The digital elevation model (DEM) is an important basic data tool applied in geoscience applications. Because of its high cost and long development cycle of enhancing hardware performance, designing the related models and algorithms to improve the resolution of DEM is of considerable significance. At present, there is little research on DEM super-resolution based on deep learning, and the results of the reconstructed DEMs obtained by existing methods are inaccurate. Therefore, deepening of the network layers is utilized to improve the accuracy of a reconstructed DEM. This paper designs a neutral network model with 30 convolutional layers to learn the feature mapping relationship between a low- and high-resolution DEM. To avoid the problem of network degradation caused by increasing the number of convolutional layers, residual learning is introduced to accelerate the convergence speed of the model, thereby preferably realizing the DEM super-resolution process. The results show that DEM super-resolution based on a deep residual network is better than that obtained using a neural network with fewer convolutional layers, and the reconstructed result of the DEM based on a deep residual network is remarkably improved in terms of the peak signal to noise ratio and visual effect.
A digital elevation model (DEM) is a digital simulation of a surface’s topography through limited terrain elevation data, and it is a digital expression of the supracrustal condition . The DEM uses a simple data organization method, which can express the terrain directly and interpret terrain factors efficiently. At present, there are two ways to obtain DEM data. The first way is to collect DEM data directly through various kinds of measurement instruments, such as using a satellite, aircraft and total station to survey and map the terrain and use LiDAR or InSAR for interferometry [2,3,4,5]. The second way is to design related models or algorithms that can be applied to existing low-resolution DEMs to obtain high-resolution DEMs, and the method based on digital topographic map and professional software to obtain high-resolution DEM is also very common . Obtaining a high-resolution DEM through the first method depends on the use of more precise instruments, but developing high-precision instruments often requires more time and resources. This requirement makes the second method cost-effective and promising. Therefore, it is of great significance to design a method to improve the accuracy of DEMs efficiently and conveniently such that DEMs can be more widely applied.
The interpolation algorithm is a kind of important scaling conversion method. At present, the frequently used interpolation algorithms for the DEM primarily include linear interpolation, polynomial interpolation, spline interpolation and kriging interpolation [7,8,9,10]. Zhang et al. compared different interpolation methods based on ASTER-DEM data and found that different interpolation methods have different experimental results under different conditions; therefore, the selection of an interpolation method should depend on the actual situation . Hutchinson algorithm  can use contour lines and other information in digital topographic maps to interpolate DEM and has been widely used in hydrological analysis and simulation. Inverse Distance Weight is a suitable interpolation method for DEM generation from LiDAR data because the LiDAR data have high sampling density .
Although the interpolation algorithm is simple and the implementation speed is fast, the algorithm often leads to fuzzy or jagged edges when reconstructing DEM. Zhang found that not only multilevel wavelet analysis could enhance the high-frequency characteristic of images, which could be used to improve the resolution of DEM , but also nonlocal similarity and neighborhood reconstruction could be combined to improve the resolution of a DEM . Multisource data fusion can combine different spatial data from different sources via different methods to generate thematic attribute data, which can further improve the geometric accuracy and quality of a DEM . Karkee et al. used a new void filling approach to effectively fuse optical images and InSAR images in order to obtain a high-precision DEM . Jhee et al. combined the super-resolution algorithm based on learning with a multiscale Kalman smoother, which has a tree structure graph to realize multiresolution and multiscale DEM modeling . Tang et al. proposed an enhanced data fusion method based on a modified FILTERSIM by integrating high-resolution but sparsely sampled DEM data to generate high-resolution DEM data, which can obtain higher accuracy . Although multisource data fusion can fully extract the useful information in all kinds of data and realize the complementary advantages of multisource data, the accuracy of the reconstruction data could not be effectively improved when the data sources were insufficient.
