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Despite the remarkable success of existing methods for few-shot segmentation, there remain two crucial challenges. First, the feature learning for novel classes is suppressed during the training on base classes in that the novel classes are always treated as background. Thus, the semantics of novel classes are not well learned. Second, most of existing methods fail to consider the underlying semantic gap between the support and the query resulting from the representative bias by the scarce support samples. To circumvent these two challenges, we propose to activate the discriminability of novel classes explicitly in both the feature encoding stage and the prediction stage for segmentation. In the feature encoding stage, we design the Semantic-Preserving Feature Learning module (SPFL) to first exploit and then retain the latent semantics contained in the whole input image, especially those in the background that belong to novel classes. In the prediction stage for segmentation, we learn an Self-Refined Online Foreground-Background classifier (SROFB), which is able to refine itself using the high-confidence pixels of query image to facilitate its adaptation to the query image and bridge the support-query semantic gap. Extensive experiments on PASCAL-5$^i$ and COCO-20$^i$ datasets demonstrates the advantages of these two novel designs both quantitatively and qualitatively.