变分模板匹配与统计融合用于图案化结构中的异常检测
Variational Template Matching with Statistical Fusion for Anomaly Detection in Patterned Structures
AI总结：
针对小数据场景下结构化图像异常检测，提出变分模板匹配与统计融合方法，结合变换空间归一化互相关和核密度估计，在免训练下达到与ResNet-50相当的性能。
AI中文摘要：
在结构化图像中进行异常检测在小数据场景下具有挑战性，此时深度学习方法成本高昂或不可行。经典模板匹配简单且可解释，但对尺度、旋转和透视等几何变化缺乏鲁棒性。我们提出了一种变分模板匹配框架，将异常模板表示为变换实例的族，并通过在变换空间上的归一化互相关进行检测。为进一步提高鲁棒性，我们引入了一种基于密度的统计异常分数，该分数使用核密度估计（KDE）从局部强度分布中导出。这产生了一种平滑表示，比基于直方图的方法更稳健地捕获分布集中性和尾部行为。结构和统计信号通过统一的融合公式集成，从而实现对几何相似性和分布偏差的互补建模。在生物细胞图像上的实验表明，所提出的方法在完全免训练设置下优于经典基线，并与ResNet-50取得竞争性性能，同时提供显式定位。该方法为结构化图像领域的异常检测提供了一种高效、可解释且实用的解决方案。
英文摘要：
Anomaly detection in structured images is challenging in small-data settings where deep learning approaches are costly or impractical. Classical template matching is simple and interpretable but lacks robustness to geometric variations such as scale, rotation, and perspective. We propose a variational template matching framework that represents anomaly templates as a family of transformed instances and performs detection via normalized cross-correlation over this transformation space. To further improve robustness, we introduce a density-based statistical anomaly score derived from local intensity distributions using kernel density estimation (KDE). This produces a smooth representation that captures distributional concentration and tail behavior more robustly than histogram-based methods. The structural and statistical signals are integrated through a unified fusion formulation, enabling complementary modeling of geometric similarity and distributional deviation. Experiments on biological cell images demonstrate that the proposed method outperforms classical baselines and achieves competitive performance with ResNet-50 under a fully training-free setting, while providing explicit localization. The approach offers an efficient, interpretable, and practical solution for anomaly detection in structured image domains.
