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Partial person re-identification (re-id) is a challenging problem, where only a partial observation of a person image is available for matching. However, few studies have offered a solution of how to identify an arbitrary patch of a person image. In this paper, we propose a fast and accurate matching method to address this problem. The proposed method leverages Fully Convolutional Network (FCN) to generate correspondingly-size spatial feature maps such that pixel-level features are consistent. To match a pair of person images of different sizes, a novel method called Deep Spatial feature Reconstruction (DSR) is further developed to avoid explicit alignment. Specifically, we exploit the reconstructing error from dictionary learning to calculate the similarity between different spatial feature maps. In that way, we expect that the proposed FCN can decrease the similarity of coupled images from different persons and vice versa. Experimental results on two partial person datasets demonstrate the efficiency and effectiveness of the proposed method in comparison with several state-of-the-art partial person re-id approaches.