2.1 Attention Mechanism

Initially, attention mechanisms were utilized in machine translation tasks. This mechanism enables the model to focus on different parts of the input sentence when translating a word, which significantly enhances the translation quality [43]. Over the past years, considerable efforts have been devoted to developing attention mechanism modules that are more applicable to the domain of computer vision [40, 44, 45].

Figure 1 Schematic representation of the network architecture for YOLOv8.

2.2 YOLOs

2.2.2 Loss Function Utilized in Bounding Box Regression

The object detector based on convolutional neural networks employs a loss function to update the network weights [48]. Historically, iterations of the YOLO object detectors have been engaged in an unrelenting pursuit of optimizing the loss function for bounding box regression, aiming to achieve superior performance [48, 49, 50]. Simultaneously, a variety of loss functions for boundary box regression are continuously being developed and refined [41, 51, 52, 53, 54], thereby enabling the improved YOLOv8-based object detector to be applied across an increasingly diverse range of scenarios.

Figure 2 Schematic representation of the loss function for bounding box regression.

The YOLOv8 model employs C-IoU [50] as the loss function for bounding box regression, as shown in Figure 2. The following presents the mathematical expression for C-IoU [50]:

$$CIoU=IoU-\frac{{\left(x-x_{gt}\right)}^2+{\left(y-y_{gt}\right)}^2}{W^2+H^2}-\alpha \upsilon$$

$$IoU=\frac{B_{Anchor}\cap B_{GroundTruth}}{B_{Anchor}\cup B_{GroundTruth}}$$

$$\alpha =\frac{\upsilon }{1-IoU+\upsilon }$$

$$\upsilon =\frac{4}{{\pi }^2}\ast {\left({\tan }^{-1}\frac{w}{h}-{\tan }^{-1}\frac{w_{gt}}{h_{gt}}\right)}^2$$

From the formulas, it is evident that C-IoU [50] takes into account both the position and shape of the bounding box in a comprehensive manner. This allows the model to learn the characteristics of the ground truth box more thoroughly.

3.1 An Attention-Based Fusion Module

We categorize these sea ice instances into three distinct groups, as elaborated in section 4.1. Although satellite imagery offers relatively high resolution, actual ice conditions can be highly complex. As shown in Figure 3, several factors make it challenging for object detection models to accurately identify sea ice of varying scales. These include the wide range of ice floe sizes, irregular shapes, and reduced contrast between ice and seawater caused by melting and accumulation of sea ice.

Figure 3 The two key issues: (a) Numerous small-scale sea ice; (b) Ambiguous demarcation between sea ice and seawater.

Figure 4 Schematic representation of the Attention-Based Fusion Module.

Besides, as the network deepens, the detection model progressively enhances semantic information in feature maps while inevitably sacrificing spatial details, particularly size characteristics crucial for sea ice analysis. When handling this task, YOLOv8 uses the Concat module to combine deep and shallow feature maps. However, we observe that relying on the feature maps after direct stitching is not sufficient for accurate size classification. To address this limitation, we propose an attention-based fusion module that can effectively enhance the spatial detail information in the feature map, so as to be able to accurately distinguish between sea ice size categories, as shown in Figure 4.

First, we calculate the channel attention weight $M_C$ of the feature map $F_1$ and multiply it with the feature map $F_1$ to obtain $F_1^{\prime }$. Secondly, we calculate the Spatial attention weights $M_S$ of the feature map $F_2$ and multiply it with the feature map $F_2$ to obtain $F_2^{\prime }$. Thirdly, we concatenate the feature map $F_1^{\prime }$ and $F_2^{\prime }$ to obtain the final feature map $F_{final}$. The detailed process is as follows:

where the feature map $F_1$ is derived from deeper layers and contains more semantic information, such as the overall shape and categories of sea ice; the feature map $F_2$ is derived from shallower layers and includes more detailed information, such as edges, textures, colors, and other low-level features of sea ice. In this way, we optimize the fusion process of different feature maps in YOLOv8, enabling the model to balance attention between the semantic information and detailed information of different feature maps, thereby improving the detection accuracy of the model for sea ice of varying scales.

3.2 Selection of Boundary Regression Loss Function Based on Sea Ice Size Characteristics

The C-IoU loss [50] employed in YOLOv8 considers the geometric relationship between the ground truth box and the predicted box, utilizing both their relative positions and shapes to compute the loss. However, in contrast to general objects, sea ice presents a more diverse aspect ratio and possesses an irregular shape that lacks any fixed pattern. In this study, if C-IoU [50] is utilized as the loss function for bounding box regression, two critical questions arise.

