# A Multichannel-Based Deep Learning Framework for Ocean SAR Scene Classification
## 3 MCNN Framework for Geophysical Phenomenon Classification
### Data Augmentation  
A sufficient amount of training data is crucial to obtain state-of-the-art results in image classification tasks based on the deep learning method. Unfortunately, many application scenarios, such as oceanography and medicine [62; 63], cannot assure enough samples for algorithm training purposes. Data augmentation has been proved to be an effective way not only to expand the quantity, but also to improve the quality of the training progress by diversifying the dataset. In this study, we address the issue of limited sample size in the TenGeoP-SARwv dataset for ocean phenomenon detection by employing image warping and oversampling techniques. When utilizing SAR images for training models, we encountered a challenge due to the scarcity of samples. The shortage of training samples poses obstacles to the model in capturing robust feature representations, ultimately impacting its ability to generalize effectively. This limitation may lead to suboptimal predictive performance, especially for categories with insufficient sample representation. In this study, we tackle the challenges of limited samples and oversampling, both critical aspects for effective model training. Abundant samples are essential for robust model training and mitigating the risks of overfitting. To enhance dataset diversity, we employ data warping techniques initially. Data warping refers to altering existing samples; typical operations include geometric transformations, random cutting, and other alternations. This type of method is straightforward and effective and a random cropping algorithm is designed for this investigation. Parameters such as the maximum crop size and position are first defined as constraints. Then, the starting point and destination point are randomly generated to reconstruct a new sample. In the majority of interactive warping systems, the researchers specify the warp parameters in a broadly defined manner or indicate a point-to-point correspondence. Then, the automated system conducts geometric interpolation procedures to generate a cartographic representation based on the specified geometric parameters with a mapping \(M_{\text{s}}:\text{D}^{2}\rightarrow\text{D}^{2}\) of the plane to itself. We apply the mapping to our input SAR images \(I(x,y)\) and define the output images as \(O(x,y)=I(M_{\text{s}}^{-1}(x,y))\), where \(M_{\text{s}}^{-1}\) is the function inverse of \(M_{\text{s}}\). Note that \(M_{\text{s}}\) does not depend on the input \(I\) and the geometric specification \(S\) is based on SAR image features. To obtain \(M_{\text{s}}\) from the specification \(S\), we compute the unique thin-plate spline satisfying \(M_{\text{s}}\) with the solution \(u\) as follows:  
\[arg\underset{u(x,y)}{\iint}\int\limits_{D^{2}}(u_{xx}^{2}+2u_{xy}^{2}+u_{yy}^{ 2})dxdy, \tag{14}\]  
where \(u_{xx}\), \(u_{xy}\), \(u_{yy}\) represent \(\frac{\partial^{2}u}{\partial x^{2}}\), \(\frac{\partial u}{\partial x}\frac{\partial u}{\partial y}\), \(\frac{\partial^{2}u}{\partial y^{2}}\), respectively. In fact, \(M_{\text{s}}\) is independent of the input parameters \(I\), causing suboptimal outcomes. The mapping function ensures the functional minimization across the specified domain. The mapping procedure serves as an intermediate component and then is applied to image \(I\) after iterative computation. To enhance the robustness and separability of SAR images, we take contemporary warping procedures with a pair of bivariate real functions as \(M_{\text{s}}=(M_{\text{s}}^{X},M_{\text{s}}^{Y})\) independently. When invoking the thin-plate regularization paradigm, the procedure divides the interpolation constraints \(S\) into \(x\)-constraints and \(y\)-constraints and calculates the two mapping functions \(M_{\text{s}}^{X}\) and \(M_{\text{s}}^{X}\) to reduce the warping function of Equation (14).