Image analysis and stereology: variance of volume and number estimators
ABSTRACT: Stereology aims at estimating quantitative properties of spatial objects using systematic sampling with test probes. The most common properties are feature number, length, surface area and volume. The main advantages of stereological methods are unbiasedness, and a high efficiency relative...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/14873 |
| Acceso en línea: | http://hdl.handle.net/10902/14873 |
| Access Level: | acceso abierto |
| Palabra clave: | Monte Carlo Computación Estereología Estimadores Varianza Volumen Nucleador Cavalieri CountEm Muestreo sistemático Computation Stereology Predictors Variance Volume Nucleator Systematic sampling |
| Sumario: | ABSTRACT: Stereology aims at estimating quantitative properties of spatial objects using systematic sampling with test probes. The most common properties are feature number, length, surface area and volume. The main advantages of stereological methods are unbiasedness, and a high efficiency relative to classical simple random sampling. The main disadvantage of systematic sampling, however, is that no unbiased predictors are generally available for the error variance of the corresponding estimators. Theoretical variance approximations have been proposed since the mid 20th century, (the mathematics underlying the corresponding formulae are rather advanced). The main problem with such predictors is that they are generally biased to unknown degrees. A number of such formulae have hitherto been used with no real warranty. Nowadays, however, powerful software and hardware exist to implement automatic Monte Carlo resampling using whatever systematic probes on whatever objects, whether synthetic, or computer reconstructions of real objects. Thus, now it is possible to check the performance of a variance prediction formula against the - nearly ’true’ - empirical variance. The conclusions may not be general inasmuch as the simulations are performed on concrete objects, but the resampling method may help (i) to discard defective predictors, and (ii) to cast some degree of confidence on others. To enter this novel, promising scenario is the purpose of the present thesis. |
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