Remote sensing image ship detection method
By constructing a remote sensing image ship detection network model with multi-scale feature enhancement and rotation perception, the problems of high false negative rate and poor accuracy in ship target detection in remote sensing images are solved, and accurate detection in complex environments is achieved.
Patent Information
- Application Number
- CN202511483129.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Priority Date
- 2025-08-31
- Filing Date
- 2025-10-16
- Publication Date
- 2025-12-26
AI Technical Summary
Existing ship target detection algorithms suffer from high false negative rates and poor accuracy in remote sensing images, especially in complex environments where they struggle to effectively detect multi-scale and rotating ship targets.
A remote sensing image ship detection network model based on multi-scale feature enhancement and rotation perception is constructed. By introducing a convolutional attention mechanism, a dilated spatial convolutional pooling pyramid module, and redesigning the hybrid loss function, the model's ability to detect ship targets is enhanced.
It improves the accuracy and robustness of ship target detection in remote sensing images, and can effectively identify multi-scale and rotating ship targets in complex backgrounds while reducing the impact of background interference.
Smart Images
Figure CN121214366A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of ship inspection technology, and more specifically to a method for ship inspection using remote sensing images. Background Technology
[0002] With the continuous advancement of remote sensing technology, remote sensing images have been widely applied in maritime management and military security to achieve continuous and accurate monitoring of various types of ships. However, the diverse sizes, variable orientations, target clustering, and complex backgrounds of ships in remote sensing images pose significant challenges to accurate ship detection. Research on ship target detection can be broadly categorized into two types. One type is based on traditional image processing techniques, achieving detection through image segmentation, feature extraction, and classification. While traditional detection methods are technically mature, they rely on manual feature extraction, limiting flexibility, making it difficult to comprehensively handle complex image information, and susceptible to noise interference, affecting detection accuracy and stability, and performing poorly in complex scenarios. The other type is based on convolutional neural network-based target detection methods, which automatically extract features end-to-end, better adapting to diverse and complex remote sensing image scenarios, such as the YOLO series, SSD, R-CNN, and Faster-RCNN. Existing ship target detection networks have made significant progress in optical images, but still face many challenges when processing remote sensing images, such as complex environmental interference, indistinct ship target features, and multi-scale targets.
[0003] Ship targets exhibit characteristics such as varying sizes, complex backgrounds, dense mooring, and diverse orientations, leading to several shortcomings in existing algorithms for ship detection tasks: high false negative rates and poor detection accuracy for small targets; horizontal bounding boxes struggle to closely fit the contours of tilted ship targets, increasing error accumulation in subsequent downstream tasks and impacting overall detection performance. Therefore, there is an urgent need to propose a ship detection method that can address the issues of high false negative rates and poor accuracy in ship detection under various complex scenarios, achieving accurate detection and rapid identification of ship targets in remote sensing images. Summary of the Invention
[0004] The purpose of this invention is to solve the technical problems mentioned above and to propose a method for detecting ships in remote sensing images, comprising the following steps:
[0005] S1. Construct a remote sensing image data set of ships, covering various background environments, different weather conditions, and common ship types;
[0006] S2. Construct a remote sensing image ship detection network model based on multi-scale feature enhancement and rotation perception;
[0007] S3, Training the remote sensing image ship detection network model constructed in step S2;
[0008] S4. Detect ship targets in the remote sensing image to be detected.
[0009] In the preferred embodiment, the construction step of the remote sensing image ship detection network model in step S2 specifically includes:
[0010] S21. Extract high-resolution image features using the backbone network CSPDarkNet53;
[0011] S22. Introduce a convolutional attention mechanism module into the output branch of the backbone network;
[0012] S23. In the feature fusion stage of the model, a dilated spatial convolutional pooling pyramid module is introduced.
[0013] S24. By incorporating the ship's rotation angle information into the detection head, the hybrid loss function is reconstructed to enhance the model's adaptability and robustness to ship target rotation transformation.
[0014] In the preferred embodiment, the convolutional attention mechanism module combines channel attention and spatial attention mechanisms to capture key features in the image at different scales, shapes, and orientations. By enhancing the weights of important features and suppressing the weights of irrelevant features, the model pays more attention to the positional information of the small ship target.
