Estereología y modelado estadístico basado en muestreo sistemático con aplicación al análisis de imagen

Resumen

In statistics, sampling is the selection of a subset of individuals samples from within a target population to estimate characteristics of the whole population. Bias and variance are the two sources of error in estimation, therefore the purpose of sampling methods is to obtain unbiased and precise estimators. Geometric sampling in stereology aims at estimating quantitative properties of spatial objects, such as volume, surface area, length or number of particles (cells or other structures). It is particularly useful when a direct measurement is not possible due to technical or economical reasons. The sample is the intersection between the object and a geometric probe of know size and shape endowed with a well defined mechanism of randomness relative to the object. A geometric probe (or test system) is usually a regular arrangement of test points, lines, planes, or slabs. In practice sampling is usually performed with imaging techniques such as for instance microscopy. Advanced computing and image processing are becoming increasingly important for testing theoretical results coming from stereology and also for practical implementations of its principles. The second and third chapters of this thesis focus on Monte Carlo resampling to check the performance of error variance prediction for two dierent stereological estimators, namely the Buon-Steinhaus curve length estimator and the CountEm particle number estimator for planar images. Advances in imaging techniques have provided large data sets of images. For instance, exploratory pharmacology experiments aim at quantifying the pharmacological response of hundreds of dierent drugs by analysing microscopy images. The large amount of images requires an automated image analysis algorithm such as the \Delta-m algorithm proposed in the fourth chapter. Statistical models are useful to characterize the behavior from a large number of samples with high variability. They can be applied to generate true random numbers, being of special interest when the physical source of randomness is available in electronic circuits. Modern implementations of true random number generators include a stochastic model to mathematically assess the performance. In the fifth chapter a stochastic model for extracting entropy from electronic noise associated to logic circuits is studied, which depends on the sampling schema assumed. The sixth chapter summarizes the conclusions and open problems. Finally, the final chapter contains a summary of the main results in Spanish.