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感兴趣的重要对象方面发挥着关键作用，支持多种应用。尽管现有方法在分割清晰图像时已取得成功，但在处理带有噪声或遮挡等退化图像时，往往难以生成准确的分割结果。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，允许用户提供有意义的输入以引导分割过程。然而，交互式分割中的一个重要问题在于如何将最少但有意义的用户引导纳入分割模型。本文提出了拟共形交互式分割（QIS）模型，该模型以正点击和负点击的形式整合用户输入。用户标记属于目标区域的若干像素作为正点击，指示分割模型应包含这些点击周围的区域；反之，负点击则标记在属于背景的像素上，指示模型从分割掩码中排除这些点击邻近的区域。此外，分割掩码通过使用保定向拟共形映射，对与感兴趣对象具有相同拓扑结构的模板掩码进行形变得到。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QIS基于用户指示包含或排除感兴趣或不感兴趣区域能力的理论支持。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开展了实验，结果证明了我们提出方法的有效性。