During the bounding box regression process, the variation in IoU is particularly significant when the regression occurs along the short side of the ground truth box. Therefore, it is essential to ensure a balanced regression effect for bounding boxes across various directions throughout this process.

In the end, we select Shape-IoU [41] as our loss function for bounding box regression, as it effectively addresses the two types of issues mentioned above. The formula for Shape-IoU [41] is presented below:

where $scale$ represents the scale factor, which can be adjusted based on the dimensions of the target. Taking the ground truth box in Figure 5 as an example(where $w_{gt}>h_{gt}$), when $scale=0$ and $ww=hh=1$, the bounding box regression lacks directional prioritization. by increasing the value of scale, the regression effectiveness can be enhanced. In this study, we set $scale=1$, resulting in $ww>hh$, which indicates that higher regression weight is assigned to the vertical dimension (height adjustment).

Equation 10 calculates the loss value for bounding box regression.

It is noteworthy that Shape-IoU dynamically emphasizes the gradient update path of bounding box parameters (e.g., center offsets and aspect ratios) during model convergence. Unlike C-IoU, which indirectly guides optimization through geometric penalties (center distance and aspect ratio matching), Shape-IoU explicitly introduces a directional weighting coefficient, thereby clarifying the prioritization of regression targets with higher shape discrepancies. This property of Shape-IoU shortens the convergence time of the model.

3.3 An Evidence Fusion Module for the Correction of Sea Ice Categories

Figure 7 Typical cases of misclassification.

Figure 8 Schematic diagram of evidence fusion module.

After extensive experimentation, we discovered that YOLOv8 is capable of accurately predicting the bounding boxes of sea ice; however, it occasionally misclassifies the categories of sea ice. More specifically, YOLOv8 occasionally misclassifies medium-scale sea ice as large-scale sea ice and conversely misclassifies large-scale sea ice as medium-scale sea ice, As illustrated in Figure 7.

In Figure 7 (a), the sea ice located in the upper left corner is classified as medium-scale, as the longest side of its circumscribed rectangle measures less than 128 pixels. However, it was incorrectly identified by YOLOv8 as large sea ice. Meanwhile, in Figure 7 (b), the sea ice situated at the center is categorized as large-scale, given that the longest side of its circumscribed rectangle exceeds 128 pixels. However, it was inaccurately classified by YOLOv8 as medium-scale sea ice.

With these issues in consideration, we conducted a more thorough examination of YOLO. The YOLO algorithm is designed to extract features from images and classify targets based on these extracted characteristics. The features encompass various types of information, including texture, color, shape, and more. More specifically, YOLO relies more heavily on the aforementioned features for target classification than on the scale information of the targets.

However, in our task of classifying sea ice, the scale information of the target cannot be overlooked. We aim to improve YOLOv8 so that the scale information of the target can serve as a more significant feature for predicting categories of sea ice.

In the inference process of YOLOv8, the role of non-maximum suppression (NMS) is to eliminate redundant prediction boxes and produce the final output. Based on this, we propose the Evidence Fusion module to address the aforementioned issues, the details of the Evidence Fusion module are illustrated in Figure 8.

First, we convert the prediction box information and prediction category information provided by YOLOv8 into evidences. Utilizing an enhanced DSmT fusion inference algorithm [42], we subsequently integrate these two types of evidence to establish a new prediction category. The algorithmic model is primarily composed of the following two components.

3.3.1 Convert the Information Predicted by YOLOv8 into Evidence Characterizing Uncertainty

1. The bounding box information predicted by YOLOv8: We begin by counting the instances of sea ice larger than 8 pixels in the satellite image dataset NWPU-RESISC45 [29]. Subsequently, we categorize these sea ice instances into three distinct groups based on their scale, as elaborated in section 4.1. Finally, we generate histograms to illustrate the frequency distribution of the longest side of the circumscribed rectangles for each type of sea ice and fit distribution curves to these histograms, as depicted in Figure 9.

   

   Figure 9 Distribution of the size of three types of sea ice in the NWPU-RESISC45 dataset: (a), (b), and (c) Frequency histograms and probability density curves showing the distribution of Small-scale sea ice, Medium-scale sea ice and Large-scale sea ice, respectively; (d) A schematic diagram is presented, showing the three curves.
   Based on the distribution shown in Figure 9, we fit the curve, as shown in equation 11, 12, and 13.
   $$f_{small}\left(l\right)=\frac{1}{7.32\ast \sqrt{2\pi }}\ast e^{-\frac{{\left(l-21.42\right)}^2}{2\ast {7.32}^2}},l>0$$
   where 21.42 represents the mean $\mu$ of the normal distribution, 7.32 represents the standard deviation $\sigma$ of the normal distribution. Here, $l$ denotes the pixel value corresponding to the longest side of the circumscribed rectangle for sea ice, and f_small(l) is the probability of occurrence of sea ice.
   $f_{medium}\left(l\right)=0.64\ast \frac{1}{2^{\frac{11.43}{2}}\ast \Gamma \left(\frac{11.43}{2}\right)}$

   $\ast {\left(\frac{l}{6.78}\right)}^{\left(\frac{11.43}{2}-1\right)}\ast e^{-\frac{l}{2\ast 6.78}},l>0$
   

    (a) Small-scale sea ice: the longest side of the circumscribed rectangle for this type of sea ice ranges between 8 pixels and 32 pixels.

