Fig 1.
a) in orange, the o-space; b) an aerial image of a circular F-formation; c) a party, something similar to a typical surveillance setting with the camera located 2–3 meters from the floor: detecting F-formations here is challenging.
Fig 2.
Sample images of the four real-world datasets.
For each dataset four frames are reported showing different situations of crowd and arrangement.
Table 1.
Gatherings categorisation on the basis of focus of attention and spatio-proxemic freedom exemplified by typical social settings/situations.
Fig 3.
Examples of gatherings categorised by focus of attention and spatio-proxemic freedom.
Jointly focused, dynamic: our case, FCGs at a cocktail party; common focused, dynamic: a parading platoon; unfocused, dynamic: a queue at the airport; jointly focused, static: a meeting; common focused, static: people in a theatre stand; unfocused, static: persons in a waiting room.
Fig 4.
Structure of an F-formation and examples of F-formation arrangements.
a) Schematization of the three spaces of an F-formation: starting from the centre, o-space, p-space and r-space. b-d) Three examples of F-formation arrangements: for each one of them, one picture highlights the head and shoulder pose, the other shows the lower body posture. For a picture of circular F-formation, see also Fig 1.
Table 2.
Algorithm 1 Finding shared focal centres.
Fig 5.
Schematic representation of the problem formulation.
Two individuals facing each other, the gray dot representing the transitional segment centre, the red cross being the o-space centre and the red area the o-space of the F-formation.
Table 3.
Summary of the features of the datasets used for experiments.
Fig 6.
Iteration 0: initialization with the candidate o-space centres {O} coincident with the transitional segment of each individual {C}. Iteration 1: first graph-cuts run; easy groups are correctly clustered while the most complex still present errors (the FCG formed by P7 and P20 violates the visibility constraint). Iteration 2: the second graph-cuts run correctly detects the O7,8,9 F-formation (at the bottom). Se text for more details.
Table 4.
Parameters used in the experiments for each dataset.
These parameters are the results of a tuning phase and the difference are due to different measure units (pixels/cm) and different social environments (indoor/outdoor, formal/informal, etc.).
Table 5.
Average precision, recall and F1 scores for all the methods and all the datasets (T = 2/3).
Please note that DS results are averaged over only 3 datasets and thus cannot be taken into account for a fair comparison.
Table 6.
Average precision, recall and F1 scores for all the methods and all the datasets (T = 1).
Please note that DS results are averaged over only 3 datasets and thus cannot be taken into account for a fair comparison.
Fig 7.
Global F1 score vs. tolerance threshold T.
Between brackets in legend the Global Tolerant Matching score. Dominant Sets (DS) is averaged over 3 datasets only, because of results availability. (Best viewed in colour)
Table 7.
Cocktail Party—F1 score vs. cardinality. (T = 1).
Table 8.
GDet– F1 score vs. cardinality. (T = 1).
Fig 8.
F1 score vs. Noise Level on position (left), orientation (centre) and combined (right). (Best viewed in colour)