## 4 Remote Sensing Image Scene Retrieval
### Retrieval by Distance Measures  
[PERSON] et al. [57] added eight similarity metrics into RSISR, and showed the impact of this. For a particular retrieval task, a suitable similarity metric can get K nearest neighbors, preferably by weighing the similarities between features, which makes the results more desirable. Distance measures in his paper include two categories: general feature vector-based metrics, which includes three distances of Minkowski, and the cosine of the angle; and histogram vector-based measures, which includes  
Figure 3: Flowchart of remote sensing image scene retrieval (RSISR). The input remote sensing (RS) scene datasets are trained in deep networks. After feature hashing, which is aimed to reduce dimension, and the first similarity matching from large-scale images, relevance ranking can be further achieved according to the similarity among the query image and retrieved images. the histogram intersection, center moment, \(\chi^{2}\) statistical distance, and Bhattacharyya distance. This research intuitively demonstrates that similarity metrics for a content-based RS retrieval task are very significant, and various similarity metrics may result in distinctive ranking results, but the distance metrics in his work were not applied here to measure the deep features. Assume the feature vectors of query image scene Q and image scene D in the data set are \(q=\{q_{1},\ldots,q_{n}\}\) and \(d=\{d_{1},\ldots,d_{n}\}\). For instance, \(L1,\ L2,\ L\infty\) that were developed from a set of distance functions known as the Minkowski r-metric can be defined. For r = l, it is the city-block distance (i.e., \(L1\) or Manhattan distance),  
\[d1(q,d)=\sum_{i=1}^{n}\bigl{|}q_{i}-d_{i}\bigr{|} \tag{3}\]  
For r = 2, it is the Euclidean distance (i.e., \(L2\)),  
\[d2(q,d)=\sqrt{\sum_{i=1}^{n}(q_{i}-d_{i})^{2}} \tag{4}\]  
And for r = \(\infty\), it is the dominance distance (i.e., \(L\infty\)),  
\[d\infty(q,d)=\max_{i}\bigl{|}q_{i}-d_{i}\bigr{|} \tag{5}\]  
For RSISR, deep learning techniques can be roughly divided into unsupervised feature learning and supervised feature learning methods. Due to the spatial complexity of image scenes, unsupervised feature learning can accurately describe semantic information. Unsupervised feature learning is attractive for RS, since RS has less labeled data than a few image analysis areas. For example, in the ImageNet data set in the field of computer vision, more than 15 million images were tagged. However, few RS data sets contain more than 10,000 annotated images. [PERSON] et al. [56] first learned features sparser from RS images utilizing the auto-encoder, as well as minimizing the memory of features. They developed an unsupervised feature learning framework (UFLF), and \(L1\) and \(L2\) were utilized to weigh the similarity for the sparse features produced by their framework. Besides these two measures, he also employed a histogram intersection. However, the auto-encoder network of the framework is very shallow, and only has a single hidden layer, which makes it incapable of producing sufficiently powerful feature representations. Furthermore, the features learned in an unsupervised way may require longer codes to attain satisfactory results of retrieval, which will largely reduce the image retrieval efficiency. Deeper networks are necessary for RSISR. In high-spatial resolution RS images retrieval, the deep features produced by the Full Connection (FC) layers are usually large, and present computational and storage challenges. This problem has been well-addressed by [PERSON] [58], and the limitations, which merely consider features produced by the last FC layer, are solved. They performed transfer learning for RSISR by taking into consideration features from the FC and convolutional layers from a wider range of CNN. In their framework, scenes were decomposed under the Quin-tree decompositional principle.