  Counting objects in digital images is a process that should be replaced by
machines. This tedious task is time consuming and prone to errors due to
fatigue of human annotators. The goal is to have a system that takes as input
an image and returns a count of the objects inside and justification for the
prediction in the form of object localization. We repose a problem, originally
posed by Lempitsky and Zisserman, to instead predict a count map which contains
redundant counts based on the receptive field of a smaller regression network.
The regression network predicts a count of the objects that exist inside this
frame. By processing the image in a fully convolutional way each pixel is going
to be accounted for some number of times, the number of windows which include
it, which is the size of each window, (i.e., 32x32 = 1024). To recover the true
count we take the average over the redundant predictions. Our contribution is
redundant counting instead of predicting a density map in order to average over
errors. We also propose a novel deep neural network architecture adapted from
the Inception family of networks called the Count-ception network. Together our
approach results in a 20% relative improvement (2.9 to 2.3 MAE) over the state
of the art method by Xie, Noble, and Zisserman in 2016.
