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 pair-wise 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.
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