We formulate object segmentation in video as a spectral graph clustering problem in space and time, in which nodes are pixels and their relations form local neighbourhoods. We claim that the strongest cluster in this pixel-level graph represents the salient object segmentation. We compute the main cluster using a novel and fast 3D filtering technique that finds the spectral clustering solution, namely the principal eigenvector of the graph's adjacency matrix, without building the matrix explicitly - which would be intractable. Our method is based on the power iteration which we prove is equivalent to performing a specific set of 3D convolutions in the space-time feature volume. This allows us to avoid creating the matrix and have a fast parallel implementation on GPU. We show that our method is much faster than classical power iteration applied directly on the adjacency matrix. Different from other works, ours is dedicated to preserving object consistency in space and time at the level of pixels. In experiments, we obtain consistent improvement over the top state of the art methods on DAVIS-2016 dataset. We also achieve top results on the well-known SegTrackv2 dataset.