Mumford and Shah Model and its Applications to Image Segmentation andImage Restoration
We present in this chapter an overview of the Mumford and Shah model for image segmentation. We discuss its various formulations, some of its properties, the mathematical framework, and several approximations. We also present numerical algorithms and segm
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ion of the Mumford and Shah Model.... ........ .....
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Background: The First Variation. .. .. ... .. ... .. .. ... .. ... .. .. ... .. ... .. ... .. .. Minimizing in u with K Fixed. .. ... .. .. .. .. .. ... .. .. .. .. ... .. .. .. .. .. ... .. .. .. .. ... . Minimizing in K ... ... .... .... ... .... .... .... ... .... .... ... .... .... ... .... .... .... ... ...
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Mathematical Modeling and Analysis: The Weak Formulation of the Mumford and Shah Functional.. .. .. . .. .. .. .. . .. .. .. . .. .. .. .. . .. .. .. . ..
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Numerical Methods: Approximations to the Mumford and Shah Functional... .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. Ambrosio and Tortorelli Phase-Field Elliptic Approximations. . .. .. .. .. .. .. .. .. Approximations of the Perimeter by Elliptic Functionals. .. . . . .. . . . .. . . . .. . . . .. . Ambrosio-Tortorelli Approximations. . . .. .. .. .. . .. .. .. .. .. . .. .. .. .. . .. .. .. .. . .. .. .. Level Set Formulations of the Mumford and Shah Functional. . . . . . . . . . . . . . . . . . Piecewise-Constant Mumford and Shah Segmentation Using Level Sets. . . . . . Piecewise-Smooth Mumford and Shah Segmentation Using Level Sets. .. . . . . . Extension to Level Set Based Mumford–Shah Segmentation with Open Edge Set K .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. .. .. .
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Case Examples: Variational Image Restoration with Segmentation-Based Regularization.. .. ... ... ... ... ... ... .. ... ... ... ... ... ... .. ... ... ... ... ... ... .. .. Non-blind Restoration. .... .... .... ..... .... .... ..... .... .... .... ..... .... .... ..... .... Semi-Blind Restoration. .. .. .. ... .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. .. .. Image Restoration with Impulsive Noise. .... ....... ....... ...... ....... ....... ..... Color Image Restoration. . .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. . .. .. .. . Space-Variant Restoration. .. ... ... ... ... ... ... ... ... ... ... ... ... .... ... ... ... ... ... ...
Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, DOI ./---_, © Springer Science+Business Media LLC
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Mumford and Shah Model and its Applications to Image Segmentation and Image Restoration
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Level Set Formulations for Joint Restoration and Segmentation. .. .. .. .. ... .. .. .. .. ... .. .. .. .. ... .. .. .. .. ... .. .. .. .. ... .. .. .. .. ... .. . Image Restoration by Nonlocal Mumford–Shah Regularizers. . .... .... .... .... .
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Conclusion.. ......... ........ ......... ........ ........ ......... ........ ......... .
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Recommended Reading.. ...... ...... ...... ...... ...... ....l.. ...... ....... ......
Mumford and Shah Model and its Applications t
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