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Object detection involves acquiring position information and classification information of objects simultaneously in an image acquired using an image sensor. In general, a small object that occupies a relatively small area within an image is difficult to detect because the information contained in the image is fundamentally inadequate. A person can recognize small objects that are very far away using contextual information, such as the background or relationship with nearby objects. Therefore, it is necessary to enhance the characteristics of small objects using various context information in the image. A new feature enhancement neural network is proposed to enhance the feature maps by extracting the relationships between the non-local features of various sizes. This paper presents an object detection algorithm that is robust against small-object detection based on the feature enhancement neural network. A feature map from the feature-extraction neural network was first branched into multiple feature maps with different receptive fields using respective convolution layers. Non-local relationships between these feature maps were then computed and added to the original feature map for feature enhancement. Finally, the proposed network reflected the overall context information of the image through the enhanced feature map, which is more robust for detecting small objects. The experimental results showed that the proposed method had better performance in small-object detection than the state-of-the-art techniques for the KITTI dataset and PASCAL VOC dataset.