inference, we feed frames $t$ through the network, obtaining a set of predicted segments ${\ensuremath{\mathcal{S}}}_t$, each with its predicted class $y_s$ and embedding vector $a_s^{y_s}$. Our objective is now to match the segments across frames in order to reconstruct a tracklet for each object in the sequence. To do this, we follow the same algorithmic framework described in Sec. \[sec:tracklets\], with a couple of modifications. First, we allow matching segments between the current frame and a sliding window of $N_w$ frames in the past. Second, we do not rely on optical flow anymore, instead measuring the similarity between segments in terms of their distance in the embedding space and temporal offset.

More formally, we redefine the payoff function in Eq.  as: $$\begin{aligned}
  \pi(\hat{s}, s) &= -\pi^*(\hat{s}, s) + \eta(s, \hat{s})\,,\\
  \pi^*(\hat{s}, s) &= \|a_s^{y_s} - a_{\hat{s}}^{y_{\hat{s}}}\| + \frac{|t_s - t_{\hat{s}}|}{N_w}\,,
  \label{eq:inference-po}\end{aligned}$$ where the characteristic function $\eta(s, \hat{s})$ is redefined as: $$\eta(s, \hat{s}) = \begin{cases}
    0 & \text{if}\,y_s = y_{\hat{s}} \land \pi^*(\hat{s}, s) \leq \tau\,, \\
    -\infty & \text{otherwise}\,,
  \end{cases}$$ and $\tau$ is a configurable threshold value. Furthermore, we replace ${\ensuremath{\mathcal{S}}}_{t-1}$ in Eq.  and Eq.  with the set: $${\ensuremath{\mathcal{U}}}_t = \left\{s\in \mathcal V_{t-1} \mid t_s \geq t-N_w \land (s,\hat s)\notin{\ensuremath{\mathcal{T}}}_{t-1} \forall 