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Stitched images provide a wide field-of-view (FoV) but suffer from unpleasant irregular boundaries. To deal with this problem, existing image rectangling methods devote to searching an initial mesh and optimizing a target mesh to form the mesh deformation in two stages. Then rectangular images can be generated by warping stitched images. However, these solutions only work for images with rich linear structures, leading to noticeable distortions for portraits and landscapes with non-linear objects. In this paper, we address these issues by proposing the first deep learning solution to image rectangling. Concretely, we predefine a rigid target mesh and only estimate an initial mesh to form the mesh deformation, contributing to a compact one-stage solution. The initial mesh is predicted using a fully convolutional network with a residual progressive regression strategy. To obtain results with high content fidelity, a comprehensive objective function is proposed to simultaneously encourage the boundary rectangular, mesh shape-preserving, and content perceptually natural. Besides, we build the first image stitching rectangling dataset with a large diversity in irregular boundaries and scenes. Experiments demonstrate our superiority over traditional methods both quantitatively and qualitatively.