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Similarly the histogram of joint distribution of two trajectories $T$ and $S$ is given by:  \[P_{hist}((x_{1},y_{1},x_{2},y_{2}),TxS) = \sum_{(x'_{1},y'_{1},x'_{2},y'_{2})\in TxS}\mathbb{1}_{(x_{1}=x'_{1},y_{1}=y'_{1},x_{2}=x'_{2},y_{2}=y'_{2})}\]  One can remark that the time parameter is here implicitly taking into account as we add contribution to $P_{hist}((x_{1},y_{1},x_{2},y_{2}),TxS)$ if and only if $T$ is in $(x_{1},y_{1})$ at the same time $S$ is in $(x_{2},y{2})$. $(x_{2},y_{2})$.