Efficient and Unbiased Estimation of Population Size

Population sizing from still aerial pictures is of wide applicability in ecological and social sciences. The problem is long standing because current automatic detection and counting algorithms are known to fail in most cases, and exhaustive manual counting is tedious, slow, difficult to verify and unfeasible for large populations. An alternative is to multiply population density with some reference area but, unfortunately, sampling details, handling of edge effects, etc., are seldom described. For the first time we address the problem using principles of geometric sampling. These principles are old and solid, but largely unknown outside the areas of three dimensional microscopy and stereology. Here we adapt them to estimate the size of any population of individuals lying on an essentially planar area, e.g. people, animals, trees on a savanna, etc. The proposed design is unbiased irrespective of population size, pattern, perspective artifacts, etc. The implementation is very simple—it is based on the random superimposition of coarse quadrat grids. Also, an objective error assessment is often lacking. For the latter purpose the quadrat counts are often assumed to be independent. We demonstrate that this approach can perform very poorly, and we propose (and check via Monte Carlo resampling) a new theoretical error prediction formula. As far as efficiency, counting about 50 (100) individuals in 20 quadrats, can yield relative standard errors of about 8% (5%) in typical cases. This fact effectively breaks the barrier hitherto imposed by the current lack of automatic face detection algorithms, because semiautomatic sampling and manual counting becomes an attractive option

Comparison of three methods for the estimation of the pituitary gland volume using magnetic resonance imaging: a stereological study

Stereological techniques using point counting and planimetry have been used to estimate pituitary gland volume. However, many studies have estimated pituitary gland volume by the mathematical approach the elliptic formula. The objective of the current study was to determine pituitary gland volume using stereological methods and elliptic formula on magnetic resonance imaging (MRI). In this study, pituitary gland volumes were estimated in a total of 28 subjects (22 females, 6 males,) who were free of any pituitary or neurological symptoms and signs. The mean ± SD pituitary gland volumes for the point counting, planimetry and elliptic formulae groups were 582.14 ± 140.16 mm3 , 610.08 ± 133.17 mm3 , and 432.82 ± 147.38 mm3 , respectively. The mean CE for the pituitary gland volume estimates derived from the point counting technique was 8.07%. No significant difference was found between point counting and planimetric methods for the pituitary gland volume (P[0.05). In addition, there was a 26.14 and 29.71% underestimation of pituitary volume as measured by the elliptic formula compared to the point counting and planimetric techniques, respectively. From these results, it can be concluded that stereological techniques are unbiased, efficient and reliable methods and are ideally suitable for in vivo examination of MRI data for pituitary gland volume estimation. Hence, we suggest that estimating pituitary gland volume using MRI study and stereology may be clinically relevant for pituitary surgeons for the investiga tion of the structure and function of the pituitary gland