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We propose a novel self-supervised Video Object Segmentation (VOS) approach that strives to achieve better object-background discriminability for accurate object segmentation. Distinct from previous self-supervised VOS methods, our approach is based on a discriminative learning loss formulation that takes into account both object and background information to ensure object-background discriminability, rather than using only object appearance. The discriminative learning loss comprises cutout-based reconstruction (cutout region represents part of a frame, whose pixels are replaced with some constant values) and tag prediction loss terms. The cutout-based reconstruction term utilizes a simple cutout scheme to learn the pixel-wise correspondence between the current and previous frames in order to reconstruct the original current frame with added cutout region in it. The introduced cutout patch guides the model to focus as much on the significant features of the object of interest as the less significant ones, thereby implicitly equipping the model to address occlusion-based scenarios. Next, the tag prediction term encourages object-background separability by grouping tags of all pixels in the cutout region that are similar, while separating them from the tags of the rest of the reconstructed frame pixels. Additionally, we introduce a zoom-in scheme that addresses the problem of small object segmentation by capturing fine structural information at multiple scales. Our proposed approach, termed CT-VOS, achieves state-of-the-art results on two challenging benchmarks: DAVIS-2017 and Youtube-VOS. A detailed ablation showcases the importance of the proposed loss formulation to effectively capture object-background discriminability and the impact of our zoom-in scheme to accurately segment small-sized objects.