Image super-resolution reconstruction refers to the technology of transforming existing low-resolution (LR) images into high-resolution (HR) images by designing relevant models or algorithms based on image processing and signal processing . Image super-resolution can further enhance the spatial resolution and the visual effect of images without changing the imaging system, which is conducive to feature extraction and information recognition for images. In 1984, Tsai et al. first proposed the concept of image super-resolution . After decades of development and progress, image super-resolution has gradually formed a research system composed of interpolation, reconstruction and learning-based image super-resolution methods. For example, Nguyen introduced the wavelet analysis into super-resolution based on the interpolation and verified the effectiveness of the algorithm by using one-dimensional and two-dimensional data . Elad et al. proposed a hybrid method combining maximum likelihood (ML) and projection onto convex sets (POCS), which has better image restoration performance . Zeyde et al. simplified and improved the K-SVD dictionary learning algorithm to promote the speed and accuracy of the algorithm on the premise of fewer data sets . In recent years, with the rapid development of deep learning, a variety of neural network models have emerged. The neural network models constructed by people can have strong feature learning abilities, which enable the models to further extract more useful information from the data. Deep learning, ranging from the supervised learning image super-resolution method based on the convolutional neural network (CNN)  at the beginning to unsupervised learning image super-resolution method based on the generative countermeasure network  in recent years, has been widely used in the field of image super-resolution. Compared with the other two methods, the learning-based image super-resolution method has higher accuracy and the texture details of the reconstructed image that is closer to the real image are abundant.
Therefore, the image super-resolution method is introduced to DEM super-resolution in this paper. A deep convolutional network was constructed to learn the feature mapping relationship between low-resolution and high-resolution DEMs, and the residual network was introduced to solve the degradation phenomenon caused by the deep network. This model could obtain more useful information from the DEM; thus, the detailed texture features of the reconstructed DEM can be better recovered, and the accuracy of the DEM can be effectively improved.
2 Related works
In this section, we will introduce some contents about super-resolution reconstruction, which could be divided into image super-resolution based on the CNN and DEM super-resolution reconstruction based on the CNN.
2.1 Image super-resolution based on the CNN
With the breakthrough of deep learning in the field of computer vision, people have attempted to construct neural network models to conduct end-to-end training to effectively solve the problem of image super-resolution reconstruction. The CNN  is a representative network in the field of deep learning. The CNN has a wide range of applications, especially in the fields of image processing and analysis. The basic structure of a CNN is composed of input layers, convolutional layers, pooling layers, fully connected layers and output layers (Figure 1). In general, the convolutional and pooling layers are connected alternately, and the total network will eventually have one or more fully connected layers .
Compared with traditional image processing algorithms, the CNN can avoid artificial participation in the process of complex image preprocessing and can directly learn the feature relationships between images. Based on the CNN, Dong et al. proposed the super-resolution convolutional neural network (SRCNN) , which is a classic neural network that can be applied to image super-resolution. This method is known as the pioneering work of deep learning applied to image super-resolution. SRCNN can directly learn the feature mapping relationship between low- and high-resolution images by building a three-layer convolutional network. Based on this feature mapping relationship, high-resolution images can be reconstructed from low-resolution images. First, the original images are interpolated into low-resolution images via bicubic interpolation. Then, the low-resolution images are input into the networks. The input images successively pass through the feature detection, nonlinear function mapping and reconstruction layers, and finally, the high-resolution image was output by the SRCNN (Figure 2).
In the training process of a neural network model, increasing the number of network layers is often adopted to extract the deep features from the data. However, when the depth of the network is increased, the exploding gradient or vanishing gradient phenomena often occur, which is not conducive to the model training. Although this problem has been effectively controlled by the standard initialization and middle layer normalization methods, network degradation is the main factor affecting the performance of the model. He et al. proposed a Residual Network  that combined residual learning with the CNN. Experimental results showed that the residual network can effectively solve the degradation problem of a deep neural network and improve the convergence speed of the model.
In this paper, the features of DEM data are extracted through the combination of a deep convolutional and residual network to effectively realize the transformation from low-resolution DEM data to high-resolution DEM data.
2.2 DEM super-resolution based on the CNN
The process of DEM super-resolution is a more micro and precise spatial expression, which is similar to the process of using a low-resolution image to generate a high-resolution image using image super-resolution . DEM data reflect the superficial information of the three-dimensional objects on the surface and the height of the objects can be regarded as the gray values of the image. Therefore, the knowledge of image super-resolution can be applied to DEM super-resolution. The concept of DEM super-resolution was first proposed in Xu's work where a nonlocal algorithm was applied to improve the resolution of the DEM and the thinking that there are multiple duplicate or similar parts in a single DEM was used as a reference . Yue et al. integrated resolution enhancement, noise suppression and data hole filling into a general framework through Markov random field regularization and then used the complementary information between different DEMs to generate a high-resolution DEM . In recent years, some researchers have also explored how to apply a deep learning method to DEM super-resolution reconstruction. Chen et al.  tried to improve the resolution of a DEM based on a CNN, and the results showed that this method could achieve a better effect than bicubic  interpolation. Xu et al.  proposed an image super-resolution algorithm for a DEM, which could obtain a high-precision DEM based on a small number of DEM samples. Although the CNN has been widely used in the field of image super-resolution, the research on DEM super-resolution reconstruction based on the CNN is relatively less. Moreover, the existing methods that only use several convolutional layers have shortcomings recovering the details of a reconstructed DEM and the texture of reconstructed images is relatively fuzzy. Therefore, there is great potential for improving accuracy.
