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.

翻译：图像分割在从图像中提取重要目标对象方面发挥着关键作用，能够支持多种应用。现有方法虽然在分割清晰图像方面取得了成功，但在处理退化图像（如含有噪声或遮挡的图像）时，往往难以产生准确的分割结果。为应对这一挑战，交互式分割作为一种有前景的方法应运而生，它允许用户提供有意义的输入来指导分割过程。然而，交互式分割中的一个重要问题在于如何将最少但有效的用户引导信息整合到分割模型中。本文提出拟共形交互分割（QIS）模型，该模型以正负点击的形式纳入用户输入。用户将属于目标区域的若干像素标记为正点击，指示分割模型应包含这些点击周围的区域；反之，在属于背景的像素上提供负点击，则指示模型从分割掩码中排除这些点击附近的区域。此外，分割掩码是通过使用保持定向的拟共形映射，对与目标对象具有相同拓扑结构的模板掩码进行形变而获得的。该方法有助于避免分割结果中的拓扑错误。我们对所提模型进行了全面分析，包括从理论上论证QIS能够根据用户指示包含或排除相关/无关区域的能力。为评估QIS的性能，我们在合成图像、医学图像、自然图像及含噪自然图像上进行了实验，结果验证了所提方法的有效性。