Vehicle target detection method and system based on lightweight YOLOv8

Abstract

The invention provides a vehicle target detection method based on lightweight YOLOv8, on the basis of a YOLOv8 model, related parts are innovated aiming at detection precision and speed, the method is named as HAF-YOLOv8, firstly, in order to avoid that a backbone network of a detector extracts redundant features, and then, the backbone network of the detector extracts the redundant features; the Faster Net containing the PConv is used for reducing redundant calculation and memory access and extracting spatial features more effectively at the same time; then, a focus modulation-based self-adaptive adjustment view field mechanism FocalNet is used for replacing an original SPPF method, and compared with a self-attention mechanism, the method has a simpler calculation process and lower complexity; and finally, selecting a converter Bi-Former of a double-layer routing dynamic sparse attention mechanism as a newly added module of the backbone network at the end of the backbone network, and filtering out the most irrelevant area to save the parameter quantity and the calculation quantity so as to realize more flexible and effective calculation distribution and content awareness.

Description

Technical Field

[0001] The present invention belongs to the technical field of deep learning and relates to a vehicle target detection method and system based on lightweight YOLOv8. Background Art

[0002] With the advancement of the process of building a strong transportation country, my country has made significant progress in the construction and upgrading of highway transportation infrastructure. According to statistics, in the past five years, the mileage of my country's highways has increased from 136,000 kilometers to 177,000 kilometers, forming a more complete transportation network system that connects all parts of the country and provides important support for economic and social development. However, with the prosperity of the economy and the increase in the diversity of people's travel options, the number of cars has reached new highs, and the number of vehicles on highways has also gradually increased, which has brought greater pressure on highway traffic safety issues, and also brought new opportunities and challenges to the sustainable development of my country's transportation industry.

[0003] In order to meet the rapidly growing traffic needs, target detection technology has been widely used in the field of intelligent transportation systems, including unmanned driving, assisted driving, and vehicle abnormal event detection. In practical applications, not only high model detection accuracy is required, but also extremely high model reasoning speed is required. Especially in the first GigaVision Challenge in 2020, it can be seen that vehicle detection and recognition has very high practical value in people's daily lives. Correctly extracting the location of the vehicle in the video image can effectively solve various problems in vehicle congestion, vehicle registration, and vehicle scheduling.

[0004] With the rapid development of technologies such as computer vision, image processing, and pattern recognition, vehicle detection and recognition technology has also made significant progress. Traditional vehicle detection methods first use image processing technology to obtain the location of the vehicle in the image, then extract valuable features, and use classifiers for classification. This is usually a vehicle recognition technology under shallow learning, which usually uses simpler models and feature representations to complete the task. Although shallow learning methods have achieved certain achievements in vehicle recognition, especially in the early stages. Its advantage is that the model is relatively simple, easy to understand and implement, and for some simple scenes and tasks that are not too demanding, shallow learning methods can achieve good results. In addition, since shallow learning methods have relatively low requirements for computing resources, they can also play a role in some resource-constrained environments. Traditional vehicle recognition and tracking technologies have been the main means for traffic management departments to track vehicle locations and status for a long time, but they often rely on manual operations or rule-based computer vision methods. For example, manual monitoring cameras record vehicle locations, or identify and track vehicles based on pre-defined rules and features such as vehicle color, size, and shape.

[0005] These traditional methods have certain limitations, such as being easily affected by factors such as weather and environment, and requiring more human or material resources. First, it usually requires manual design of feature extraction algorithms, and the selection and extraction of features rely on manual experience, which may be limited when dealing with complex and changeable vehicle images. Secondly, shallow learning methods usually do not perform as well as deep learning methods for nonlinear and complex pattern recognition tasks because it is difficult to automatically learn complex abstract features and patterns. With the rise of deep learning methods, deep learning-based vehicle recognition uses deep neural networks and artificial intelligence technology to detect vehicles, especially the successful application of convolutional neural networks (CNN), which has made great breakthroughs in vehicle detection and recognition technology. Deep learning can automatically learn features and perform advanced pattern recognition through training with large-scale data sets, thereby achieving robust detection and recognition of complex scenes and occlusion situations. This technology can not only reduce resource waste and meet management needs, but also cope with the variability of complex scenes and improve the accuracy and reliability of vehicle detection. By using deep learning models, such as Region-based Convolutional Neural Networks (R-CNN), Fast R-CNN, One-Stage Detectors, etc., researchers have achieved remarkable results in vehicle detection and recognition, and then widely promoted and further innovated them in applications such as traffic management and intelligent transportation systems, urban safety and public security monitoring, intelligent parking systems, logistics distribution and warehousing management, providing technical support for achieving more efficient and safer levels of intelligent traffic management and promoting the sustainable development of road traffic.

