基于加权有界Hessian变分的选择性分割问题的研究

A Study on Selective Segmentation Problems Based on Weighted Bounded Hessian Variations

摘要: 选择性图像分割广泛应用于医疗影像与目标识别等领域，但传统方法在处理平滑区域和强度不均匀图像时常出现“阶梯效应”及分割不连续性等问题。针对这些问题本文结合与Hessian变分模型与测地距离选择性分割模型，提出一种新选择性分割方法，并且通过自动估计一阶和二阶正则化权函数提升分割精度与鲁棒性。此外，设计了基于交替方向乘子法(ADMM)的高效算法进行求解。实验结果表明，本文方法在边界捕捉精度、分割连续性和计算效率方面均优于现有方法，为选择性分割任务提供了一种精准高效的解决方案。

Abstract: Selective image segmentation is widely applied in medical imaging and object recognition. However, traditional methods often encounter issues such as the “staircase effect” and segmentation discontinuity when processing smooth regions and intensity inhomogeneous images. To address these challenges, this paper proposes a novel selective segmentation method by integrating the Hessian variation model with the geodesic distance-based selective segmentation model. The method enhances segmentation accuracy and robustness by automatically estimating first- and second-order regularization weights. Additionally, an efficient optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) is designed for solving the model. Experimental results demonstrate that the proposed method outperforms existing approaches in terms of boundary accuracy, segmentation continuity, and computational efficiency, providing a precise and efficient solution for selective segmentation tasks.