Current unsupervised anomaly localization approaches rely on generative models to learn the distribution of normal images, which is later used to identify potential anomalous regions derived from errors on the reconstructed images. To address the limitations of residual-based anomaly localization, very recent literature has focused on attention maps, by integrating supervision on them in the form of homogenization constraints. In this work, we propose a novel formulation that addresses the problem in a more principled manner, leveraging well-known knowledge in constrained optimization. In particular, the equality constraint on the attention maps in prior work is replaced by an inequality constraint, which allows more flexibility. In addition, to address the limitations of penalty-based functions we employ an extension of the popular log-barrier methods to handle the constraint. Last, we propose an alternative regularization term that maximizes the Shannon entropy of the attention maps, reducing the amount of hyperparameters of the proposed model. Comprehensive experiments on two publicly available datasets on brain lesion segmentation demonstrate that the proposed approach substantially outperforms relevant literature, establishing new state-of-the-art results for unsupervised lesion segmentation.

当前的无监督异常定位方法依赖于生成模型来学习正常图像的分布，随后用于识别源自重建图像上的错误的潜在异常区域。为了解决基于残差的异常定位的局限性，最近的文献集中在注意力图上，通过以同质化约束的形式整合对它们的监督。在这项工作中，我们提出了一种新颖的公式，它利用约束优化中的众所周知的知识，以更有原则的方式解决问题。特别是，先前工作中注意力图上的等式约束被不等式约束所取代，从而提供了更大的灵活性。此外，为了解决基于惩罚的函数的局限性，我们采用了流行的对数障碍方法的扩展来处理约束。最后，我们提出了一个替代正则化项，它可以最大化注意力图的香农熵，减少所提出模型的超参数数量。对两个公开可用的脑病变分割数据集的综合实验表明，所提出的方法大大优于相关文献，为无监督的病变分割建立了新的最先进的结果。