Variational Methods in Image Segmentation: with seven image processing experiments [1 ed.] 9780817637200, 9783764337209, 0817637206, 3764337206
This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the
198 2 3MB
English Pages 248 [264] Year 1995
Table of contents :
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Edge Detection and Segmentation....Pages 3-7
Linear and Nonlinear Multiscale Filtering....Pages 8-20
Region and Edge Growing....Pages 21-34
Variational Theories of Segmentation....Pages 35-45
The Piecewise Constant Mumford and Shah Model: Mathematical Analysis....Pages 46-62
Front Matter....Pages 63-63
Hausdorff Measure....Pages 65-78
Covering Lemmas in a Metric Space....Pages 79-85
Density Properties....Pages 86-93
Tangency Properties of Regular Subsets of ℝ N ....Pages 94-117
Semicontinuity Properties of the Hausdorff Measure....Pages 118-126
Rectifiable Sets....Pages 127-135
Properties of Regular and Rectifiable Sets....Pages 136-147
Front Matter....Pages 149-149
Properties of the Approximating Image in the Mumford-Shah Model....Pages 151-164
Small Oscillation Coverings and the Excision Method....Pages 165-181
Density Properties and Existence Theory for the Mumford-Shah Minimizers....Pages 182-198
Further Properties of Minimizers: Covering the Edge Set with a Single Curve....Pages 199-208
Back Matter....Pages 209-248
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Edge Detection and Segmentation....Pages 3-7
Linear and Nonlinear Multiscale Filtering....Pages 8-20
Region and Edge Growing....Pages 21-34
Variational Theories of Segmentation....Pages 35-45
The Piecewise Constant Mumford and Shah Model: Mathematical Analysis....Pages 46-62
Front Matter....Pages 63-63
Hausdorff Measure....Pages 65-78
Covering Lemmas in a Metric Space....Pages 79-85
Density Properties....Pages 86-93
Tangency Properties of Regular Subsets of ℝ N ....Pages 94-117
Semicontinuity Properties of the Hausdorff Measure....Pages 118-126
Rectifiable Sets....Pages 127-135
Properties of Regular and Rectifiable Sets....Pages 136-147
Front Matter....Pages 149-149
Properties of the Approximating Image in the Mumford-Shah Model....Pages 151-164
Small Oscillation Coverings and the Excision Method....Pages 165-181
Density Properties and Existence Theory for the Mumford-Shah Minimizers....Pages 182-198
Further Properties of Minimizers: Covering the Edge Set with a Single Curve....Pages 199-208
Back Matter....Pages 209-248
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