由调和贝尔特拉米签名引导的形状先验分割
Shape Prior Segmentation Guided by Harmonic Beltrami Signature
AI总结：
本文提出以调和贝尔特拉米签名作为形状先验，结合拟共形拓扑保持分割框架，通过两阶段迭代优化提升低质量或遮挡图像的分割精度与鲁棒性。
摘要：
本文提出了一种由调和贝尔特拉米签名（Harmonic Beltrami Signature，HBS）引导的新型形状先验分割方法。HBS 是一种能够完整刻画二维单连通形状的形状表示，对扰动具有鲁棒性，并且对平移、旋转和缩放具有不变性。所提方法将 HBS 集成到一个拟共形拓扑保持分割框架中，利用形状先验知识显著提升分割性能，尤其是在低质量或遮挡图像上。其关键创新在于将优化过程分为两个迭代阶段：1）计算拟共形形变映射，将单位圆盘变换到目标分割区域，该过程由图像数据和其他正则化项驱动；2）随后对该映射进行细化，细化的依据是最小化其贝尔特拉米系数与参考 HBS 之间的 $L_2$ 距离。这种形状约束细化利用 HBS 固有的不变性、鲁棒性和形状判别能力，确保分割结果符合参考形状。在合成图像和真实图像上的大量实验验证了该方法能够相较基线提高分割精度、消除预处理需求、抵抗噪声破坏，并灵活获取和应用形状先验。总体而言，HBS 分割框架提供了一种高效策略，能够鲁棒地引入形状先验知识，从而推动关键的低层视觉任务发展。
英文摘要：
This paper presents a novel shape prior segmentation method guided by the Harmonic Beltrami Signature (HBS). The HBS is a shape representation fully capturing 2D simply connected shapes, exhibiting resilience against perturbations and invariance to translation, rotation, and scaling. The proposed method integrates the HBS within a quasi-conformal topology preserving segmentation framework, leveraging shape prior knowledge to significantly enhance segmentation performance, especially for low-quality or occluded images. The key innovation lies in the bifurcation of the optimization process into two iterative stages: 1) The computation of a quasi-conformal deformation map, which transforms the unit disk into the targeted segmentation area, driven by image data and other regularization terms; 2) The subsequent refinement of this map is contingent upon minimizing the $L_2$ distance between its Beltrami coefficient and the reference HBS. This shape-constrained refinement ensures that the segmentation adheres to the reference shape(s) by exploiting the inherent invariance, robustness, and discerning shape discriminative capabilities afforded by the HBS. Extensive experiments on synthetic and real-world images validate the method's ability to improve segmentation accuracy over baselines, eliminate preprocessing requirements, resist noise corruption, and flexibly acquire and apply shape priors. Overall, the HBS segmentation framework offers an efficient strategy to robustly incorporate the shape prior knowledge, thereby advancing critical low-level vision tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
