# Improved Sea Ice Image Segmentation Using U\({}^{2}\)-Net and Dataset Augmentation
## 2 Materials and Methods  
### Data Augmentation  
Difficulty in acquiring optical images of sea ice, the high cost of labeling, and an insufficient number of samples are obstacles to sea ice segmentation, classification, and detection. Owing to complex sensor factors and special weather conditions, image noise and cloud occlusion are major obstacles to the inversion of optical sea ice images. Image augmentation is an effective method for solving data limitations in deep learning model training. Data augmentation not only increases the number of samples in the dataset but also improves the generalization ability of neural networks. The main data augmentation methods used in this study were affine transform, fuzzy, mirror image, noise, and optical spatial transform augmentations [22]. In noisy data augmentation experiments, the Gaussian random noise is representative of noise type in image processing. In this study, we used the Box-Muller transform method to generate Gaussian random noise and studied the effects of noise with different parameters on the model accuracy and generalization ability. The principle is as follows: the joint two-dimensional distribution of two mutually independent Gaussian random numbers with zero mean and the same variance is radially symmetrical, and the Gaussian random number output by the algorithm can be considered to be the coordinates of a random point in the two-dimensional plane, the amplitude of which is transformed from a random number obeying a uniform distribution on the interval. Its phase is obtained by multiplying a uniform random number on the interval, and the random point is mapped onto the Cartesian coordinate axis. The corresponding coordinate point is a random number that follows a Gaussian distribution. \(X\) and \(Y\) are assumed to obey normal distributions and the random variables; \(X\) and \(Y\), are transformed as (Equations (1) and (2)):  
\[X=R\cos(\theta) \tag{1}\]  
\[Y=R\sin(\theta) \tag{2}\]  
The distribution functions are described by Equations (3)-(5):  
\[P_{R}(R\leq r)=\int_{0}^{2\pi}\int_{0}^{r}\frac{1}{2\pi}e^{\frac{-R^{2}}{2}}Rd \theta dR=1-e^{-\frac{r^{2}}{2}} \tag{3}\]  
\[P_{b}(\theta\leq\phi)=\int_{0}^{\phi}\int_{0}^{\infty}\frac{1}{2\pi}e^{\frac{- R^{2}}{2}}Rd\theta dR=\frac{\phi}{2\pi} \tag{4}\]  
Retrieved from \(P_{R}\) inverse function  
\[R=F_{R}^{-1}(1-z)=\sqrt{-2\ln(1-z)} \tag{5}\]  
When \(z\) follows a uniform distribution in [0, 1], the distribution function of \(R\) is \(P_{R}\). Thus, two random variables, \(U_{1}\) and \(U_{2}\), which obey a uniform distribution on [0, 1], can be selected such that  
\[\theta=2\pi U_{1},1-z=U_{2},R=\sqrt{-2\ln U_{2}} \tag{6}\]  
By substituting this into Equations (1) and (2), the normally distributed random quantities, \(X\) and \(Y\), were constructed. In this study, based on this principle, Gaussian random numbers were generated from uniformly distributed, pseudorandom numbers to approximately obey a normal distribution [23]. To intuitively understand the strength of the noise, this study used the following strategy to generate the noise: first, the image grayscale value was divided by 255 to normalize to the interval [0, 1]. Then, a noisy image was generated with a mean value of 0 and a variance of a given value of \(\sigma\). The noise and image were superimposed and set to 1 if the pixel value was greater than 1, and set to 0 if the pixel value was less than 0. Finally, the value was multiplied by 255 to map the pixel grayscale value back to 0-255. The \"0.1 noise\" mentioned in this paper indicates that \"0.1\" is the value of the parameter, \(\sigma\), in the noise generation process. The study area was the Bohai Sea ice monitoring dataset, and the dataset was the sea ice target monitoring dataset from the visible image of HY-1. The sea ice tag images were obtained from manual image interpretation.