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" Computational topology for biomedical image and data analysis : "
Rodrigo Rojas Moraleda, Nektarios A. Valous, Wei Xiong, Niels Halama.
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BL
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| Record Number
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877904
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| Main Entry
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Moraleda, Rodrigo Rojas.
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| Title & Author
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Computational topology for biomedical image and data analysis : : theory and applications /\ Rodrigo Rojas Moraleda, Nektarios A. Valous, Wei Xiong, Niels Halama.
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| Publication Statement
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Boca Raton, FL :: CRC Press, Taylor & Francis Group,, [2020]
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| Series Statement
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CRC focus series
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Series in medical physics and biomedical engineering
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| Page. NO
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1 online resource
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| ISBN
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0429443072
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: 0429810970
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: 0429810989
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: 0429810997
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: 9780429443077
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: 9780429810978
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: 9780429810985
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: 9780429810992
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1138336343
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9781138336346
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Section I: Theoretical foundations -- Chapter 1: Elements of topology and homology -- 1.1 ELEMENTS OF GROUP THEORY -- 1.2 TOPOLOGICAL SPACES -- 1.3 METRIC SPACES -- 1.4 ELEMENTS OF AFFINE VECTOR SPACES -- 1.5 SIMPLICIAL COMPLEXES -- 1.6 HOMOLOGY -- 1.7 CHAPTER FIGURES -- Chapter 2: Persistent homology of images -- 2.1 INTRODUCTION -- 2.2 DIGITAL IMAGES -- 2.3 A NEIGHBORHOOD SYSTEM FOR IMAGES -- 2.4 COMPUTING HOMOLOGY FROM IMAGES -- 2.5 PERSISTENT HOMOLOGY -- 2.6 COMPUTATIONAL COST -- 2.7 CHAPTER FIGURES -- Section II: Case studies -- Chapter 3: Recognizing noise -- 3.1 SYNTHETIC IMAGES -- 3.2 WORKFLOW -- 3.3 RESULTS -- 3.4 CHAPTER FIGURES -- Chapter 4: Image segmentation -- 4.1 INTRODUCTION -- 4.2 MATERIALS AND IMAGE ACQUISITION -- 4.3 FEATURE SPACE -- 4.4 IMAGE DISMANTLING AND INCLUSION TREE -- 4.5 FILTRATION -- 4.6 HOMOLOGY AND PERSISTENCE DIAGRAM -- 4.7 STATISTICAL INFERENCE -- 4.8 MASK SEGMENTATION -- 4.9 VALIDATION WITH CASE STUDY DATA -- 4.10 VALIDATION WITH ILASTIK -- 4.11 RESULTS WITH CASE STUDY DATA -- 4.12 RESULTS WITH ILASTIK -- 4.13 CHAPTER FIGURES -- Chapter 5: Point cloud characterization -- 5.1 INTRODUCTION -- 5.2 POINT CLOUD -- 5.3 WORKFLOW -- 5.4 RESULTS -- 5.5 CHAPTER FIGURES
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| Abstract
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This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data
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Homology theory.
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Image analysis-- Data processing.
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Imaging systems in medicine-- Data processing.
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Topology-- Data processing.
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Homology theory.
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Image analysis-- Data processing.
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Imaging systems in medicine-- Data processing.
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MEDICAL-- Radiology Nuclear Medicine.
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TECHNOLOGY-- Imaging Systems.
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Topology-- Data processing.
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Computational Biology.
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Biomechanical Phenomena.
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Models, Statistical.
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| Dewey Classification
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616.07/54
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| LC Classification
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R857.O6M67 2020
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| Added Entry
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Halama, Niels.
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Valous, Nektarios A.
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Xiong, Wei,1966-
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