Unbiased Population Size Estimation On Still Gigapixel Images

Population sizing is essential in sociology and in various other real-life applications. Gigapixel cameras can provide high-resolution images of an entire population in many cases. However, exhaustive manual counting is tedious, slow, and difficult to verify, whereas current computer vision methods are biased and known to fail for large populations. A design unbiased method based on geometric sampling has recently been proposed. It typically requires only between 50 and 100 manual counts to achieve relative standard errors of 5-10 percent irrespective of population size. However, the large perspective effect introduced by gigapixel images may boost the relative standard error to 30-40 percent. Here, we show that projecting the sampling grid from a map onto the gigapixel image using the camera projection neutralizes the variance due to perspective effects and restores the relative standard errors back into the 5-10 percent range. The method is tested on six simulated images. A detailed step-by-step illustration is provided with a real image of a 30,000 people crowd.