以非一致性为异常：通过免训练图拉普拉斯能量最小化进行异常检测
Anomaly as Non-Conformity via Training-Free Graph Laplacian Energy Minimization
把「查询图像块偏离正常特征流形的程度」量化为带锚定正常节点的二部图拉普拉斯能量的闭式解，异常分数取满足正常性约束所需的特征更新幅度；这一「优化诱导特征漂移」可作为免训练、无参数的异常打分算子，直接替换基于余弦相似度的记忆库检索，用于工业缺陷检测与医学异常定位。
原文依据 the anomaly score is the magnitude of the update required to satisfy normality constraints
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论在图像中检测细微的视觉异常仍然具有挑战性，尤其是在先验仅有正常样本的情况下。这类无监督异常检测通常通过度量查询图像块与正常图像块记忆库之间的特征相似度来求解。然而，仅凭相似度无法揭示查询图像块在多大程度上违背了正常特征流形的结构。我们提出一种免训练的拉普拉斯图能量优化形式，命名为 ANoCo，它以查询图像块与固定正常流形对齐所需的非一致性代价来为异常打分。对于每个查询图像块，我们构建一个以余弦亲和度加权的查询—正常二部图，并显式去除查询—查询边与正常—正常边，以防止证据被稀释。我们将异常打分表述为带有锚定正常节点的凸拉普拉斯能量，并以闭式解求解。特别地，我们并不使用优化后的特征本身——异常分数是满足正常性约束所需的更新幅度，从而将图拉普拉斯重新诠释为非一致性算子，而非平滑先验。所提方法不引入可学习参数、消息传递或采样，复杂度与单次线性求解相当。在标准基准上，它取得了较强的图像级 AUROC、稳定的定位图，并相较先前方法具有更好的鲁棒性，证明了以优化诱导的特征漂移作为异常度量的有效性。
英文原文摘要 1496 字符
Detecting subtle visual anomalies in images remains challenging, particularly when only normal samples are available a priori. Such unsupervised anomaly detection is typically solved by measuring feature similarity of a query patch to a memory of normal patches. However, similarity alone does not reveal how strongly a query patch violates the structure of the normal feature manifold. We propose a training-free Laplacian graph energy optimization formulation, named ANoCo that scores Anomaly by the cost of Non-Conformity of a query patch to align with a fixed normal manifold. For each query patch, we construct a bipartite query to normal graph weighted by cosine affinity, explicitly removing query-query and normal-normal edges to prevent evidence dilution. We formulate anomaly scoring as a convex Laplacian energy with anchored normal nodes, and solve in closed form. In particular, we do not use the optimized features themselves--the anomaly score is the magnitude of the update required to satisfy normality constraints, reframing the graph Laplacian as a non-conformity operator rather than a smoothing prior. The proposed method introduces no learnable parameters, message passing, or sampling, and has complexity comparable to a single linear solve. Across standard benchmarks, it delivers strong image-level AUROC, stable localization maps, and improved robustness over prior methods, demonstrating the effectiveness of using optimization-induced feature drift as anomaly measure.