发表机构
School of Mathematics, Harbin Institute of Technology（哈尔滨工业大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对图像分割中多种退化情况分割的难题，该研究基于对长度项的理论分析，构建灰度水平集，提出将偏微分方程演化转化为一维阈值搜索的快速分割框架，有效提升计算速度，经实验验证了其在多种退化图像上的分割性能。
AI 中文摘要
在图像分割领域，对多种退化情况进行分割一直是个具有挑战性的问题。现有水平集方法通常采用长度正则化项来约束分割轮廓的几何形状，但这常导致数值不稳定和高计算成本。本文表明在一定平滑约束下长度项并非必要，并从理论上证明其影响|\nabla \phi| = 1的性质。基于此定义一类平滑图像，构建灰度水平集，提出针对如严重噪声图像和强度不均匀图像等退化图像的快速分割框架，该框架将偏微分方程演化转化为一维阈值搜索，在计算速度上优势显著，尤其对于大规模图像。实验验证了该框架在各种退化图像上的分割性能。
英文摘要
The segmentation of multiple degradations has been a challenging problem in the field of image segmentation. Existing level set approaches commonly adopt a length regularization term to constrain the geometric shape of the segmentation contour. However, the introduction of the length term often results in numerical instability and high computational cost. In this paper, we show that the length term is not essential under certain smoothness constraints, and theoretically prove that the presence of the length term affects the property of $|\nabla ϕ|=1$. Based on the finding, we define a class of smooth images, construct the grayscale level set, and propose a fast segmentation framework for degraded images, such as heavily noisy images and intensity inhomogeneous images. The framework transforms PDE evolution into one-dimensional threshold search, which has significant advantages in computational speed, especially on large-scale images. Experiments validate the segmentation performance of the proposed framework on various degraded images.