[0015] In the preferred scheme, the core purpose of the channel attention mechanism is to focus on the correlation between different channels in the image feature map; each channel represents a specific feature, but their contribution to the final task is different. The channel attention mechanism distinguishes the level of the channels by assigning different weights to each channel.
[0016] For the input feature map F, the channel attention weights M are obtained through the channel attention module. c (F) is multiplied by the original input feature map to obtain feature map F', and then F' is input into the spatial attention module to obtain spatial attention weights M. s Multiplying (F') by the feature map F', the final output is a refined feature map F''. The mathematical expression is as follows:
[0017]
[0018] in, Indicates element-wise multiplication;
[0019] For an input feature map F of size H×W×C, firstly, global max pooling and global average pooling are performed in the spatial dimension to obtain two 1×1×C feature maps, which are global max pooling and global average pooling, respectively. Then, they are fed into a shared multilayer perceptron for learning. The multilayer perceptron structure is Conv-ReLU-Conv, with weights W0 and W1. To reduce computational parameters, a dimensionality reduction coefficient is used in the multilayer perceptron. Finally, after mapping processing by the Sigmoid activation function, the channel attention weights are obtained.
[0020] Therefore, the expression for the channel attention mechanism is:
[0021]
[0022] Where σ is the Sigmoid activation function.
[0023] In the preferred scheme, the spatial attention mechanism dynamically models the spatial positional relationship of feature maps and assigns adaptive weights to different regions, thereby enhancing the model's ability to focus on important regions while suppressing irrelevant information.
[0024] For the input feature layer F', the maximum value and average value are taken in the channel of each feature point to obtain two H×W×1 feature maps; then, the two feature maps are concatenated in the channel dimension to obtain a 2×H×W tensor, and then a 7×7 convolution is performed to compress the channel to 1. Finally, the weight coefficient of each spatial location is obtained through the Sigmoid activation function.
[0025] Therefore, the mathematical expression for the spatial channel attention mechanism is as follows:
[0026] M c (F)=σ(f 7×7 ([AvgPool(F);
[0027]
[0028] In the preferred embodiment, the hollow spatial convolutional pooling pyramid module captures target features at different scales, thereby improving the model's ability to detect ship targets at multiple scales.
[0029] In the preferred scheme, the dilated spatial convolution pooling pyramid module is designed with several parallel dilated convolutions to capture multi-scale information. By directly capturing multi-scale information on a single input through dilated convolution, the computational burden is reduced; and by expanding the receptive field of the convolution kernel, a wider range of contextual information is captured.
[0030] In the hollow spatial convolutional pooling pyramid module, each convolutional branch combines different dilation rates to capture features in different receptive fields; then the feature maps output by the branches are spliced and fused, and finally a 1×1 convolution is used to output the fused features.
[0031] In the preferred embodiment, the reconstructed hybrid loss function incorporates angle parameters, and a bounding box is constructed based on the actual orientation and shape of the ship in the image;
[0032] The reconstructed hybrid loss function consists of three parts: regression loss, confidence loss, and classification loss;
[0033] The rotating frame is defined by five parameters: center point coordinates (x, y ... c ,y c ), long side a, short side b, and rotation angle θ;
[0034] Therefore, the reconstructed hybrid loss function is defined as:
[0035] L=αL reg_box +βL confidence +γL class ;
[0036] Among them, L reg_box For regression loss, L confidence For confidence loss, L class For classification loss, α, ρ, and γ control the hyperparameters of the loss weights for each part, with default values of 1.0, 10.0, and 1.0, respectively.
[0037] In the preferred scheme, the regression loss function is specifically expressed as:
[0038]
[0039] Where K represents the total number of anchor frames, q = 1 represents the foreground, q = 0 represents the background, and Δθ pred Δθ represents the offset between the predicted bounding box and the ground truth bounding box. gt Denotes the target vector, δ(Δθ) pred ,Δθ gt F(IoU) is the key part that determines the gradient update direction, while ensuring the differentiability of the loss function and enabling effective optimization. rot IoU is a key component that determines the direction of gradient updates. rot Used to calculate the intersection-union ratio (IoU) between the rotated rectangle and the label box.
