Abstract. Object detection and instance segmentation are dominated by region-based methods such as Mask RCNN. However, there is a growing interest in reducing these problems to pixel labeling tasks, as the latter could be more efficient, could be integrated seamlessly in imageto-image network architectures as used in many other tasks, and could be more accurate for objects that are not well approximated by bounding boxes. In this paper we show theoretically and empirically that constructing dense pixel embeddings that can separate object instances cannot be easily achieved using convolutional operators. At the same time, we show that simple modifications, which we call semi-convolutional, have a much better chance of succeeding at this task. We use the latter to show a connection to Hough voting as well as to a variant of the bilateral kernel that is spatially steered by a convolutional network. We demonstrate that these operators can also be used to improve approaches such as Mask RCNN, demonstrating better segmentation of complex biological shapes and PASCAL VOC categories than achievable by Mask RCNN alone