  Previous work generally believes that improving the spatial invariance of
convolutional networks is the key to object counting. However, after verifying
several mainstream counting networks, we surprisingly found too strict
pixel-level spatial invariance would cause overfit noise in the density map
generation. In this paper, we try to use locally connected Gaussian kernels to
replace the original convolution filter to estimate the spatial position in the
density map. The purpose of this is to allow the feature extraction process to
potentially stimulate the density map generation process to overcome the
annotation noise. Inspired by previous work, we propose a low-rank
approximation accompanied with translation invariance to favorably implement
the approximation of massive Gaussian convolution. Our work points a new
direction for follow-up research, which should investigate how to properly
relax the overly strict pixel-level spatial invariance for object counting. We
evaluate our methods on 4 mainstream object counting networks (i.e., MCNN,
CSRNet, SANet, and ResNet-50). Extensive experiments were conducted on 7
popular benchmarks for 3 applications (i.e., crowd, vehicle, and plant
counting). Experimental results show that our methods significantly outperform
other state-of-the-art methods and achieve promising learning of the spatial
position of objects.