[0006] Although the two-stage target detection algorithm is constantly being improved and optimized, the detection performance has been greatly improved. However, since the two-stage target detection algorithm has to go through complex feature extraction and calculation, it cannot meet the real-time requirements. Therefore, a single-stage target detection algorithm is proposed. The core idea of ​​this algorithm is to transform the target classification problem into a regression problem of the target detection box and the bounding box. The position of the object can be directly predicted from the input image, meeting the requirements of real-time image processing.

[0007] At present, due to the small size of vehicles, it is necessary to deploy edge detection equipment on the vehicle, such as Nvidia Jetson Nano, etc., but the computing power of the on-board equipment is insufficient and it is impossible to deploy a computing-intensive network; at the same time, the lightweight methods proposed in current research have problems such as low detection accuracy to a certain extent. Therefore, vehicle detection and recognition technology should continue to improve to better meet actual needs. Summary of the invention

[0008] In order to solve the problems existing in the prior art, the present invention provides a vehicle target detection method based on lightweight YOLOv8. On the basis of the YOLOv8 model, innovations are proposed for relevant parts in terms of detection accuracy and speed, and this method is named HAF-YOLOv8. Firstly, in order to avoid the detector backbone network from extracting redundant features, FasterNet containing PConv is used to reduce redundant calculations and memory accesses while more effectively extracting spatial features; then, FocalNet, an adaptive adjustment field of view mechanism based on focal modulation, is used to replace the original SPPF method, which has a simpler calculation process and lower complexity than the self-attention mechanism; finally, at the end of the backbone network, a converter (Bi-Former) of a double-layer routing dynamic sparse attention mechanism is selected as a new module of the backbone network, which saves parameters and calculations by filtering out the most irrelevant areas, so as to achieve more flexible and effective calculation allocation and content perception.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is: In a first aspect, the present invention provides a vehicle target detection method based on lightweight YOLOv8, comprising the following steps: The enhanced image data is input into the trained HAF-YOLOv8 model, which is processed by the FasterNet module, the Focal-Modulation Net module, and the Bi-Former module in turn to obtain a new feature set. Perform false positive prediction and splicing on the new feature set to achieve image enhancement; The enhanced images are passed through the HAF-YOLOv8 model again to obtain the final recognized image set.

[0010] Furthermore, the three-dimensional feature map Enter FasterNet and use it for each channel The single-channel convolution and kernel are deep convolution to obtain the output with the same number of channels as the original feature map; the output feature map of the deep convolution is then fused with channels using a 1×1 convolution kernel, i.e., point-by-point convolution; the two are residually connected to enhance their stability and feature reuse capabilities; finally, activation functions and batch normalization are used to introduce nonlinearity and accelerate training to improve the generalization ability of the model, and finally the output feature map of FasterNet is obtained.

[0011] Furthermore, Focal-Modulation Net first aggregates features and interacts the query with the aggregated features to fuse contextual information; the aggregation process includes: extracting contextual information from local to global scope at different granularity levels through hierarchical contextualization; Through gated aggregation, all contextual features at different levels of granularity are condensed into a single feature vector.

[0012] Furthermore, through hierarchical contextualization, context information is extracted from local to global scope at different granularity levels: given an input feature map , firstly map the feature Projected into a new feature space, the new feature space has a linear layer ;use Depth-wise convolution obtains the hierarchical representation of the context and outputs It is expressed as:

[0013] Hierarchical contextualization generates L-level feature maps, in the Apply global average pooling on the level feature map , get the total Level feature map , The level feature maps jointly capture local and long-range contexts at different levels of granularity.

