Stereology, 1st ed. 2024 Theory and Applications Interdisciplinary Applied Mathematics Series, Vol. 59

This book presents a comprehensive set of methods for quantifying geometric quantities such as the volume of a tumor, the total surface area of the alveoli in a lung, the length of plant roots, or of blood vessels, the number of neurons in a brain compartment, the connectivity number of trabecular bone, the mean size of grains in a rock, etc.. The methods, illustrated by twenty solved case studies, are based on properly sampled slices, sections, or projections of the material, observable under light, laser, or electron microscopy, or under non-invasive radiological devices such as ecography, computed tomography, or magnetic resonance imaging. Thus, the input usually consists of flat images, and the output consists of relevant quantities defined in three dimensions. Stereology is the discipline of providing sampling designs which warrant unbiased estimation of the corresponding quantities, that is, estimation with zero mean deviation from the target. Sampling is usually systematic (i.e., with regularly spaced probes), and sparse (as opposed to reconstructions) and it is thereby efficient and easy to implement.

Stereology is essentially geometric sampling, grounded on integral geometry. The necessary elements of both disciplines are detailed in textbook style, and may be used for postgraduate courses, or to serve the interest of scientists in general. Hitherto no other book on stereology has appeared which encompasses the theory, methodology, and applications of stereology in an interconnected and comprehensive way. The currently available error variance prediction formulae under systematic sampling, and their (non-obvious) derivation, are all gathered, for the first time, in the last chapter. The exposition is augmented by 127 line drawings for the theory, and 27 color pictures of real materials for the case studies.

Luis Manuel Cruz-Orive is a retired professor from the University of Cantabria in Santander (E). He was born in 1944 in Miranda de Ebro (Burgos, E), from a working-class family. In 1968 he graduated from the Escuela Técnica Superior de Ingenieros Agrónomos, and in 1970 from the Escuela de Estadística, both of the Complutense University of Madrid (E). In 1970 he moved to the University of Edinburgh (UK) to obtain the Diploma in Statistics (1971). There he was the sole student of David J. Finney in his Sampling Theory course. In 1974 he was awarded a PhD from the University of Sheffield (UK), (Department of Probability and Statistics, directed by J. Gani). Following a Science Research Council research assistantship in stereology and geometric probability, in 1976 he moved to the University of Berne (CH), to work in Ewald R. Weibel’s group at the Institute of Anatomy.  Motivated by challenging projects, he contributed to the development of stereology. Between 1979 and 1998 he was a member of the teaching squad at 25 International Stereology Courses in Europe, USA, Canada, Australia and Hong Kong. Most modern stereological methods were inspired by these courses. In 1994 he obtained a Chair of Statistics at the University of Cantabria, where he moved with his wife Soledad and son Marcos. There he created a Laboratory of Stereology. He led four three-year research projects on stereology funded by the Swiss National Science Foundation, and another four supported by national Spanish funds. In 1971 he was elected Member of the Biometric Society, and Fellow of the Royal Statistical Society. Since 1981 he is a member of the Royal Microscopical Society and of the Editorial Board of the Journal of Microscopy (Oxford). He is Honorary Member of the International Society for Stereology and Image Analysis.

Encompassing theory, methodology, applications of stereology in an interconnected and comprehensive way

127 line drawings for the theory, plus 27 color pictures of real materials for the solved case studies

Comprehensive set of methods