Existing methods in planar region segmentation suffer the problems of vague boundaries and failure to detect small-sized regions. To address these, this study presents an end-to-end framework, named PlaneSeg, which can be easily integrated into various plane segmentation models. Specifically, PlaneSeg contains three modules, namely, the edge feature extraction module, the multiscale module, and the resolution-adaptation module. First, the edge feature extraction module produces edge-aware feature maps for finer segmentation boundaries. The learned edge information acts as a constraint to mitigate inaccurate boundaries. Second, the multiscale module combines feature maps of different layers to harvest spatial and semantic information from planar objects. The multiformity of object information can help recognize small-sized objects to produce more accurate segmentation results. Third, the resolution-adaptation module fuses the feature maps produced by the two aforementioned modules. For this module, a pairwise feature fusion is adopted to resample the dropped pixels and extract more detailed features. Extensive experiments demonstrate that PlaneSeg outperforms other state-of-the-art approaches on three downstream tasks, including plane segmentation, 3-D plane reconstruction, and depth prediction. Code is available at https://github.com/nku-zhichengzhang/PlaneSeg.