###### Abstract  
As satellite observation technology rapidly develops, the number of remote sensing (RS) images dramatically increases, and this leads RS image retrieval tasks to be more challenging in terms of speed and accuracy. Recently, an increasing number of researchers have turned their attention to this issue, as well as hashing algorithms, which map real-valued data onto a low-dimensional Hamming space and have been widely utilized to respond quickly to large-scale RS image search tasks. However, most existing hashing algorithms only emphasize preserving point-wise or pairwise similarity, which may lead to an inferior approximate nearest neighbor (ANN) search result. To fix this problem, we propose a novel triplet ordinal cross entropy hashing (TOCEH). In TOCEH, to enhance the ability of preserving the ranking orders in different spaces, we establish a tensor graph representing the Euclidean triplet ordinal relationship among RS images and minimize the cross entropy between the probability distribution of the established Euclidean similarity graph and that of the Hamming triplet ordinal relation with the given binary code. During the training process, to avoid the non-deterministic polynomial (NP) hard problem, we utilize a continuous function instead of the discrete encoding process. Furthermore, we design a quantization objective function based on the principle of preserving triplet ordinal relation to minimize the loss caused by the continuous relaxation procedure. The comparative RS image retrieval experiments are conducted on three publicly available datasets, including UC Merced Land Use Dataset (UCMD), SAT-4 and SAT-6. The experimental results show that the proposed TOCEH algorithm outperforms many existing hashing algorithms in RS image retrieval tasks. remote sensing image retrieval; hashing algorithm; binary code; triplet ordinal relation preserving; cross entropy +
Footnote †: journal:  
0000-0001-9399-2278-2227]N.W. to Hamming distance; this measure effectively improves the retrieval speed. In summary, the content-based image retrieval method assisted by hashing algorithms enables the efficient and effective retrieval of target remote sensing images from a large-scale dataset. In recent years, many hashing algorithms [10; 11; 12; 13; 14] have been proposed to achieve the approximate nearest neighbor (ANN) search task, due to its advantage of computation and storage. According to the learning framework, the existing hashing algorithms can be roughly divided into two types: the shallow model [12; 13; 14] and the deep model [10; 11; 15; 16]. Conventional shallow hashing algorithms, such as locality sensitive hashing (LSH) [14], spectral hashing (SH) [17], iterative quantization hashing (ITQ) [13] and k-means hashing (KMH) [12], have been applied to various approximate nearest neighbor search tasks, including image retrieval. Locality sensitive hashing [14] is a kind of data-independent method, which learns hashing functions without a training process. LSH [14] randomly generates linear hashing functions and encodes data into binary codes according to their projection signs. Spectral hashing (SH) [17] utilizes a spectral graph to represent the similarity relationship among data points. The binary codes in SH are generated by partitioning a spectral graph. Iterative quantization hashing [13] considers the vertexes of a hyper cubic as encoding centers. ITQ [13] rotates the principal component analysis (PCA) projected data and maps the rotated data to the nearest encoding center. The encoding centers in ITQ are fixed and they are not adaptive to the data distribution [12]. To fix this problem, k-means hashing [12] learns the encoding centers by simultaneously minimizing the quantization error and the similarity loss. KMH [12] encodes the data as the same binary code as the nearest center.