  Local counts, or the number of objects in a local area, is a continuous value
by nature. Yet recent state-of-the-art methods show that formulating counting
as a classification task performs better than regression. Through a series of
experiments on carefully controlled synthetic data, we show that this
counter-intuitive result is caused by imprecise ground truth local counts.
Factors such as biased dot annotations and incorrectly matched Gaussian kernels
used to generate ground truth counts introduce deviations from the true local
counts. Standard continuous regression is highly sensitive to these errors,
explaining the performance gap between classification and regression. To
mitigate the sensitivity, we loosen the regression formulation from a
continuous scale to a discrete ordering and propose a novel
discrete-constrained (DC) regression. Applied to crowd counting, DC-regression
is more accurate than both classification and standard regression on three
public benchmarks. A similar advantage also holds for the age estimation task,
verifying the overall effectiveness of DC-regression.
