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Benggang is a typical erosional landform in southern and southeastern China. Since benggang poses significant risks to local ecological environments and economic infrastructure, it is vital to accurately detect benggang-eroded areas. Relying only on remote sensing imagery for benggang detection cannot produce satisfactory results. In this study, we propose integrating high-resolution Digital Orthophoto Map (DOM) and Digital Surface Model (DSM) data for efficient and automatic benggang discovery. The fusion of complementary rich information hidden in both DOM and DSM data is realized by a two-stream convolutional neural network (CNN), which integrates aggregated terrain and activation image features that are both extracted by supervised deep learning. We aggregate local low-level geomorphic features via a supervised diffusion-convolutional embedding branch for expressive representations of benggang terrain variations. Activation image features are obtained from an image-oriented convolutional neural network branch. The two sources of information (DOM and DSM) are fused via a gated neural network, which learns the most discriminative features for the detection of benggang. The evaluation of a challenging benggang dataset demonstrates that our method exceeds several baselines, even with limited training examples. The results show that the fusion of DOM and DSM data is beneficial for benggang detection via supervised convolutional and deep fusion networks. [ABSTRACT FROM AUTHOR]