Variational Methods in Image Segmentation: with seven image processing experiments
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1995
|
| Schriftenreihe: | Progress in Nonlinear Differential Equations and Their Applications
14 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image: in the variational seg mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con cepts from geometric measure theory, which proves to be central in im age processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals") |
| Beschreibung: | 1 Online-Ressource (XVI, 248 p) |
| ISBN: | 9781468405675 9781468405699 |
| DOI: | 10.1007/978-1-4684-0567-5 |
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Datensatz im Suchindex
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| author | Morel, Jean Michel |
| author_facet | Morel, Jean Michel |
| author_role | aut |
| author_sort | Morel, Jean Michel |
| author_variant | j m m jm jmm |
| building | Verbundindex |
| bvnumber | BV042421061 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863898649 (DE-599)BVBBV042421061 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-0567-5 |
| format | Electronic eBook |
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| id | DE-604.BV042421061 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468405675 9781468405699 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856478 |
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| physical | 1 Online-Ressource (XVI, 248 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
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| publisher | Birkhäuser Boston |
| record_format | marc |
| series2 | Progress in Nonlinear Differential Equations and Their Applications |
| spelling | Morel, Jean Michel Verfasser aut Variational Methods in Image Segmentation with seven image processing experiments by Jean Michel Morel, Sergio Solimini Boston, MA Birkhäuser Boston 1995 1 Online-Ressource (XVI, 248 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 14 This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image: in the variational seg mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con cepts from geometric measure theory, which proves to be central in im age processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals") Mathematics Computer science / Mathematics Visualization Computational Mathematics and Numerical Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Informatik Mathematik Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Geometrische Maßtheorie (DE-588)4125258-5 gnd rswk-swf Bildsegmentierung (DE-588)4145448-0 gnd rswk-swf Bildsegmentierung (DE-588)4145448-0 s Variationsrechnung (DE-588)4062355-5 s 1\p DE-604 Geometrische Maßtheorie (DE-588)4125258-5 s 2\p DE-604 Solimini, Sergio Sonstige oth https://doi.org/10.1007/978-1-4684-0567-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Morel, Jean Michel Variational Methods in Image Segmentation with seven image processing experiments Mathematics Computer science / Mathematics Visualization Computational Mathematics and Numerical Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Informatik Mathematik Variationsrechnung (DE-588)4062355-5 gnd Geometrische Maßtheorie (DE-588)4125258-5 gnd Bildsegmentierung (DE-588)4145448-0 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4125258-5 (DE-588)4145448-0 |
| title | Variational Methods in Image Segmentation with seven image processing experiments |
| title_auth | Variational Methods in Image Segmentation with seven image processing experiments |
| title_exact_search | Variational Methods in Image Segmentation with seven image processing experiments |
| title_full | Variational Methods in Image Segmentation with seven image processing experiments by Jean Michel Morel, Sergio Solimini |
| title_fullStr | Variational Methods in Image Segmentation with seven image processing experiments by Jean Michel Morel, Sergio Solimini |
| title_full_unstemmed | Variational Methods in Image Segmentation with seven image processing experiments by Jean Michel Morel, Sergio Solimini |
| title_short | Variational Methods in Image Segmentation |
| title_sort | variational methods in image segmentation with seven image processing experiments |
| title_sub | with seven image processing experiments |
| topic | Mathematics Computer science / Mathematics Visualization Computational Mathematics and Numerical Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Informatik Mathematik Variationsrechnung (DE-588)4062355-5 gnd Geometrische Maßtheorie (DE-588)4125258-5 gnd Bildsegmentierung (DE-588)4145448-0 gnd |
| topic_facet | Mathematics Computer science / Mathematics Visualization Computational Mathematics and Numerical Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Informatik Mathematik Variationsrechnung Geometrische Maßtheorie Bildsegmentierung |
| url | https://doi.org/10.1007/978-1-4684-0567-5 |
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