[0040] In the preferred scheme, the principal gradient function of the regression loss is specifically expressed as:
[0041]
[0042] Where CIoU(·) represents the horizontal bounding box IoU calculation function, pred represents the predicted data, and gt represents the label data;
[0043] The confidence loss uses the Focal Loss function, and its calculation expression is as follows:
[0044]
[0045] in, It is a balancing factor used to adjust the influence between positive and negative samples, R = (1-p) / 2. t ) χ It is the regulating factor, χ is the focal factor, and χ is greater than or equal to 0, p t This represents the model's predicted probability for the target class.
[0046] The probability distribution of each category is represented by p. c The target is labeled with d. c The classification loss calculated using binary cross-entropy is specifically expressed as:
[0047]
[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0049] (1) By introducing a multi-scale feature fusion mechanism, the model’s ability to capture the shape and orientation of ship targets is effectively improved, the influence of background interference and redundant information is reduced, and the accurate detection of ship targets in complex environments is achieved.
[0050] (2) A completely new loss function was redesigned and optimized by rotation perception, which significantly enhanced the recognition accuracy of ships rotating at any angle and can be well adapted to the diverse orientation features of targets in remote sensing images.
[0051] (3) By using the attention mechanism to guide the focus on key features of the ship and suppress irrelevant interference, the distinction between the target and the background is improved; at the same time, a global context fusion strategy is adopted to integrate multi-scale information and global scene information to further optimize the detection robustness of the model in complex backgrounds.
[0052] (4) The proposed algorithm framework can be more easily extended to ship detection tasks in high-resolution remote sensing images in other industrial fields. Attached Figure Description
[0053] Figure 1 This invention presents a remote sensing image ship detection network structure based on multi-scale feature enhancement and rotation perception.
[0054] Figure 2 This is a structural diagram of the attention mechanism module in the convolution module.
[0055] Figure 3 This is a structural diagram of the channel attention mechanism.
[0056] Figure 4 This is a structural diagram of the spatial attention mechanism.
[0057] Figure 5 This is a structural diagram of a hollow spatial convolutional pooling pyramid module. Detailed Implementation
[0058] Two embodiments of the present invention are given below. These specific embodiments are only used to further illustrate the present invention and do not limit the scope of protection of this application.
[0059] This invention aims to propose a ship detection algorithm for remote sensing images based on multi-scale feature enhancement and rotation perception, in order to solve the problems of high false negative rate and poor accuracy of existing models in ship detection in complex scenes, and to achieve accurate detection and rapid identification of ship targets in remote sensing images.
[0060] Remote sensing image ship detection algorithms based on multi-scale feature enhancement and rotation sensing include:
[0061] Step 1: Construct a remote sensing image ship dataset, covering various background environments, different weather conditions, and common ship types.
[0062] Step 2: Construct a remote sensing image ship detection network model based on multi-scale feature enhancement and rotation perception.
[0063] like Figure 1As shown, this invention proposes a remote sensing image ship detection algorithm based on multi-scale feature enhancement and rotation awareness (hereinafter referred to as MSFE-RotDet). The overall network model first extracts high-resolution image features through the backbone network CSPDarkNet53. Then, a convolutional block attention module (CBAM) is introduced into the output branch of the backbone network. This module increases the attention to important information and suppresses interference from irrelevant information, enhancing the model's feature representation ability. Simultaneously, in the feature fusion stage, an atrous spatial pyramid pooling (ASPP) module is introduced. This module captures multi-scale contextual information through multiple parallel atrous convolutions and fuses global information, improving the model's ability to perceive complex scenes. Finally, the ship's rotation angle information is incorporated into the detection head, and the hybrid loss function is reconstructed to enhance the model's adaptability and robustness to ship target rotation transformations.
[0064] The Convolutional Attention Mechanism Module (CABM) is specifically as follows:
[0065] Remote sensing images often feature complex backgrounds and are susceptible to effects from lighting, clouds, and other factors, making target recognition difficult. Furthermore, the high similarity between ship targets and the background makes it challenging for models to extract regions of interest, further increasing the detection difficulty. To address this issue, this invention introduces a convolutional attention module, such as... Figure 2 As shown, CBAM combines the Channel Attention module (CAM) and the Spatial Attention module (SAM) to more effectively and comprehensively capture key features in images, overcoming the limitations of traditional convolutional neural networks in handling different scales, shapes, and orientations. This module enhances the weights of important features and suppresses the weights of irrelevant features, making the model more focused on the positional information of small ship targets.
