https://github.com/wangjuan313/wsis-beyond-tightBB}.
Weakly supervised image segmentation approaches in the literature usually achieve high segmentation performance using tight bounding box supervision and decrease the performance greatly when supervised by loose bounding boxes. However, compared with loose bounding box, it is much more difficult to acquire tight bounding box due to its strict requirements on the precise locations of the four sides of the box. To resolve this issue, this study investigates whether it is possible to maintain good segmentation performance when loose bounding boxes are used as supervision. For this purpose, this work extends our previous parallel transformation based multiple instance learning (MIL) for tight bounding box supervision by integrating an MIL strategy based on polar transformation to assist image segmentation. The proposed polar transformation based MIL formulation works for both tight and loose bounding boxes, in which a positive bag is defined as pixels in a polar line of a bounding box with one endpoint located inside the object enclosed by the box and the other endpoint located at one of the four sides of the box. Moreover, a weighted smooth maximum approximation is introduced to incorporate the observation that pixels closer to the origin of the polar transformation are more likely to belong to the object in the box. The proposed approach was evaluated on two public datasets using dice coefficient when bounding boxes at different precision levels were considered in the experiments. The results demonstrate that the proposed approach achieves state-of-the-art performance for bounding boxes at all precision levels and is robust to mild and moderate errors in the loose bounding box annotations. The codes are available at \url{