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Shape Reconstruction from Apparent Contours [electronic resource] : Theory and Algorithms / by Giovanni Bellettini, Valentina Beorchia, Maurizio Paolini, Franco Pasquarelli.

By: Bellettini, Giovanni [author.].
Contributor(s): Beorchia, Valentina [author.] | Paolini, Maurizio [author.] | Pasquarelli, Franco [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Computational Imaging and Vision: 44Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015Description: XXIV, 365 p. 156 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783662451915.Subject(s): Mathematics | Image processing | Computer science -- Mathematics | Computer mathematics | Computer software | Calculus of variations | Manifolds (Mathematics) | Complex manifolds | Mathematics | Mathematical Applications in Computer Science | Image Processing and Computer Vision | Manifolds and Cell Complexes (incl. Diff.Topology) | Calculus of Variations and Optimal Control; Optimization | Mathematical SoftwareAdditional physical formats: Printed edition:: No titleDDC classification: 004.0151 Online resources: Click here to access online
Contents:
Introduction -- Chapter 1.A Variational Model on Labelled Graphs with Cusps and Crossings -- Chapter 2.Stable Maps and Morse Descriptions of an Apparent Contour -- Chapter 3.Apparent Contours of Embedded Surfaces -- Chapter 4.Solving the Completion Problem -- Chapter 5.Topological Reconstruction of a Three-dimensional Scene -- Chapter 6.Completeness of Reidemeister-type Moves on Labelled Apparent Contours -- Chapter 7.Invariants of an Apparent Contour -- Chapter 8.Elimination of Cusps -- Chapter 9.The Program "Visible" -- Chapter 10.The Program "Appcontour": User's Guide -- Chapter 11.Variational Analysis of the Model on Labelled Graphs -- Bibliography -- Nomenclature -- Index.
In: Springer eBooksSummary: Motivated by a variational model concerning the depth of the objects in a picture and the problem of hidden and illusory contours, this book investigates one of the central problems of computer vision: the  topological and algorithmic reconstruction of a smooth three dimensional scene starting from the visible part of an apparent contour. The authors focus their attention on the manipulation of apparent contours using a finite set of elementary moves, which correspond to diffeomorphic deformations of three dimensional scenes. A large part of the book is devoted to the  algorithmic part, with implementations, experiments, and computed examples. The book is intended also as a user's guide to the software code appcontour, written for the manipulation of apparent contours and their invariants. This book is addressed to theoretical and applied scientists working in the field of mathematical models of image segmentation.
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Introduction -- Chapter 1.A Variational Model on Labelled Graphs with Cusps and Crossings -- Chapter 2.Stable Maps and Morse Descriptions of an Apparent Contour -- Chapter 3.Apparent Contours of Embedded Surfaces -- Chapter 4.Solving the Completion Problem -- Chapter 5.Topological Reconstruction of a Three-dimensional Scene -- Chapter 6.Completeness of Reidemeister-type Moves on Labelled Apparent Contours -- Chapter 7.Invariants of an Apparent Contour -- Chapter 8.Elimination of Cusps -- Chapter 9.The Program "Visible" -- Chapter 10.The Program "Appcontour": User's Guide -- Chapter 11.Variational Analysis of the Model on Labelled Graphs -- Bibliography -- Nomenclature -- Index.

Motivated by a variational model concerning the depth of the objects in a picture and the problem of hidden and illusory contours, this book investigates one of the central problems of computer vision: the  topological and algorithmic reconstruction of a smooth three dimensional scene starting from the visible part of an apparent contour. The authors focus their attention on the manipulation of apparent contours using a finite set of elementary moves, which correspond to diffeomorphic deformations of three dimensional scenes. A large part of the book is devoted to the  algorithmic part, with implementations, experiments, and computed examples. The book is intended also as a user's guide to the software code appcontour, written for the manipulation of apparent contours and their invariants. This book is addressed to theoretical and applied scientists working in the field of mathematical models of image segmentation.

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