  Current state-of-the-art methods solve spatiotemporal action localisation by
extending 2D anchors to 3D-cuboid proposals on stacks of frames, to generate
sets of temporally connected bounding boxes called \textit{action micro-tubes}.
However, they fail to consider that the underlying anchor proposal hypotheses
should also move (transition) from frame to frame, as the actor or the camera
does. Assuming we evaluate $n$ 2D anchors in each frame, then the number of
possible transitions from each 2D anchor to the next, for a sequence of $f$
consecutive frames, is in the order of $O(n^f)$, expensive even for small
values of $f$. To avoid this problem, we introduce a Transition-Matrix-based
Network (TraMNet) which relies on computing transition probabilities between
anchor proposals while maximising their overlap with ground truth bounding
boxes across frames, and enforcing sparsity via a transition threshold. As the
resulting transition matrix is sparse and stochastic, this reduces the proposal
hypothesis search space from $O(n^f)$ to the cardinality of the thresholded
matrix. At training time, transitions are specific to cell locations of the
feature maps, so that a sparse (efficient) transition matrix is used to train
the network. At test time, a denser transition matrix can be obtained either by
decreasing the threshold or by adding to it all the relative transitions
originating from any cell location, allowing the network to handle transitions
in the test data that might not have been present in the training data, and
making detection translation-invariant. Finally, we show that our network can
handle sparse annotations such as those available in the DALY dataset. We
report extensive experiments on the DALY, UCF101-24 and Transformed-UCF101-24
datasets to support our claims.