[0066] Specifically, for the input feature map F, the channel attention weights M are obtained through the channel attention module. c (F) is multiplied by the original input feature map to obtain feature map F', and then F' is input into the spatial attention module to obtain spatial attention weights M. s(F') is multiplied by the feature map F', and finally the refined feature map F is output. The mathematical expression for element-wise multiplication is as follows:
[0067]
[0068] The core purpose of channel attention mechanisms is to focus on the correlation between different channels in an image feature map, such as... Figure 3 As shown, each channel represents a specific feature, but their contribution to the final task is different. The channel attention mechanism distinguishes the channel levels by assigning different weights to each channel.
[0069] For an input feature map F of size H×W×C, global max pooling and global average pooling are first performed in the spatial dimension to obtain two 1×1×C feature maps, representing global max pooling and global average pooling, respectively. Then, these are fed into a shared multilayer perceptron (MLP) for learning. The MLP structure is Conv-ReLU-Conv, with weights W0 and W1. To reduce computational parameters, a dimensionality reduction coefficient is used in the MLP. Finally, after mapping using the sigmoid activation function, the channel attention weights are obtained.
[0070] Therefore, the channel attention mechanism is expressed as follows:
[0071]
[0072] Where σ is the Sigmoid activation function.
[0073] Spatial attention mechanisms dynamically model the spatial relationships between feature maps, assigning adaptive weights to different regions to enhance the model's ability to focus on important areas while suppressing irrelevant information, such as... Figure 4 As shown. Specifically, for the input feature layer F', the maximum and average values are taken in the channels of each feature point to obtain two H×W×1 feature maps; then, the two feature maps are concatenated along the channel dimension to obtain a 2×H×W tensor, and then a 7×7 convolution is performed to compress the channels to 1. Finally, the weight coefficients of each spatial location are obtained through the Sigmoid activation function. Therefore, the mathematical expression of the spatial channel attention mechanism is as follows:
[0074] M c (F)=σ(f 7×7 ([AvgPool(F);
[0075]
[0076] The hollow spatial convolutional pooling pyramid module is specifically as follows:
[0077] Ships in remote sensing images typically exhibit significant size variations and a dense distribution of small targets, posing a considerable challenge to accurate detection of ship targets on the sea surface. In convolutional neural networks, shallow feature maps focus primarily on local details. While deeper feature maps possess richer semantic information as the network deepens, they often lose details and localization information of small targets. Particularly after multiple convolution and pooling operations, the image resolution continuously decreases, leading to a gradual reduction in the features of small targets and impacting detection accuracy. To address these issues, this invention introduces the Atrous Spatial Pyramid Pooling (ASPP) module. This module captures target features at different scales, thereby improving the model's ability to detect ship targets at multiple scales.
[0078] The ASPP module employs multiple parallel dilated convolutions to capture multi-scale information. Compared to traditional multi-scale processing methods, this module directly captures multi-scale information on a single input through dilated convolutions, thus reducing computational burden. The core advantage of dilated convolutions lies in capturing a wider range of contextual information by expanding the receptive field of the convolutional kernel. In the ASPP module, each convolutional branch combines different dilation rates to capture features within different receptive fields. The feature maps output from each branch are then concatenated and fused, and finally, a 1×1 convolution is used to output the fused features.
[0079] The reconstruction loss function is as follows:
[0080] This invention addresses the characteristics of ships in remote sensing images, such as varying target orientations and high aspect ratios, by proposing a loss function reconstruction method for rotating targets. Traditional horizontal anchor box detection methods cannot closely fit the geometric contours of ships with diverse orientations, resulting in bounding boxes containing a large amount of background information. In contrast, the reconstructed rotating target detection method incorporates angle parameters, constructing bounding boxes based on the actual orientation and shape of the ship in the image. This allows for more accurate target localization, significantly improving detection accuracy and more precisely measuring the difference between predicted and ground truth bounding boxes.
