  While most state-of-the-art instance segmentation methods produce binary
segmentation masks, geographic and cartographic applications typically require
precise vector polygons of extracted objects instead of rasterized output. This
paper introduces PolyWorld, a neural network that directly extracts building
vertices from an image and connects them correctly to create precise polygons.
The model predicts the connection strength between each pair of vertices using
a graph neural network and estimates the assignments by solving a
differentiable optimal transport problem. Moreover, the vertex positions are
optimized by minimizing a combined segmentation and polygonal angle difference
loss. PolyWorld significantly outperforms the state of the art in building
polygonization and achieves not only notable quantitative results, but also
produces visually pleasing building polygons. Code and trained weights are
publicly available at https://github.com/zorzi-s/PolyWorldPretrainedNetwork.
