04299nam a22006015i 4500 978-3-031-52451-6 DE-He213 20251030111419.0 cr nn 008mamaa 240207s2024 sz | s |||| 0|eng d 9783031524516 978-3-031-52451-6 10.1007/978-3-031-52451-6 doi QA440-699 PBM bicssc MAT012000 bisacsh PBM thema Cruz-Orive, Luis Manuel. author. aut http://id.loc.gov/vocabulary/relators/aut 70739 Stereology [electronic resource] : Theory and Applications / by Luis Manuel Cruz-Orive. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVI, 486 p. 152 illus., 95 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Interdisciplinary Applied Mathematics, 2196-9973 ; 59 1 Basic Results of Integral Geometry -- 2 Basic Ideas of Geometric Sampling -- 3 Model and Second-Order Stereology -- 4 Sampling and Estimation for Stereology -- 5 Variance Predictors for Systematic Sampling -- Appendix -- List of Notation -- References -- Author Index -- Subject Index. 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. Geometry. 68763 Image processing Digital techniques. 64228 Computer vision. Anatomy. 70740 Radiology. Cancer Imaging. 69161 Geometry. 68763 Computer Imaging, Vision, Pattern Recognition and Graphics. 65550 Anatomy. 70740 Radiology. Cancer Imaging. 69163 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031524509 Printed edition: 9783031524523 Printed edition: 9783031524530 Interdisciplinary Applied Mathematics, 2196-9973 ; 59 70741 https://doi.org/10.1007/978-3-031-52451-6 ZDB-2-SMA ZDB-2-SXMS 57531 57531