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Semantic object cutout serves as a basic unit in various image editing systems. In a typical scenario, users are required to provide several strokes which indicate part of the pixels as image background or objects. However, most existing approaches are passive in the sense of accepting input strokes without checking the consistence with user's intention. Here we argue that an active strategy may potentially reduce the interaction burden. Before any real calculation for segmentation, the program can roughly estimate the uncertainty for each image element and actively provide useful suggestions to users. Such a pre-processing is particularly useful for beginners unaware of feeding the underlying cutout algorithms with optimal strokes. We develop such an active object cutout algorithm, named ActiveCut, which makes it possible to automatically detect ambiguity given current user-supplied strokes, and synthesize "suggestive strokes" as feedbacks. Generally, suggestive strokes come from the ambiguous image parts and have the maximal potentials to reduce label uncertainty. Users can continuously refine their inputs following these suggestive strokes. In this way, the number of user-program interaction iterations can thus be greatly reduced. Specifically, the uncertainty is modeled by mutual information between user strokes and unlabeled image regions. To ensure that ActiveCut works at a user-interactive rate, we adopt superpixel lattice based image representation, whose computation depends on scene complexity rather than original image resolution. Moreover, it retains the 2-D-lattice topology and is thus more suitable for parallel computing. While for the most time-consuming calculation of probabilistic entropy, variational approximation is utilized for acceleration. Finally, based on submodular function theory, we provide a theoretic analysis for the performance lower bound of the proposed greedy algorithm. Various user studies are conducted on the MSRC image dataset to - - validate the effectiveness of our proposed algorithm.