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Automatic detection and localization of anomalies in nanofibrous materials help to reduce the cost of the production process and the time of the post-production visual inspection process. Amongst all the monitoring methods, those exploiting Scanning Electron Microscope (SEM) imaging are the most effective. In this paper, we propose a region-based method for the detection and localization of anomalies in SEM images, based on Convolutional Neural Networks (CNNs) and self-similarity. The method evaluates the degree of abnormality of each subregion of an image under consideration by computing a CNN-based visual similarity with respect to a dictionary of anomaly-free subregions belonging to a training set. The proposed method outperforms the state of the art.