73.5%, respectively (Fig. 9b). These indicated that, generally, the smaller the learning rate, the higher the final accuracy. This is because large lr may have difficulty converging (Buduma and Locascio, 2017), and small lr can approximate optimal solution. In addition, the accuracies of DGS were higher than those of the improved SSD. It was demonstrated that introducing DB and GIS technologies can greatly improve accuracy. The curve shapes of the accuracies of the improved SSD and DGS were similar and showed a small tendency to increase because the improved SSD was used for identification in DGS. Moreover, how learning rate affects the values of loss, accuracy, and convergence rate should be considered for the optimal solution. Hence, 1 × 10−4 was regarded as the learning rate used for the best identification results.
Next, we set the learning rate to 1 × 10−4 and batch sizes to 4, 8, 16, 32, 64, and 128, whereas the data and other parameters were the same. The effect of batch size on identification was discussed. The results are shown in Figures 10 and 11.
As shown in Figure 10, in the first 25 epochs, the values of all the curves showed a fast convergence. As the epoch number increased, loss fluctuated. The larger the batch size, the larger the amplitude of the fluctuation. When batch sizes were 4, 8, 16, 32, 64, and 128, the final values of loss were 0.016, 0.010, 0.005, 0.004, 0.003, and 0.004, respectively. These indicated that the final values of loss decreased initially and then increased as batch size increased. Therefore, batch size should be more than 32 if a small value of loss is desired.
When analyzing the effect of batch size on accuracy, we still found that the accuracies of DGS were higher than those of the improved SSD (Fig. 11). When batch sizes were 4, 8, 16, 32, 64, and 128, the accuracies of the improved SSD were 89.4%, 59.0%, 38.1%, 24.5%, 22.3%, and 16.8%, respectively. The corresponding accuracies of DGS were 98.4%, 84.2%, 67.4%, 56.8%, 49.0%, and 50.6%, respectively. Generally, the accuracies decreased as batch size increased. For all batch sizes, the accuracy tended to be stable after training within 25 epochs. When batch size was 4, the highest accuracy was obtained and the curve had the fastest ascending rate. Because the methods with large batch sizes tended to converge to sharp minimizers and led to poor generalization, the methods with small batch sizes converged to flat minimizers (Keskar et al., 2016). In addition, a small batch size can result in more trainings so that more image features can be extracted. Although small batch size caused a large value of loss, it had better generalization for identifications of testing dataset. A proper batch size should provide high accuracy instead of a low value of loss. Hence, 4 was regarded as the optimal batch size. In Figure 11, the curve shapes of the accuracies of the improved SSD and DGS were similar. This also appears in Figure 9. Overall, although the learning rate of 1 × 10−4 and batch size of 4 could not provide minimum loss and maximum accuracy simultaneously, they were still considered the optimal parameters for the training of the improved SSD and DGS.
Finally, the improved SSD and DGS were compared with YOLOv5s to further verify the proposed methods’ superiority in in situ lithology identification. The dataset and training parameters were the same for the improved SSD, DGS and YOLOv5s. The metrics in the section of Assessment Methodology were used for evaluation (Table 2), where the values behind @ represent the thresholds of intersection over union when computing mAP. As shown in Table 2, compared with YOLOv5s, the improved SSD had higher accuracy, precision, F1-score, mAP@0.5:0.95, and close recall and mAP@0.5. The metrics of DGS showed that identification was improved to varying degrees compared with the improved SSD. As DGS was developed by adding constraints based on the improved SSD, their recalls were the same. Except for the recall, the accuracy, precision, F1-score, and mAP of DGS were superior to those of YOLOv5s. YOLOv5s has the advantage of a shorter identification time; however, the identification times of DGS and the improved SSD were also fast. Faster-RCNN was also chosen for comparison, but its metrics were very low regardless of the identification speed. Hence, Faster-RCNN was considered unsuitable for identification in this study, and its metrics are thus not shown. We demonstrated that DGS and the improved SSD were very effective in in situ lithology identification compared with other methods.
Conclusions
Aiming at solving low-accuracy problems of in situ lithology identification in the field, an improved SSD was proposed and was combined with DB and GIS to propose a method called DGS. The methods were applied to the images of typical rocks in Xingcheng area. The average accuracies of the improved SSD and DGS were 89.4% and 98.4%, respectively, and the maximum accuracies could reach 100%. The two proposed methods could identify lithology accurately. Moreover, DGS with constraints helped improve the accuracy based on the improved SSD and support future identifications by building a lithology database. A series of tests were designed and implemented to discuss the effects of various parameters on identification. Different learning rates and batch sizes were used to train the model, and the values of loss and accuracies were recorded and analyzed. Generally, the smaller the learning rate, the smaller the value of loss, the faster the convergence rate, and the higher final accuracy; the smaller the batch size, the larger the value of loss and the higher final accuracy. Furthermore, learning rate had a small impact on the ascending rate of accuracy, whereas batch size had a small impact on the convergence rate. The values of learning rate and batch size should be determined correctly, or else loss increased. Hence, the appropriate parameter combination was provided for the optimal model. In this study, the optimal parameters were a learning rate of 1 × 10−4 and batch size of 4. The superiority of the proposed methods was further proven based on various metrics, including accuracy, precision, recall, F1-score, and mAP. Compared with YOLOv5s, DGS had a stronger identification ability; however, the former had a faster identification speed. Moreover, the improved SSD and DGS were effective and feasible, and could provide new insights into and support for in situ lithology identification in the field.
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Acknowledgments
We will thank the editors and the anonymous reviewers for their work. This work was supported by Liaoning Provincial Natural Science Foundation of China (2022-MS-107), and the National Natural Science Foundation of China (42204140).
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Zhenlong, H., Jikang, W., Jinrong, S. et al. Intelligent Lithology Identification Methods for Rock Images Based on Object Detection. Nat Resour Res 32, 2965–2980 (2023). https://doi.org/10.1007/s11053-023-10271-8
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DOI: https://doi.org/10.1007/s11053-023-10271-8