Gatherings of thousands to millions of people frequently occur for an enormous variety of educational, social, sporting, and political events, and automated counting of these high-density crowds is useful for safety, management, and measuring significance of an event. In this work, we show that the regularly accepted labeling scheme of crowd density maps for training deep neural networks may not be the most effective one. We propose an alternative inverse k-nearest neighbor (ikNN) map mechanism that, even when used directly in existing state-of-the-art network structures, shows superior performance. We also provide new network architecture mechanisms that we demonstrate in our own MUD-ikNN network architecture, which uses multi-scale drop-in replacement upsampling via transposed convolutions to take full advantage of the provided ikNN labeling. This upsampling combined with the ikNN maps further improves crowd counting accuracy. We further analyze several variations of the ikNN labeling mechanism, which apply transformations on the kNN measure before generating the map, in order to consider the impact of camera perspective views, image resolutions, and the changing rates of the mapping functions. To alleviate the effects of crowd density changes in each image, we also introduce an attenuation mechanism in the ikNN mapping. Experimentally, we show that inverse square root kNN map variation (iRkNN) provides the best performance. Discussions are provided on computational complexity, label resolutions, the gains in mapping and upsampling, and details of critical cases such as various crowd counts, uneven crowd densities, and crowd occlusions.
