QIS : Interactive Segmentation via Quasi-conformal Mappings

Interactive segmentation allows users to provide meaningful input to guide the segmentation process. However, an important problem in interactive segmentation lies in determining how to incorporate minimal yet meaningful user guidance into the segmentation model. In this paper, we propose the quasi-conformal interactive segmentation (QIS) model, which incorporates user input in the form of positive and negative clicks. Users mark a few pixels belonging to the object region as positive clicks, indicating that the segmentation model should include a region around these clicks. Conversely, negative clicks are provided on pixels belonging to the background, instructing the model to exclude the region near these clicks from the segmentation mask. By solving our proposed theoretical supported model, the segmentation mask is obtained by deforming a template mask with the same topology as the object of interest using a quasi-conformal mapping. This approach makes each user input effectively used and helps to avoid topological errors in the segmentation results. We provide a thorough theoretical analysis of the proposed model for its ability to include or exclude regions of interest or disinterest based on the user's indication. To evaluate the performance of QIS, we conduct experiments on synthesized images, medical images, and natural images. The results demonstrate the efficacy of our proposed method. © 2025 Society for Industrial and Applied Mathematics.