[0014] Furthermore, through gated aggregation, all contextual features at different granularity levels are condensed into a single feature vector including: Use linear layers to obtain spatially and level-aware gating weights ; Perform a weighted sum by element-wise multiplication to get the same value as the input A single feature map of the same size :

[0015] in, It is A channel of level; Using a linear layer Get the modulator .

[0016] Furthermore, in the feature map input to the Bi-Former module, queries are obtained by linear mapping ,keys ,values , the attention mechanism of the Bi-Former module represents the correlation between two regions through the adjacency matrix:

[0017] According to the adjacency matrix , only the front of each region is retained Links, get the routing index between areas with high correlation:

[0018] By collecting tensor indexes of key-value pairs and , and then focus on the collected key-value pairs, as follows:

[0019] It is a local context enhancement item.

[0020] Furthermore, false positive prediction and splicing are performed on the new feature set to enhance the image, including: The optimized images are stitched together, and the stitched images are denoised and sharpened.

[0021] In a second aspect, the present invention provides a vehicle target detection system based on lightweight YOLOv8, including a feature extraction module, an image enhancement module and a recognition module; The feature extraction module is used to input the enhanced image data into the trained HAF-YOLOv8 model, which is processed by the FasterNet module, the Focal-Modulation Net module, and the Bi-Former module in turn to obtain a new feature set; The image enhancement module is used to perform false positive prediction and splicing on the new feature set to achieve image enhancement; The recognition module is used to pass the enhanced images through the HAF-YOLOv8 model again to obtain the final recognized image set.

[0022] In a third aspect, the present invention may also provide a computer device, including a processor and a memory. The memory is used to store a computer executable program, and the processor reads and executes the computer executable program from the memory. When the processor executes the computer executable program, the vehicle target detection method based on lightweight YOLOv8 described in the present invention can be implemented.

[0023] At the same time, the present invention provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the vehicle target detection method based on lightweight YOLOv8 described in the present invention can be implemented.

[0024] Compared with the prior art, the present invention has at least the following beneficial effects: First, in order to avoid the detector backbone network from extracting redundant features, FasterNet containing PConv is used to reduce redundant calculations and memory accesses while extracting spatial features more efficiently. Then, FocalNet, an adaptive adjustment field of view mechanism based on focus modulation, is used to replace the original SPPF method, which has a simpler calculation process and lower complexity than self-attention. Finally, at the end of the backbone network, a converter (Bi-Former) of a double-layer routing dynamic sparse attention mechanism is selected as a new module of the backbone network, which saves parameters and calculations by filtering out the most irrelevant areas, so as to achieve more flexible and effective calculation allocation and content perception; the present invention integrates the three modules of FasterNet, FocalNet and Bi-Former into the YOLOv8 network; wherein FasterNet is placed in the backbone to reduce GFLOPs, and FocalNet is used to replace the backbone SPPF to better focus the field of view on the feature area, and Bi-Former is added to the last layer of the backbone to enhance the feature extraction capability of the network. The present invention combines a new paradigm for vehicle detection, and after the TensorRT quantization model is used, the detection speed is further improved without losing detection accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is the overall framework diagram of the present invention; Figure 2 This is a specific structural diagram of the FasterNet part of the present invention; Figure 3 This is a specific structural diagram of the FocalNet part of the present invention; Figure 4 This is a specific structural diagram of the Bi-Former part of the present invention; Figure 5 This is a performance comparison chart of the present invention and other typical methods in various aspects on the Road-Vehicle dataset.

[0026] Figure 6 The present invention is a flowchart of an implementable method. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] Combined with Figure 1, Figure 6 The invention is described in detail with each part of the method. The invention proposes a high-precision, efficient and lightweight YOLOv8 vehicle target detection method, which improves three key modules and has obtained less calculation amount and higher detection accuracy.