   

    (b) Medium-scale sea ice: the longest side of the circumscribed rectangle for this type of sea ice ranges between 32 pixels and 128 pixels.

   

    (c) Large-scale sea ice: the longest side of the circumscribed rectangle for this type of sea ice exceeds 128 pixels.

   Figure 10 Three distinct categories of sea ice.
   where 0.64 serves as the scaling parameter for the function, 6.78 is the scale parameter, 11.43 denotes the degrees of freedom for the chi-square distribution, and $\Gamma (\cdot )$ is the symbol for the gamma function. Here, $l$ denotes the pixel value corresponding to the longest side of the circumscribed rectangle for sea ice, and f_medium(l) is the probability of occurrence of sea ice.
   $f_{large}\left(l\right)=1.06\ast \frac{1}{2^{\frac{69.06}{2}}\ast \Gamma \left(\frac{69.06}{2}\right)}$

   $\ast {\left(\frac{l}{2.43}\right)}^{\left(\frac{69.06}{2}-1\right)}\ast e^{-\frac{l}{2\ast 2.43}},l>0$
   where 1.06 serves as the scaling parameter for the function, 2.43 is the scale parameter, 69.06 denotes the degrees of freedom for the chi-square distribution, and $\Gamma (\cdot )$ is the symbol for the gamma function. Here, $l$ denotes the pixel value corresponding to the longest side of the circumscribed rectangle for sea ice, and f_large(l) is the probability of occurrence of sea ice.We normalize the distribution rules mentioned above, as shown in equations 14, and finally transform the bounding box information predicted by YOLOv8 into evidence that describes the uncertainty.
   $$\{\begin{array}{c}{a}_1=\frac{f_{small}\left(l\right)}{f_{small}\left(l\right)+f_{middle}\left(l\right)+f_{large}\left(l\right)}\\ a_2=\frac{f_{medium}\left(l\right)}{f_{small}\left(l\right)+f_{medium}\left(l\right)+f_{large}\left(l\right)}\\ a_3=\frac{f_{large}\left(l\right)}{f_{small}\left(l\right)+f_{medium}\left(l\right)+f_{large}\left(l\right)}\end{array}$$
   where a₁, a₂, a₃ represent the scale reliability for the three types of sea ice, respectively.

2. The category information predicted by YOLOv8: The prediction values for the three types of sea ice—cls_small, cls_medium, cls_large—are included in the prediction information provided by YOLOv8. The category with the highest prediction value indicates the model's predicted target. We convert this set of data into category evidence, as shown in equations 15.

   $$\{\begin{array}{c}{b}_1=cl{s}_{small}\\ b_2=cl{s}_{medium}\\ b_3=cl{s}_{large}\end{array}$$
   where b₁, b₂, b₃ represent the category reliability for the three types of sea ice, respectively.

Algorithm 1

• Input: The bounding box evidence $a_i$, The category evidence $b_i$;

• Output: New category result $New\_cat{e}_i$;

• for $i=1,2,3$ do

•    $m{a}_i=1-b_i$;

•    $m{b}_i=1-a_i$;

•    $B_i=a_i^2\cdot b_i+\frac{a_i^2\cdot m{a}_i}{a_i+m{a}_i}+\frac{a_i\cdot b_i^2\cdot m{b}_i}{b_i+m{b}_i}$;

•   

• end for

• $sumB={\sum }_{i=1}^3{B}_i$;

• $New\_cat{e}_i=0$;

• for $i=1,2,3$ do

•    $New\_cat{e}_i=\frac{B_i}{sumB}$;

•   

• end for

Optimized DSmT fusion inference algorithm

 (a) Small-scale sea ice: the longest side of the circumscribed rectangle for this type of sea ice ranges between 8 pixels and 32 pixels.

 (b) Medium-scale sea ice: the longest side of the circumscribed rectangle for this type of sea ice ranges between 32 pixels and 128 pixels.

 (c) Large-scale sea ice: the longest side of the circumscribed rectangle for this type of sea ice exceeds 128 pixels.

Figure 11 Three distinct categories of sea ice.

Table 1 Summary of the labels for the three types of sea ice.