In this paper, we build a model based on a deep residual network to reconstruct DEM data with super-resolution. The specific implementation process is shown in Figure 3. First, the data need to be normalized before the data are input. After the data are input, bicubic interpolation is adopted to generate low- and high-resolution DEM data to participate in model training. The residual of the input data will be obtained after the original data passed through the 30 convolutional layers. At last, the original input data and the residual data should be added to get the final output of the network, and the output is the reconstructed high-resolution DEM.
In the existing work on DEM super-resolution reconstruction based on deep learning, the network structure of the model is only composed of several simple convolutional layers, which often leads to blurred textures and details in the reconstructed images. Considering that the deep network can extract the deep feature information of data, this paper tried to construct a model with 30 convolutional layers in which each convolutional layer contains a rectified linear unit (ReLU) . Furthermore, our model also used a larger receptive field to obtain contextual information. After each convolutional operation, 0 should be padded in the output data to prevent the image size from increasing. In this way, the deep network model can further extract the feature information from DEM data, which is helpful to restore the texture of the reconstructed image.
In the image super-resolution reconstruction process, the low-frequency information contained in the input low-resolution image and the output high-resolution image is similar; therefore, the model only needs to learn the high-frequency residual between the low-resolution images and the high-resolution images. As such, the residual learning strategy should be adopted in DEM super-resolution. In this paper, the residual block structure is introduced to optimize the model. The basic structure of a block of the residual network is shown in Figure 4, where x is the input data of the residual block, the expected output is H(x) and f(x) is the residual error in this block. The residual block constructs an identity map H(x) = x when redundant layers exist in the model. The redundant layers can be skipped by constructing identity mapping in the model training process to ensure that the input and output are equal when data pass through the layers. Therefore, adding a residual block structure to our 30-layer convolution network can effectively speed up the convergence of the model and avoid the influence of network degradation on the accuracy of the reconstructed DEM.
4.1 Experimental data
At present, the Shuttle Radar Topography Mission (SRTM) DEM and Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM) are open DEM data sources with the characteristics of simple acquisition, wide application and coverage over most parts of the world . The SRTM data are a global DEM that was jointly surveyed by NASA and the national mapping agency of the United States Department of Defense (NIMA), and it has experienced several revisions. The ASTER GDEM is based on the detailed observation results of NASA’s new generation earth observation satellite Terra . When evaluating the accuracy of DEM data at the same resolution, the accuracy of the SRTM DEM is higher than that of the ASTER GDEM data. In the more mountainous areas, the effect of the terrain relief on the accuracy of the SRTM is more significant .
In this paper, the SRTM DEM data at a 30 m resolution for the range of eastern China are selected as the experimental data. The DEM data are located 29° N to 30° N and 117° E to 118° E. The study area encompassing the experimental DEM data is shown in Figure 5. There are many mountains and gullies in this region where the land surface is undulating and rugged, and the textures of the mountains and gullies area are notably clear; thus, these DEM data in this area are much suitable for the judgement and evaluation of the reconstruction effect. Therefore, this paper selects the SRTM data at a 30 m resolution in this region as the experimental data for the related experiments.
4.2 Data preprocessing
The data set used in this paper is composed of 200 DEM images with a size of 256 × 256 pixels. Data preprocessing is conducted to normalize the DEM data, that is, to normalize the gray values of the DEM from 0 to 1 to eliminate the influence of local perception characteristics. Before the DEM data are input into the model, Matlab is used to interpolate the data and cut the bigger images into smaller images. The data are generated by cutting the grayscale DEM images to a size of 41 × 41 pixels. The total data include the original resolution data and the 2-fold, 3-fold and 4-fold resolution data, which are generated by scaling. At last, the total data encompass 57,599 groups.
