  In this paper, we explore the problem of training one-look regression models
for counting objects in datasets comprising a small number of high-resolution,
variable-shaped images. We illustrate that conventional global average pooling
(GAP) based models are unreliable due to the patchwise cancellation of true
overestimates and underestimates for patchwise inference. To overcome this
limitation and reduce overfitting caused by the training on full-resolution
images, we propose to employ global sum pooling (GSP) instead of GAP or fully
connected (FC) layers at the backend of a convolutional network. Although
computationally equivalent to GAP, we show through comprehensive
experimentation that GSP allows convolutional networks to learn the counting
task as a simple linear mapping problem generalized over the input shape and
the number of objects present. This generalization capability allows GSP to
avoid both patchwise cancellation and overfitting by training on small patches
and inference on full-resolution images as a whole. We evaluate our approach on
four different aerial image datasets - two car counting datasets (CARPK and
COWC), one crowd counting dataset (ShanghaiTech; parts A and B) and one new
challenging dataset for wheat spike counting. Our GSP models improve upon the
state-of-the-art approaches on all four datasets with a simple architecture.
Also, GSP architectures trained with smaller-sized image patches exhibit better
localization property due to their focus on learning from smaller regions while
training.
