发表机构
Henan Provincial Center for Applied Mathematics, Henan University; College of Mathematics and Statistics, Henan University; Advanced Institute of Finance, Henan University; School of Software, Henan Agricultural University（河南大学河南省应用数学中心; 河南大学数学与统计学院; 河南大学高等金融研究院; 河南农业大学软件学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对医学图像分割中像素级训练缺乏几何先验信息及分割区域表征不足的问题，提出深度活动轮廓和平均曲率（DACMC）损失函数，用卷积核近似平均曲率，在多数据集上验证性能，展现新最优表现。
AI 中文摘要
医学图像分割在临床分析和应用领域是一项关键任务。尽管深度学习技术在多个场景中发挥关键作用，但像素级训练导致缺乏几何先验信息。学者们将Chan-Vese模型整合到损失函数中训练，能考虑分割内外区域及长度以提升性能，但仍缺乏对分割区域的有效表征。为克服此问题，引入平均曲率作为几何自然约束，提出深度活动轮廓和平均曲率（DACMC）损失函数，用卷积核近似平均曲率以节省计算成本。在肝脏和脾脏数据集上验证了该方法性能，在多个分割数据集上展现了新的最优性能。
英文摘要
Medical image segmentation is an important task in clinical analysis. Although deep learning techniques are widely used, training at the individual pixel level ignores geometric prior information about the region being segmented. Integrating the Chan-Vese model into the loss function is a well-established remedy that accounts for the regions inside and outside the segmentation and, through its length term, for boundary regularity. However, such losses still lack an effective characterisation of local boundary geometry. We introduce the mean curvature as a natural geometric constraint and propose a Deep Active Contour and Mean Curvature (DACMC) loss function, in which a fixed convolution kernel approximates the mean curvature at negligible computational cost. The loss has a single hyper-parameter, the curvature weight $λ$, fixed at $10^{-3}$ for all experiments. We evaluate DACMC on three public datasets - liver computed tomography (CT), spleen magnetic resonance imaging (MRI) and dermoscopy images from the International Skin Imaging Collaboration (ISIC) - using two encoder-decoder networks as backbones and the Dice similarity coefficient (DSC), the 95th-percentile Hausdorff distance (HD95), the Jaccard similarity (JS) and the average surface distance (ASD) as metrics, against the cross-entropy, Dice, active contour and elastica losses. DACMC attains the best or second-best DSC in five of the six dataset-backbone settings; on spleen MRI it reduces HD95 to 16.28 millimetres and ASD to 1.90 millimetres, and on ISIC it reduces HD95 to 7.08 millimetres. A sensitivity study shows a broad plateau for $λ\leq 10^{-3}$ and degeneration only when the curvature term dominates.
CommentsRevised version: updated the abstract, unified method naming and reference formatting, and clarified the presentation. This work has been submitted to Engineering Applications of Artificial Intelligence