[0029] Step 1: standardize and enhance the collected image data set; Step 2: Input the enhanced image data into the HAF-YOLOv8 algorithm framework, which includes three modules: FasterNet, FocalNet, and Bi-Former; and obtain a new feature set; Step 3, performing false positive prediction and splicing on the new feature set to enhance the image again; splicing the optimized image, and denoising and sharpening the spliced ​​image; Step 4: Pass the newly enhanced image through the HAF-YOLOv8 framework again to obtain the latest recognized image set, output it and end.

[0030] like Figure 2 As shown, the three-dimensional feature map Enter FasterNet and use it for each channel Single-channel convolution and kernel are used for deep convolution to obtain the output with the same number of channels as the original feature map; then the output feature map of the deep convolution is fused with channels using a 1×1 convolution kernel, i.e., point-by-point convolution; the two are connected with residuals to enhance their stability and feature reuse capabilities; finally, activation functions and batch normalization are used to introduce nonlinearity and accelerate training to improve the generalization ability of the model, and finally the output feature map of FasterNet is obtained; the FasterNet module containing efficient convolution PConv is introduced on the original YOLOv8 backbone network. Compared with the original Conv in YOLOv8 which only performs simple tensor numerical operations on the input data, PConv can extract spatial features more effectively while reducing redundant calculations and memory accesses. The FLOPs of PConv is , the FLOPs of a typical PConv is only 1 / 16 of that of a regular Conv. In addition, PConv has a smaller memory access, i.e., for r=1 / 4, it is only 1 / 4 of that of a regular Conv. In order to avoid Pconv from degenerating into a regular Conv with fewer channels, PWConv is further attached to PConv to fully and effectively utilize information from all channels. Similarly, the FLOPs of PConv and PWconv are:

[0031] The FLOPs is much smaller than that of Conv, so the FasterNet module can be obtained and added to the improved model of the present invention as a part of the optimization.

[0032] like Figure 3 As shown, in order to expand the receptive field, Focal-Modulation Net uses farther summarized tokens to capture coarse-grained, long-distance visual dependencies through focal modulation. As shown in the figure, features are aggregated first, and then queries interact with aggregated features to fuse contextual information. This method greatly simplifies the calculation process by decoupling aggregated features from a single query. The formula is as follows:

[0033] Polymerization process It consists of two steps: first, hierarchical contextualization to extract contextual information from local to global range at different granularity levels, and second, gated aggregation to condense all contextual features at different granularity levels into a single feature vector, i.e., the modulator. As an example, given an input feature map , first projecting it into a new feature space with a linear layer , then use Depth-wise convolution obtains the hierarchical representation of the context and outputs It is expressed as:

[0034] Hierarchical contextualization generates L-level feature maps. In order to capture the global context of the entire input, Apply global average pooling on the level feature map The total Level feature map , The level feature maps jointly capture local and long-range contexts at different levels of granularity.

[0035] like Figure 4 As shown in the gated aggregation, a gating mechanism is used to control each query from different levels of feature graphs. Specifically, a linear layer is used to obtain spatially and level-aware gating weights ,The gating weight G is a dynamic weight mechanism, generated by the gating function, which depends on different sizes and levels. Here, L is the level, HW is the spatial size, and the function is the weight matrix obtained by two parts and three scales to obtain the gating weight G. Then decide which information should be retained.

[0036] Then, a weighted sum is performed by element-wise multiplication to obtain the same value as the input A single feature map of the same size .

[0037]

[0038] in, It is level. So far, all aggregations have been spatial aggregations. To model the relationship between different channels, another linear layer is used. Get the modulator .

[0039] The self-attention mechanism will cause serious scalability problems related to the spatial resolution of the input due to its high complexity of multi-head attention. Therefore, the present invention introduces a dynamic sparse attention Bi-Former module through double-layer routing awareness to achieve more flexible computing allocation and content awareness, so that it has dynamic query-aware sparsity. The key idea is to filter out most of the irrelevant key-value pairs at a coarse granularity and only retain a small part of the routing area to save parameters and computation.

