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.

翻译：本文提出了一种由调和Beltrami签名（HBS）引导的新型形状先验分割方法。HBS是一种能够完整表征二维单连通形状的表示方法，具有对扰动的强鲁棒性，并保持平移、旋转和缩放不变性。该方法将HBS集成于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，尤其适用于低质量或遮挡图像。其核心创新在于将优化过程分解为两个迭代阶段：1）计算拟共形变形映射，该映射在图像数据及其他正则化项驱动下将单位圆盘变换为目标分割区域；2）随后通过最小化该映射的Beltrami系数与参考HBS之间的$L_2$距离来细化映射。这种形状约束的细化过程充分利用HBS固有的不变性、鲁棒性和形状判别能力，确保分割结果与参考形状保持一致。在合成图像和真实图像上的大量实验表明，该方法相较于基线模型能够提升分割精度，无需预处理步骤，具有抗噪声干扰能力，并能灵活获取与应用形状先验知识。总体而言，HBS分割框架为鲁棒地融合形状先验知识提供了高效策略，从而推动了关键底层视觉任务的发展。