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Image matting is a key technique for image and video editing and composition. Conventionally, deep learning approaches take the whole input image and an associated trimap to infer the alpha matte using convolutional neural networks. Such approaches set state-of-the-arts in image matting; however, they may fail in real-world matting applications due to hardware limitations, since real-world input images for matting are mostly of very high resolution. In this paper, we propose HDMatt, a first deep learning based image matting approach for high-resolution inputs. More concretely, HDMatt runs matting in a patch-based crop-and-stitch manner for high-resolution inputs with a novel module design to address the contextual dependency and consistency issues between different patches. Compared with vanilla patch-based inference which computes each patch independently, we explicitly model the cross-patch contextual dependency with a newly-proposed Cross-Patch Contextual module (CPC) guided by the given trimap. Extensive experiments demonstrate the effectiveness of the proposed method and its necessity for high-resolution inputs. Our HDMatt approach also sets new state-of-the-art performance on Adobe Image Matting and AlphaMatting benchmarks and produce impressive visual results on more real-world high-resolution images.