  Image segmentation plays a crucial role in extracting important objects of
interest from images, enabling various applications. While existing methods
have shown success in segmenting clean images, they often struggle to produce
accurate segmentation results when dealing with degraded images, such as those
containing noise or occlusions. To address this challenge, interactive
segmentation has emerged as a promising approach, allowing 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. Additionally, the segmentation mask is obtained by
deforming a template mask with the same topology as the object of interest
using an orientation-preserving quasiconformal mapping. This approach helps to
avoid topological errors in the segmentation results. We provide a thorough
analysis of the proposed model, including theoretical support for the ability
of QIS 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, natural images and noisy natural images.
The results demonstrate the efficacy of our proposed method.