4.3 Parameter setting
Our model consists of a 30-layer convolutional network (each layer is 3 × 3). The input data need to be filled with 0 s after the input data pass through a convolutional layer to avoid a large change in the DEM image size. This paper selected the Adam  optimization algorithm to reduce the model loss and selected the exponential decay method to set the learning rate of the model. About 64 samples are selected from the training set for each iteration in the model training, and the number of training epochs is set to 120. The learning rate of the model is 0.0001. The experimental code is run in the Anaconda software based on Python 3.6 and TensorFlow 1.12. Training takes approximately 12 h on a single NVIDIA GTX 1060 GPU.
4.4 Comparison method of experimental results
Image super-resolution methods based on interpolation mainly include the nearest neighbor, bilinear and bicubic methods. The main idea of image super-resolution based on interpolation is that the neighborhood pixels are used to calculate the pixels that should be interpolated. Bicubic interpolation calculates the pixel values of four adjacent points around the interpolation points, and then the calculated pixel values are linearly weighted and assigned to the interpolation points . Because the edge of an image that is reconstructed via bicubic interpolation is smooth and the visual effect is very good, this paper chooses bicubic interpolation as the experimental comparison method.
In addition, a three-layer convolutional network is designed for DEM super-resolution based on the SRCNN. The contrast experimental data set is composed of 200 DEM gray-scale images (each image is sized 256 × 256). Before inputting the data into the three-layer convolutional network, the DEM with a 30 m resolution should also be interpolated via bicubic interpolation. The low-resolution DEM data are selected as the input data and the original high-resolution DEM data are selected as the label data. Then, both sets are input into the 3-layer convolutional network. The sizes of the convolutional kernels used by three-layer convolutional network are 9 × 9, 1 × 1 and 5 × 5. At the end of the model training, the results of DEM reconstruction are compared with those of the deep residual network to explore the influence of the network layers on the reconstruction quality. The DEM super-resolution process based on the CNN is shown in Figure 6.
4.5 Evaluation method of experimental results
At present, visual effect and quantitative evaluation are two main methods to evaluate the quality of reconstructed images. The visual effect mainly refers to comparing the images reconstructed by different methods and judges the visual quality of reconstructed images by using the naked eye. The peak signal to noise ratio (PSNR)  is a measure of the pixel difference between the reconstructed high-resolution images and the real high-resolution images. The PSNR (formula (1)) represents the ratio of the maximum signal power to the noise power and it can be used to measure the quality of a processed image. It is the most widely used standard to evaluate image quality.
MSE refers to the mean squared error between the original image and the reconstructed image. Although the pixel value of a common image is generally from 0 to 255, the gray values of DEM data are often considerably greater than 255. Therefore, it is necessary to improve the calculation formula of the PSNR. According to the definition of the PSNR, the maximum value (255) defined in the original formula can be changed to the difference between the maximum and minimum gray values in DEM data. Therefore, the calculation formula of the PSNR used in DEM super-resolution is shown in formula (2), where ΔS is the difference between the maximum and minimum gray values of the DEM.
This paper also introduced the mean absolute error (MAE)  and root mean square error (RMSE)  to evaluate the quality of a reconstructed DEM. The MAE (formula (3)) can better reflect the actual situation of prediction error.
The RMSE (formula (4)) is a kind of numerical accuracy index that is widely used to evaluate the accuracy of DEM. It does not reflect the size of a single point’s error, but rather it describes the discrete degree of terrain parameters and true values in the overall sense.
5 Analysis of experimental results
5.1 Analysis of reconstructed results
The results of DEM super-resolution at different scale factors (2, 3 and 4) are compared (Table 1) and a scatter plot (Figure7) was constructed for more intuitive understanding. When the sampling factor of the DEM is the same, the experimental results show that the PSNRs of the reconstructed DEM based on the CNN are higher than those of the bicubic interpolation. The PSNRs of the reconstructed DEM based on the deep residual network are greatly improved compared with the bicubic interpolation and the CNN. Therefore, we found that the structure of the deep network can further improve the PSNRs of the reconstructed DEM.
|Scale factor||Bicubic||CNN||Deep residual network|
The results of DEM super-resolution based on the bicubic interpolation method are shown in Figure 8, the results of DEM super-resolution based on the CNN are shown in Figure 9 and the results of DEM super-resolution based on the deep residual network are shown in Figure 10. It can be found that the quality of the reconstructed DEM worsens when the scale factor of the DEM increases. The deep residual network can get better reconstructed details for the DEM than the shallow convolutional networks.
