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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Variational Methods in Image Segmentation: With Seven Image Processing Experiments

Variational Methods in Image Segmentation: With Seven Image Processing Experiments

Solimini, Sergio
Morel, Jean-Michel

Paperback

Series: Progress in Nonlinear Differential Equations and Their Appli, Book 14

General Mathematics

ISBN10: 1468405691
ISBN13: 9781468405699
Publisher: Birkhauser
Published: Feb 22 2012
Pages: 248
Weight: 0.84
Height: 0.56 Width: 6.14 Depth: 9.21
Language: English
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).

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