Abstract
Population size estimation is relevant to social and ecological sciences. Exhaustive manual counting, the density method and automated computer vision are some of the estimation methods that are currently used. Some of these methods may work in concrete cases but they do not provide a fast, efficient and unbiased estimation in general. Recently, the CountEm method, based on systematic sampling with a grid of quadrats, was proposed. It offers an unbiased estimation that can be applied to any population. However, choosing suitable grid parameters is sometimes cumbersome. Here we define a more intuitive grid parametrization, using initial number of quadrats and sampling fraction. A crowd counting dataset with 51 images and their corresponding, manually annotated position point patterns, are used to analyze the variation of the coefficient of error with respect to different parameter choices. Our Monte Carlo resampling results show that the error depends on the sample size and the number of nonempty quadrats, but not on the size of the target population. A procedure to choose suitable parameter values is described, and the expected coefficients of error are given. Counting about 100 particles in 30 nonempty quadrats usually yields coefficients of error below 10%.
Highlights
Population sizing is a longstanding problem with a wide range of applications such as security, social sciences and ecology
The traditional density method [1, 2] is widely used by media, police and convention organizers for crowd size estimation, but the estimation usually ignores sampling and relies on imprecise visual estimation
Suitable parameter values should be chosen for each image, but for the present dataset n0 = 100 works rather well for all images, as shown in Fig 5, where the sampling fraction was selected a posteriori as f = Q/N, with Q = 50, 100, 200 and N the number of manually annotated points in each image
Summary
Population sizing is a longstanding problem with a wide range of applications such as security, social sciences and ecology. A population is a finite set of N separate items or “particles” of interest, e.g. humans, birds, etc. Several approaches have been taken to address the problem. The traditional density method [1, 2] is widely used by media, police and convention organizers for crowd size estimation, but the estimation usually ignores sampling and relies on imprecise visual estimation. Bird censuses lean on visual estimation [3,4,5,6] or exhaustive manual counting [7, 8] that is slow, tedious and difficult to verify. Automatic algorithms are generally biased and may show a poor performance [16]
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