		Small-Scale Sea Ice	Medium-Scale Sea Ice	Big-Scale Sea Ice
NWPU- RESISC45 [29]	Quantity	6820	3710	382
	Percentage	62.5%	34.0%	3.5%
Our Sea Ice Dataset	Quantity	3162	1170	256
	Percentage	69.0%	25.5%	5.5%
Note: We randomly select 70% of the images to train the model, and the remaining 30% of the images were used to verify the training effect.

Table 2 Important information about the exclusive Landsat8-based sea ice dataset.

Attribute	Attribute Value
	1	2
SPACECRAFT_ID	LANDSAT8	LANDSAT8
ORIGIN	Image courtesy of the U.S. Geological Survey	Image courtesy of the U.S. Geological Survey
LANDSAT_SCENE_ID	LC80482392019215LGN00	LC81300082018179LGN00
LANDSAT_PRODUCT_ID	LC08_L1GT_048239_ 20190803_20190819_01_T2	LC08_L1TP_130008_ 20180628_20180704_01_T1
FILE_DATE	2019-08-19T23:27:47Z	2018-07-04T09:14:55Z
OUTPUT_FORMAT	GEOTIFF	GEOTIFF
SENSOR_ID	OLI_TIRS	OLI_TIRS
TARGET_WRS_PATH	48	130
TARGET_WRS_ROW	239	8
DATE_ACQUIRED	2019-08-03	2018-06-28
SCENE_CENTER_TIME	20:32:39.0212890Z	03:26:15.2127540Z
CLOUD_COVER	1.55	2.20
CLOUD_COVER_LAND	0.02	0.12
IMAGE_QUALITY_OLI	9	9
IMAGE_QUALITY_TIRS	9	9
Note: This dataset pertains to the sea ice data corresponding to the aforementioned two scenes. The dataset comprises a total of 430 images, each with dimensions of 256 * 256 pixels.

Table 3 Experimental configuration.

Attribute	Attribute Value
CPU	Core i5 12450H
GPU	NVIDIA GeForce RTX 3050
Running memory	16GB
Storage memory	256GB
Operating system	Win 10
Interpreter	Python 3.9
Deep Learning Frameworks	PyTorch 1.9
IDEA	PyCharm

Table 4 Hyper-parameters of improved YOLOv8 Algorithm.

Attribute	Attribute Value
epochs	500
batch size	16
imgsz	256
workers	8
close mosaic	Last 10 epochs
optimizer	AdamW
initial learning rate	0.01
final learning rate	0.0001
momentum	0.937
weight decay	0.0005
warm-up epochs	3.0
warm-up momentum	0.8
warm-up bias learning rate	0.1
box loss gain	7.5
class loss gain	0.5
DFL loss gain	1.5
hsv hue augmentation	0.015
hsv saturation augmentation	0.7
hsv value augmentation	0.4
translation augmentation	0.1
scale augmentation	0.9
mosaic augmentation	1.0
mixup augmentation	0.1
copy-paste augmentation	0.1

Table 5 Comparisons with the baseline model and state-of-the-arts.

Model	Precision (%)	Recall (%)	mAP50 (%)	mAP50-95 (%)	F1 (%)	Training time (h)	FPS
Faster R-CNN	62.7	80.3	79.2	47.1	70.4	6.09	4.4
SSD	62.3	76.0	78.0	47.6	68.5	0.98	6.9
RT-DETR	74.9	66.1	73	54.2	70.2	3.213	68.0
YOLOv3	66.8	86	74.7	50.9	75.2	5.719	59.2
YOLOv5	73.3	73.3	82.2	52.5	73.3	0.728	208.3
YOLOv6	72.4	69.3	78.4	47.0	70.8	3.262	69.4
YOLOv7	76.7	64.6	81.5	49.1	70.1	4.529	87.7
YOLOv9	65.6	82.3	78.0	44.2	73.0	5.46	108.7
YOLOv10	84.2	68.1	81.9	49.0	75.3	0.483	128.2
ASF-YOLO	64.6	77.9	80.3	45.1	70.6	3.983	53.5
GOLD-YOLO	73.4	74.7	81.1	47.8	74.0	6.118	58.5
Hyper-YOLO	69.2	76.9	83.1	50.5	72.8	6.307	44.4
Improved YOLOv5[39]	71.2	75.1	82.6	51.5	73.1	3.52	126.4
YOLOv8	84.7	62.4	81.6	56.2	71.9	1.113	82.6
Our Improved YOLOv8	79.4	78.0	87.2	59.3	78.7	0.959	48.3
In the same group of experiments, the best-performing data is highlighted in bold.

Figure 12 Schematic diagram of the sea ice satellite imagery.