In this paper, we propose PolyTransform, a novel instance segmentation algorithm that produces precise, geometry-preserving masks by combining the strengths of prevailing segmentation approaches and modern polygon-based methods. In particular, we first exploit a segmentation network to generate instance masks. We then convert the masks into a set of polygons that are then fed to a deforming network that transforms the polygons such that they better fit the object boundaries. Our experiments on the challenging Cityscapes dataset show that our PolyTransform significantly improves the performance of the backbone instance segmentation network and ranks 1st on the Cityscapes test-set leaderboard. We also show impressive gains in the interactive annotation setting.