  The growth of the number of people in the monitoring scene may increase the
probability of security threat, which makes crowd counting more and more
important. Most of the existing approaches estimate the number of pedestrians
within one frame, which results in inconsistent predictions in terms of time.
This paper, for the first time, introduces a quadratic programming model with
the network flow constraints to improve the accuracy of crowd counting.
Firstly, the foreground of each frame is segmented into groups, each of which
contains several pedestrians. Then, a regression-based map is developed in
accordance with the relationship between low-level features of each group and
the number of people in it. Secondly, a directed graph is constructed to
simulate constraints on people's flow, whose vertices represent groups of each
frame and arcs represent people moving from one group to another. Then, the
people flow can be viewed as an integer flow in the constructed digraph.
Finally, by solving a quadratic programming problem with network flow
constraints in the directed graph, we obtain consistency in people counting.
The experimental results show that the proposed method can reduce the crowd
counting errors and improve the accuracy. Moreover, this method can also be
applied to any ultramodern group-based regression counting approach to get
improvements.