5.2 Analysis of reconstructed quality for DEM
The reconstructed effects of the DEM based on bicubic interpolation (b), the CNN (c) and the deep residual network (d) when the scale factor is 3 are shown in Figure 11 (the original DEM is (a)). Through the comparison of the three methods, we found that the details of the DEM reconstructed by the CNN and deep residual network are more abundant, the texture of mountains in DEM data is clearer, and the trend of the mountains can be seen. In addition, the reconstructed DEMs were displayed intuitively by cross-section analysis, the results show that the curve of cross-section analysis obtained from the deep residual network is closer to that of the original DEM data (Figure 12).
Taking the scale factor (3) of the DEM as an example, the quality of the reconstructed DEM is evaluated by the MAE and RMSE (Table 2), the basic parameters (Maximum, Minimum and Standard Deviation) of that DEMs are also showed visually in Table 3, besides, the frequency distribution of reconstructed DEMs is shown by histogram (Figure 13). The data in the table show that the MAE and RMSE of the reconstructed DEM based on the deep residual network are far less than those of the bicubic interpolation and the CNN. The histogram shows that the results of our method are closer to the original DEM.
|Compared with origin DEM||MAE||RMSE|
|Deep residual network||3.691||4.829|
|DEM type||Elevation differences [m]|
|Deep residual network-DEM||289||1,300||204.853|
In addition, we also extracted the regions of the mountain valley (Figure 14) and mountain ridge (Figure 15) in the reconstructed DEM for a comparison. By comparing the results of the mountain valleys and ridges that were extracted from the reconstructed DEM, we see that the deep residual network could acquire clearer details and textural features than other methods, and the details and textures are closer to the original data.
5.3 Extend our approach to other study areas
In this paper, the texture of the DEM data in mountainous area is very clear so that this type of area is suitable for research and analysis of DEM, but our research has not been applied to the DEM data of urban, coastal or other areas. However, we have noticed that more and more scholars have gradually used deep learning technology to research in related fields. For example, some scholars have proposed that neural network model can be used to eliminate the positive vertical error in SRTM data in coastal regions  and the multiscale mapping approach based on CNN can also be used to deal with the complex features of urban topography and to reconstruct high-resolution urban DEMs . Therefore, we believe that the improvement of our method may achieve good results according to the characteristics of urban and coastal areas.
For different types of data, such as LiDAR and bathymetric data, neural network models have also achieved certain results with its strong feature extraction ability. In the urban scene classification based on LiDAR point cloud data, the combination of CNN and RNN can effectively realize the efficient semantic analysis of large-scale 3D point cloud  and the combination of Mask R-CNN and LiDAR has great potential for mapping anthropogenic and natural landscape features . In the field of bathymetric survey, deep learning methods are becoming more and more active, for example, some experts and scholars obtained high-resolution water depth data by introducing convolution neural network to process the remote sensing image data and water depth data in shallow water area . It can be seen that neural network model can play an important role in feature extraction of different data, but there is no universal neural network model that could be involved in the feature extraction of various types of data.
Therefore, we will also pay more attention to the applicability of our method in other areas, and further explore the mapping and feature extraction of deep residual network in various kinds of geospatial and remote sensing data in the future work.
In this paper, a method of DEM super-resolution based on a deep residual network is proposed. Our method can effectively extract the feature mapping relationship between a low- and high-resolution DEM using a deep convolutional network. In addition, a residual network was introduced to our model to accelerate the convergence speed of the model to quickly and effectively realize DEM super-resolution process.
The results show that the deep residual network has a greater impact on DEM super-resolution. Compared with the convolutional network with fewer layers, our method based on the deep residual network significantly improves the DEM’s reconstructed details and recovered textures. It can be seen that the structure of the deep network is of considerable value for improving the resolution of DEMs.
We would like to thank Wei He for providing important feedback, suggestions and code contributions to the project. This research was funded by the National Natural Science Foundation of China, grant number 41471329 and 41101358.
Author contributions: Donglai Jiao: writing – original draft, writing – review and editing. Dajiang Wang: software, validation, methodology. Haiyang Lv: investigation, data curation. Yang Peng: project administration.
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