Scale Space and Variational Methods in Computer Vision

1. Front Matter

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2. Segmentation and Detection

   1. Graph Cut Optimization for the Piecewise Constant Level Set Method Applied to Multiphase Image Segmentation

      • Egil Bae, Xue-Cheng Tai

      Pages 1-13

   2. Tubular Anisotropy Segmentation

      • Fethallah Benmansour, Laurent D. Cohen

      Pages 14-25

   3. An Unconstrained Multiphase Thresholding Approach for Image Segmentation

      • Benjamin Berkels

      Pages 26-37

   4. Extraction of the Intercellular Skeleton from 2D Images of Embryogenesis Using Eikonal Equation and Advective Subjective Surface Method

      • Paul Bourgine, Peter Frolkovič, Karol Mikula, Nadine Peyriéras, Mariana Remešíková

      Pages 38-49

   5. On Level-Set Type Methods for Recovering Piecewise Constant Solutions of Ill-Posed Problems

      • Adriano DeCezaro, Antonio Leitão, Xue-Cheng Tai

      Pages 50-62

   6. The Nonlinear Tensor Diffusion in Segmentation of Meaningful Biological Structures from Image Sequences of Zebrafish Embryogenesis

      • Olga Drblíková, Karol Mikula, Nadine Peyriéras

      Pages 63-74

   7. Composed Segmentation of Tubular Structures by an Anisotropic PDE Model

      • Elena Franchini, Serena Morigi, Fiorella Sgallari

      Pages 75-86

   8. Extrapolation of Vector Fields Using the Infinity Laplacian and with Applications to Image Segmentation

      • Laurence Guillot, Carole Le Guyader

      Pages 87-99

   9. A Schrödinger Equation for the Fast Computation of Approximate Euclidean Distance Functions

      • Karthik S. Gurumoorthy, Anand Rangarajan

      Pages 100-111

   10. Semi-supervised Segmentation Based on Non-local Continuous Min-Cut

       • Nawal Houhou, Xavier Bresson, Arthur Szlam, Tony F. Chan, Jean-Philippe Thiran

       Pages 112-123

   11. Momentum Based Optimization Methods for Level Set Segmentation

       • Gunnar Läthén, Thord Andersson, Reiner Lenz, Magnus Borga

       Pages 124-136

   12. Optimization of Divergences within the Exponential Family for Image Segmentation

       • Francois Lecellier, Stephanie Jehan-Besson, Jalal Fadili, Gilles Aubert, Marinette Revenu

       Pages 137-149

   13. Convex Multi-class Image Labeling by Simplex-Constrained Total Variation

       • Jan Lellmann, Jörg Kappes, Jing Yuan, Florian Becker, Christoph Schnörr

       Pages 150-162

   14. Geodesically Linked Active Contours: Evolution Strategy Based on Minimal Paths

       • Julien Mille, Laurent D. Cohen

       Pages 163-174

   15. Validation of Watershed Regions by Scale-Space Statistics

       • Tomoya Sakai, Atsushi Imiya

       Pages 175-186

   16. Adaptation of Eikonal Equation over Weighted Graph

       • Vinh-Thong Ta, Abderrahim Elmoataz, Olivier Lézoray

       Pages 187-199

   17. A Variational Model for Interactive Shape Prior Segmentation and Real-Time Tracking

       • Manuel Werlberger, Thomas Pock, Markus Unger, Horst Bischof

       Pages 200-211

3. Image Enhancement and Reconstruction

   1. A Nonlinear Probabilistic Curvature Motion Filter for Positron Emission Tomography Images

      • Musa Alrefaya, Hichem Sahli, Iris Vanhamel, Dinh Nho Hao

      Pages 212-223

   2. Finsler Geometry on Higher Order Tensor Fields and Applications to High Angular Resolution Diffusion Imaging

      • Laura Astola, Luc Florack

      Pages 224-234

This book contains 71 original, scienti?c articles that address state-of-the-art researchrelatedto scale space and variationalmethods for image processing and computer vision. Topics covered in the book range from mathematical analysis of both established and new models, fast numerical methods, image analysis, segmentation, registration, surface and shape construction and processing, to real applications in medical imaging and computer vision. The ideas of scale spaceandvariationalmethodsrelatedtopartialdi?erentialequationsarecentral concepts. The papers re?ect the newest developments in these ?elds and also point to the latest literature. All the papers were submitted to the Second International Conference on Scale Space and Variational Methods in Computer Vision, which took place in Voss, Norway, during June 1–5, 2009. The papers underwent a peer review process similar to that of high-level journals in the ?eld. We thank the authors, the Scienti?c Committee, the Program Committee and the reviewers for their hard work and helpful collaboration. Their contribution has been crucial for the e?cient processing of this book, and for the success of the conference.

• algorithms
• anisotropic smoothin
• computational geometry
• curvelets
• dejittering
• denoising
• filtering
• finsler geometry
• image restoration
• image segmentation
• level set segmentation
• noise removal
• optical nanoscopy
• statistics
• wiener filter

• Department of Mathematics, University of Bergen, Bergen, Norway

  Xue-Cheng Tai

• Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

  Knut Mørken

• Simula Research Laboratory, Lysaker, Norway

  Marius Lysaker

• SINTEF ICT, Oslo, Norway

  Knut-Andreas Lie

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