Region growing is a classical image segmentation method based on hierarchical region aggregation using local similarity rules. Our proposed method differs from classical region growing in three important aspects. First, it works on the level of superpixels instead of pixels, which leads to a substantial speed-up. Second, our method uses learned statistical shape properties that encourage plausible shapes. In particular, we use ray features to describe the object boundary. Third, our method can segment multiple objects and ensure that the segmentations do not overlap. The problem is represented as an energy minimization and is solved either greedily or iteratively using graph cuts. We demonstrate the performance of the proposed method and compare it with alternative approaches on the task of segmenting individual eggs in microscopy images of Drosophila ovaries.