[0040] In the input feature map, queries are obtained by linear mapping ,keys ,values , the attention mechanism of the dynamic sparse attention Bi-Former module is through the adjacency matrix (representing the correlation between two regions):

[0041] According to the adjacency matrix, only the first links to obtain routing indexes between areas with high correlation:

[0042] Finally, by collecting the tensor index of the key-value pairs and , and then focus on the collected key-value pairs, as shown below:

[0043] It is a local context enhancement item.

[0044] The effect of the present invention can be further illustrated by the following simulation example.

[0045] In the simulation of the present invention, the computer system is Win10, and the simulation environment is a deep learning environment built by pytorch, which is carried out under the Road-Vehicle dataset. Table 1 is a performance comparison of FasterNet and other typical methods. It can be seen that the performance of FasterNet is better than all other algorithms, especially in terms of lightweight. mPram is an important indicator for detecting the lightweight ability of the algorithm. On the benchmark dataset Road-Vehicle, FasterNet saves 6.9% compared with YOLOv8. In addition, GFLOP is reduced by 12.9%, further reducing the difficulty of deploying the detector.

[0046] Table 2 shows the performance comparison of FocalNet and other typical methods. As shown in Table 2, FocalNet performs best in terms of detection accuracy on the benchmark dataset Road-Vehicle. Compared with SPPF, FocalNet improves mAP50 by 1.3% and mAP50-95 by 1.6%, further improving the overall performance of the method.

[0047] Table 3 shows the performance comparison of FocalNet and other typical methods. It can be observed from Table 3 that, compared with the baseline, Bi-formar improves the detection accuracy of the benchmark dataset Road-Vehicle by 1.3% on mAP50 and 2.0% on mAP50-95. This improvement is conducive to the application of detection methods.

[0048] Table 1

[0049] Table 2

[0050] Table 3

[0051] Figure 5 The performance comparison chart of the present invention in various aspects with other typical methods under the Road-Vehicle dataset. It can be seen that the seven evaluation indicators in the current benchmark Road-Vehicle dataset are comprehensively superior to mainstream object detectors and have achieved SOTA performance. mParam is the most important and reliable indicator for evaluating the lightweight challenge of object detection. Compared with YOLOv8, HAF-YOLOv9 saves 3.9% and reduces GFLOPs by 10.8%. In terms of detection accuracy, HAF-YOLOv8 is 3.2% higher than YOLOv9 in mAP50-95. From the experiments of the present invention, it can be concluded that HAF-YOLOv8 can outperform mainstream vehicle detection algorithms in terms of lightweight and detection accuracy, and can therefore be applied to the field of vehicle detection.

[0052] Embodiment 2, based on the concept of the above detection method, the present invention provides a vehicle target detection system based on lightweight YOLOv8, including a feature extraction module, an image enhancement module and a recognition module; The feature extraction module is used to input the enhanced image data into the trained HAF-YOLOv8 model, which is processed by the FasterNet module, the Focal-Modulation Net module, and the Bi-Former module in turn to obtain a new feature set; The image enhancement module is used to perform false positive prediction and splicing on the new feature set to achieve image enhancement; The recognition module is used to pass the enhanced images through the HAF-YOLOv8 model again to obtain the final recognized image set.

[0053] Embodiment 3, the present invention further provides a computer device, the device comprising a processor and a memory. The memory is used to store a computer executable program, and the processor reads and executes the computer executable program from the memory. When the processor executes the computer executable program, the vehicle target detection method based on lightweight YOLOv8 described in the present invention can be implemented.

[0054] On the other hand, the present invention provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the vehicle target detection method based on lightweight YOLOv8 described in the present invention can be implemented.

[0055] The computer device may be a laptop computer, a desktop computer or a workstation.

[0056] The processor described in the present invention may be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC) or a readily available field programmable gate array (FPGA).

[0057] The memory of the present invention may be an internal storage unit of a laptop computer, a desktop computer or a workstation, such as a memory or a hard disk; or an external storage unit, such as a mobile hard disk or a flash memory card.