[0081] The loss function consists of three parts: regression loss, confidence loss, and classification loss. The rotated box is defined by five parameters: center point coordinates (x, y, z). c ,y c The long side a, the short side b, and the rotation angle θ are considered. Therefore, the overall loss function reconstructed in this paper is defined as follows:
[0082] L=αL reg_box +βL confidence +γL class
[0083] Among them, L reg_box For regression loss, Lconfidence For confidence loss, L class This is the classification loss. α, ρ, and γ control the hyperparameters of the loss weights for each part, with default values of 1.0, 10.0, and 1.0, respectively.
[0084] The regression loss function is specifically expressed as:
[0085]
[0086] Where K represents the total number of anchor frames, q = 1 represents the foreground, and q = 0 represents the background. Δθ pred Δθ represents the offset between the predicted bounding box and the ground truth bounding box. gt Represents the target vector. δ(Δθ) pred ,Δθ gt F(IoU) is the key part that determines the gradient update direction while ensuring the differentiability of the loss function and enabling effective optimization. rot IoU is a key component that determines the direction of gradient updates. rot Used to calculate the intersection-union ratio (IoU) between the rotated rectangle and the label box.
[0087] The principal gradient function of the regression loss is specifically expressed as:
[0088]
[0089] Where CIoU(·) represents the IoU calculation function for the horizontal bounding box. pred represents the predicted data; gt represents the label data.
[0090] The confidence loss uses the Focal Loss function, and its calculation expression is as follows:
[0091]
[0092] In the above formula It is a balancing factor used to adjust the influence between positive and negative samples, R = (1-p) / 2. t ) χ χ is the moderating factor, and χ is the focal factor, with χ being greater than or equal to 0. t This represents the model's predicted probability for the target class.
[0093] The probability distribution of each category is represented by p. c The target is labeled with d. c The classification loss calculated using binary cross-entropy is specifically expressed as follows:
[0094]
[0095] Step 3: Train a remote sensing image ship detection network model based on multi-scale feature enhancement and rotation perception.
[0096] Step 4: Detect ship targets in the remote sensing image to be detected.
[0097] The network is trained by inputting an image containing a ship target and outputting the detection results of each bounding rectangle containing the ship target in the image.
[0098] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for detecting ships in remote sensing images, characterized by: Includes the following steps: S1. Construct a remote sensing image data set of ships, covering various background environments, different weather conditions, and common ship types; S2. Construct a remote sensing image ship detection network model based on multi-scale feature enhancement and rotation perception; S3, Training the remote sensing image ship detection network model constructed in step S2; S4. Detect ship targets in the remote sensing image to be detected.
2. The method for detecting ships in remote sensing images according to claim 1, characterized in that: The specific steps in constructing the remote sensing image ship detection network model in step S2 include: S21. Extract high-resolution image features using the backbone network CSPDarkNet53; S22. Introduce a convolutional attention mechanism module into the output branch of the backbone network; S23. In the feature fusion stage of the model, a dilated spatial convolutional pooling pyramid module is introduced. S24. By incorporating the ship's rotation angle information into the detection head, the hybrid loss function is reconstructed to enhance the model's adaptability and robustness to ship target rotation transformation.
3. The remote sensing image ship detection method according to claim 2, characterized in that: The convolutional attention mechanism module combines channel attention and spatial attention mechanisms to capture key features in images at different scales, shapes, and orientations. By enhancing the weights of important features and suppressing the weights of irrelevant features, the model pays more attention to the positional information of small ship targets.
4. The method for detecting ships in remote sensing images according to claim 3, characterized in that: The core purpose of the channel attention mechanism is to focus on the correlation between different channels in the image feature map; each channel represents a specific feature, but their contribution to the final task is different. The channel attention mechanism distinguishes the level of the channels by assigning different weights to each channel. For the input feature map F, the channel attention weights M are obtained through the channel attention module. c (F) is multiplied by the original input feature map to obtain feature map F', and then F' is input into the spatial attention module to obtain spatial attention weights M. s Multiplying (F') by the feature map F', the final output is a refined feature map F''. The mathematical expression is as follows: in, Indicates element-wise multiplication; For an input feature map F of size H×W×C, firstly, global max pooling and global average pooling are performed in the spatial dimension to obtain two 1×1×C feature maps, which are global max pooling and global average pooling, respectively. Then, they are fed into a shared multilayer perceptron for learning. The multilayer perceptron structure is Conv-ReLU-Conv, with weights W0 and W1. To reduce computational parameters, a dimensionality reduction coefficient is used in the multilayer perceptron. Finally, after mapping processing by the Sigmoid activation function, the channel attention weights are obtained. Therefore, the expression for the channel attention mechanism is: Where σ is the Sigmoid activation function.
