Documentation about pair-distribution function

[mirakuepper]

Some comments / questions about the documentation/ setup of the pair distribution function:

1. At some places the name is spelled incorrectly (see also spelling mistake in compute_pair_distRibution_function #369 )
2. How are the "interacting pedestrians" defined and how does PedPy calculate/pick them?
3. “Quantifies the probability that two interacting pedestrians are found a given distance r apart, renormalized by the probability
   of measuring this distance for pedestrians that do not interact.” This probability is approximated here by randomising the time information (randomisation of the time frames).
   To which of the two probabilities does the second sentence (bold part) refer to?
4. How does the randomization of time-frames work?

[ThoChat]

Regarding - 2)
Indeed, the notion of "interacting pedestrians" is not well defined. It refers here to pedestrians that are in the same space-time domain, i.e., pedestrians that could react to each other's motion as then are present in the same place at the same time. This notion of "interaction" is directly taken from the work "Universal Power Law Governing Pedestrian Interactions" (Karamouzas et al., 2014), this should be mentioned as well. One should also keep in mind that in its current implementation, the method does not take into account walls and corners, which should in theory block any "interaction" between any pedestrians on opposite sides of the obstacle.

[ThoChat]

Regarding -3)
The "probability" here refers to, the probability of measuring this distance for pedestrians that do not interact.

Regarding -4)
The original trajectory dataframe contains the "space" position (x,y) and the "time" position (frame number). The randomization of time-frames reshuffles the frame numbers only. After the randomization process, a given frame contains random pedestrian "space" positions (x,y), but these positions were at some point used by a participant in the original trajectory dataframe. This method helps to take into account preferred route choices (like pavements) or penitential obstacles that are difficult to set as not part of the walkable area (like a puddle).

[ThoChat]

Forgot to write this, but thanks for all these comments @mirakuepper !
I will add all these details in the documentation.

[mirakuepper]

Regarding - 2) Indeed, the notion of "interacting pedestrians" is not well defined. It refers here to pedestrians that are in the same space-time domain, i.e., pedestrians that could react to each other's motion as then are present in the same place at the same time. This notion of "interaction" is directly taken from the work "Universal Power Law Governing Pedestrian Interactions" (Karamouzas et al., 2014), this should be mentioned as well. One should also keep in mind that in its current implementation, the method does not take into account walls and corners, which should in theory block any "interaction" between any pedestrians on opposite sides of the obstacle.

Sorry for nitpicking: But I still wonder about the "same place - same time" part. Is there a certain distance in which pedestrians are considered as "interacting"? Or are 2 pedestrians which are e.g. 300m apart still interacting if present in the same time frame?

[ThoChat]

Don't be sorry. I'm glad to discus this anytime 👍
Indeed, this seems a bit overestimated, but it's one of the assumptions of the power law modeling. The idea is that when considering a pedestrian, the level of interaction induced by very far-away other individuals is so tiny that it does not affect the local behavior.
Of course, this is a physics-based modeling, meaning that the hypothesis might (or must) be different for pedestrians. However, as it works as such, nobody investigated what would be the "interaction threshold", at least to my knowledge.