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CNN visualization and interpretation methods, like class-activation maps (CAMs), are typically used to highlight the image regions linked to class predictions. These models allow to simultaneously classify images and extract class-dependent saliency maps, without the need for costly pixel-level annotations. However, they typically yield segmentations with high false-positive rates and, therefore, coarse visualisations, more so when processing challenging images, as encountered in histology. To mitigate this issue, we propose an active learning (AL) framework, which progressively integrates pixel-level annotations during training. Given training data with global image-level labels, our deep weakly-supervised learning model jointly performs supervised image-level classification and active learning for segmentation, integrating pixel annotations by an oracle. Unlike standard AL methods that focus on sample selection, we also leverage large numbers of unlabeled images via pseudo-segmentations (i.e., self-learning at the pixel level), and integrate them with the oracle-annotated samples during training. We report extensive experiments over two challenging benchmarks -- high-resolution medical images (histology GlaS data for colon cancer) and natural images (CUB-200-2011 for bird species). Our results indicate that, by simply using random sample selection, the proposed approach can significantly outperform state-of the-art CAMs and AL methods, with an identical oracle-supervision budget. Our code is publicly available.