Medical image segmentation is often a prerequisite for clinical applications. As an ill-posed problem, it leads to uncertain estimations of the region of interest which may have a significant impact on downstream applications, such as therapy planning. To quantify the uncertainty related to image segmentations, a classical approach is to measure the effect of using various plausible segmentations. In this paper, a method for producing such image segmentation samples from a single expert segmentation is introduced. A probability distribution of image segmentation boundaries is defined as a Gaussian process, which leads to segmentations that are spatially coherent and consistent with the presence of salient borders in the image. The proposed approach outperforms previous generative segmentation approaches, and segmentation samples can be generated efficiently. The sample variability is governed by a parameter which is correlated with a simple DICE score. We show how this approach can have multiple useful applications in the field of uncertainty quantification, and an illustration is provided in radiotherapy planning.