The objective of this paper is to design an embedding method that maps local features describing an image (e.g., SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship between the linear approximation of a nonlinear function in high dimensional space and the state-of-the-art feature representation used in image retrieval, i.e., VLAD, we propose a new approach for the approximation. The embedded vectors resulted by the function approximation process are then aggregated to form a single representation for image retrieval. Second, in order to make the proposed embedding method applicable to large scale problem, we further derive its fast version in which the embedded vectors can be efficiently computed, i.e., in the closed-form. We compare the proposed embedding methods with the state of the art in the context of image search under various settings: when the images are represented by medium length vectors, short vectors, or binary vectors. The experimental results show that the proposed embedding methods outperform existing the state of the art on the standard public image retrieval benchmarks.

中文翻译：

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基于函数逼近的大规模图像搜索嵌入

本文的目的是设计一种嵌入方法，该方法将描述图像的局部特征（例如SIFT）映射到对图像检索问题有用的更高维表示。首先，根据高维空间中非线性函数的线性逼近与图像检索中使用的最新特征表示（即VLAD）之间的关系，我们提出了一种新的逼近方法。然后，将由函数逼近过程产生的嵌入矢量进行汇总，以形成用于图像检索的单个表示形式。其次，为了使所提出的嵌入方法适用于大规模问题，我们进一步推导了其快速版本，在该版本中可以有效地计算嵌入矢量，即以封闭形式。我们在各种设置下（当图像由中等长度向量，短向量或二进制向量表示）时，将提出的嵌入方法与现有技术在图像搜索的上下文中进行比较。实验结果表明，在标准公共图像检索基准上，所提出的嵌入方法优于现有技术。