We investigate the problem of image retrieval based on visual queries when the latter comprise arbitrary regionsof-interest (ROI) rather than entire images. Our proposal is a compact image descriptor that combines the state-of-the-art in content-based descriptor extraction with a multi-level, Voronoibased spatial partitioning of each dataset image. The proposed multi-level Voronoi-based encoding uses a spatial hierarchical K-means over interest-point locations, and computes a contentbased

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... ptor over each cell. In order to reduce the matching complexity with minimal or no sacrifice in retrieval performance: (i) we utilize the tree structure of the spatial hierarchical Kmeans to perform a top-to-bottom pruning for local similarity maxima; (ii) we propose a new image similarity score that combines relevant information from all partition levels into a single measure for similarity; (iii) we combine our proposal with a novel and efficient approach for optimal bit allocation within quantized descriptor representations. By deriving both a Voronoi-based VLAD descriptor (termed as Fast-VVLAD) and a Voronoi-based deep convolutional neural network (CNN) descriptor (termed as Fast-VDCNN), we demonstrate that our Voronoi-based framework is agnostic to the descriptor basis, and can easily be slotted into existing frameworks. Via a range of ROI queries in two standard datasets, it is shown that the Voronoibased descriptors achieve comparable or higher mean Average Precision against conventional grid-based spatial search, while offering more than two-fold reduction in complexity. Finally, beyond ROI queries, we show that Voronoi partitioning improves the geometric invariance of compact CNN descriptors, thereby resulting in competitive performance to the current state-of-theart on whole image retrieval. Index Terms-visual queries, Voronoi partitioning, vector of locally aggregated descriptors, convolutional neural networks, deep learning.