  High-density object counting in surveillance scenes is challenging mainly due
to the drastic variation of object scales. The prevalence of deep learning has
largely boosted the object counting accuracy on several benchmark datasets.
However, does the global counts really count? Armed with this question we dive
into the predicted density map whose summation over the whole regions reports
the global counts for more in-depth analysis. We observe that the object
density map generated by most existing methods usually lacks of local
consistency, i.e., counting errors in local regions exist unexpectedly even
though the global count seems to well match with the ground-truth. Towards this
problem, in this paper we propose a constrained multi-stage Convolutional
Neural Networks (CNNs) to jointly pursue locally consistent density map from
two aspects. Different from most existing methods that mainly rely on the
multi-column architectures of plain CNNs, we exploit a stacking formulation of
plain CNNs. Benefited from the internal multi-stage learning process, the
feature map could be repeatedly refined, allowing the density map to approach
the ground-truth density distribution. For further refinement of the density
map, we also propose a grid loss function. With finer local-region-based
supervisions, the underlying model is constrained to generate locally
consistent density values to minimize the training errors considering both the
global and local counts accuracy. Experiments on two widely-tested object
counting benchmarks with overall significant results compared with
state-of-the-art methods demonstrate the effectiveness of our approach.