[0058] Computer-readable storage media may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media may include: read-only memory (ROM), random access memory (RAM), solid-state drive (SSD) or optical disk, etc. Among them, random access memory may include resistance random access memory (ReRAM) and dynamic random access memory (DRAM).

[0059] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A vehicle target detection method based on lightweight YOLOv8, characterized in that: The following steps are involved: The enhanced image data is input into the trained HAF-YOLOv8 model, which is processed by the FasterNet module, the Focal-Modulation Net module, and the Bi-Former module in turn to obtain a new feature set. Perform false positive prediction and splicing on the new feature set to achieve image enhancement; The enhanced images are passed through the HAF-YOLOv8 model again to obtain the final recognized image set.

2. The vehicle target detection method based on lightweight YOLOv8 according to claim 1, characterized in that: The enhanced image data is input into FasterNet, and each channel is Single-channel convolution and kernel depth convolution are performed to obtain an output with the same number of channels as the original feature map; Then use a 1×1 convolution kernel to perform channel fusion on the output feature map of the deep convolution; A residual connection is made between the two, and nonlinearity is introduced using activation function and batch normalization, finally obtaining the output feature map of FasterNet.

3. The vehicle target detection method based on lightweight YOLOv8 according to claim 1, characterized in that: Focal-Modulation Net first aggregates features and interacts the query with the aggregated features to fuse contextual information; The aggregation process includes: extracting contextual information from local to global scope at different granularity levels through hierarchical contextualization; Through gated aggregation, all contextual features at different levels of granularity are condensed into a single feature vector.

4. The vehicle target detection method based on lightweight YOLOv8 according to claim 1, characterized in that: Through hierarchical contextualization, context information is extracted from local to global scope at different granularity levels: given an input feature map , firstly map the feature Projected into a new feature space, the new feature space has a linear layer ;use Depth-wise convolution obtains the hierarchical representation of the context and outputs It is expressed as: Hierarchical contextualization generates L-level feature maps, in the Apply global average pooling on the level feature map , get the total Level feature map , The level feature maps jointly capture local and long-range contexts at different levels of granularity.

5. The vehicle target detection method based on lightweight YOLOv8 according to claim 1, characterized in that: Through gated aggregation, all contextual features at different levels of granularity are condensed into a single feature vector including: Use linear layers to obtain spatially and level-aware gating weights ; Perform a weighted sum by element-wise multiplication to get the same value as the input A single feature map of the same size : in, It is A channel of level; Using a linear layer Get the modulator .

6. The vehicle target detection method based on lightweight YOLOv8 according to claim 1, characterized in that: In the feature map of the input Bi-Former module, queries are obtained by linear mapping ,keys ,values , the attention mechanism of the Bi-Former module represents the correlation between two regions through the adjacency matrix: According to the adjacency matrix , only the front of each region is retained Links, get the routing index between areas with high correlation: By collecting tensor indexes of key-value pairs and , and then focus on the collected key-value pairs, as follows: It is a local context enhancement item.

7. The vehicle target detection method based on lightweight YOLOv8 according to claim 1, characterized in that: False positive prediction and splicing of new feature sets to enhance the image include: The optimized images are stitched together, and the stitched images are denoised and sharpened.

8. A vehicle target detection system based on lightweight YOLOv8, characterized in that: It includes feature extraction module, image enhancement module and recognition module; The feature extraction module is used to input the enhanced image data into the trained HAF-YOLOv8 model, which is processed by the FasterNet module, the Focal-Modulation Net module, and the Bi-Former module in turn to obtain a new feature set; The image enhancement module is used to perform false positive prediction and splicing on the new feature set to achieve image enhancement; The recognition module is used to pass the enhanced images through the HAF-YOLOv8 model again to obtain the final recognized image set.

9. A computer device, characterized in that: It includes a processor and a memory, the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and when the processor executes the computer executable program, it can implement the vehicle target detection method based on lightweight YOLOv8 as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored in a computer-readable storage medium, and when the computer program is executed by a processor, the vehicle target detection method based on lightweight YOLOv8 as described in any one of claims 1 to 7 can be implemented.

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