Supervoxel hierarchies provide a rich multiscale decomposition of a given video suitable for subsequent processing in video analysis. The hierarchies are typically computed by an unsupervised process that is susceptible to undersegmentation at coarse levels and over-segmentation at fine levels, which make it a challenge to adopt the hierarchies for later use. In this paper, we propose the first method to overcome this limitation and flatten the hierarchy into a single segmentation. Our method, called the uniform entropy slice, seeks a selection of supervoxels that balances the relative level of information in the selected supervoxels based on some post hoc feature criterion such as objectness. For example, with this criterion, in regions nearby objects, our method prefers finer supervoxels to capture the local details, but in regions away from any objects we prefer coarser supervoxels. We formulate the uniform entropy slice as a binary quadratic program and implement four different feature criteria, both unsupervised and supervised, to drive the flattening. Although we apply it only to supervoxel hierarchies in this paper, our method is generally applicable to segmentation tree hierarchies. Our experiments demonstrate both strong qualitative performance and superior quantitative performance to state of the art baselines on benchmark internet videos.

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