Predicting a binary mask for an object is more accurate but also more computationally expensive than a bounding box. Polygonal masks as developed in CenterPoly can be a good compromise. In this paper, we improve over CenterPoly by enhancing the classical regression L1 loss with a novel region-based loss and a novel order loss, as well as with a new training process for the vertices prediction head. Moreover, the previous methods that predict polygonal masks use different coordinate systems, but it is not clear if one is better than another, if we abstract the architecture requirement. We therefore investigate their impact on the prediction. We also use a new evaluation protocol with oracle predictions for the detection head, to further isolate the segmentation process and better compare the polygonal masks with binary masks. Our instance segmentation method is trained and tested with challenging datasets containing urban scenes, with a high density of road users. Experiments show, in particular, that using a combination of a regression loss and a region-based loss allows significant improvements on the Cityscapes and IDD test set compared to CenterPoly. Moreover the inference stage remains fast enough to reach real-time performance with an average of 0.045 s per frame for 2048$\times$1024 images on a single RTX 2070 GPU. The code is available $\href{https://github.com/KatiaJDL/CenterPoly-v2}{\text{here}}$.

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