5. The remote sensing image ship detection method according to claim 3, characterized in that: spatial... The attention mechanism dynamically models the spatial relationships of feature maps and assigns adaptive weights to different regions, thereby enhancing the model's ability to focus on important regions while suppressing irrelevant information. For the input feature layer F', the maximum value and average value are taken in the channel of each feature point to obtain two H×W×1 feature maps; then, the two feature maps are concatenated in the channel dimension to obtain a 2×H×W tensor, and then a 7×7 convolution is performed to compress the channel to 1. Finally, the weight coefficient of each spatial location is obtained through the Sigmoid activation function. Therefore, the mathematical expression for the spatial channel attention mechanism is as follows:
6. The method for detecting ships in remote sensing images according to claim 2, characterized in that: The hollow spatial convolutional pooling pyramid module improves the model's ability to detect ship targets at multiple scales by capturing target features at different scales.
7. The method for detecting ships in remote sensing images according to claim 2, characterized in that: The dilated spatial convolution pooling pyramid module is designed with several parallel dilated convolutions to capture multi-scale information. By directly capturing multi-scale information on a single input through dilated convolutions, the computational burden is reduced. By expanding the receptive field of the convolution kernel, a wider range of contextual information is captured. In the hollow spatial convolutional pooling pyramid module, each convolutional branch combines different dilation rates to capture features in different receptive fields; then the feature maps output by the branches are spliced and fused, and finally a 1×1 convolution is used to output the fused features.
8. The method for detecting ships in remote sensing images according to claim 2, characterized in that: The reconstructed hybrid loss function incorporates angle parameters and constructs bounding boxes based on the actual orientation and shape of the ships in the image; The reconstructed hybrid loss function consists of three parts: regression loss, confidence loss, and classification loss; The rotating frame is defined by five parameters: center point coordinates (x, y ... c ,y c ), long side a, short side b, and rotation angle θ; Therefore, the reconstructed hybrid loss function is defined as: L=αL reg_box +βL confidence +γL class ; Among them, L reg_box For regression loss, L confidence For confidence loss, L class For classification loss, α, ρ, and γ control the hyperparameters of the loss weights for each part, with default values of 1.0, 10.0, and 1.0, respectively.
9. The method for detecting ships in remote sensing images according to claim 8, characterized in that: The regression loss function is specifically expressed as: Where K represents the total number of anchor frames, q = 1 represents the foreground, q = 0 represents the background, and Δθ pred Δθ represents the offset between the predicted bounding box and the ground truth bounding box. gt Denotes the target vector, δ(Δθ) pred ,Δθ gt F(IoU) is the key part that determines the gradient update direction, while ensuring the differentiability of the loss function and enabling effective optimization. rot IoU is a key component that determines the direction of gradient updates. rot Used to calculate the intersection-union ratio (IoU) between the rotated rectangle and the label box.
10. The method for detecting ships in remote sensing images according to claim 8, characterized in that: The principal gradient function of the regression loss is specifically expressed as: f reg =L smooth-l1 (Dth pred ,Dth gt )-CIoU(pred,gt); Where CIoU(·) represents the horizontal bounding box IoU calculation function, pred represents the predicted data, and gt represents the label data; The confidence loss uses the Focal Loss function, and its calculation expression is as follows: in, It is a balancing factor used to adjust the influence between positive and negative samples, R = (1-p) / 2. t ) χ It is the regulating factor, χ is the focal factor, and χ is greater than or equal to 0, p t This represents the model's predicted probability for the target class. The probability distribution of each category is represented by p. c The target is labeled with d. c The classification loss calculated using binary cross-entropy is specifically expressed as: