Geometric Level Set Methods in Imaging, Vision, and Graphics

by Osher, Stanley; Paragios, Nikos

• ISBN13: 9780387954882
• ISBN10: 0387954880
• Format: Hardcover
• Copyright: 2003-08-01
• Publisher: Springer-Verlag New York Inc

Summary

The topic of level sets is currently very timely and useful for creating realistic 3-D images and animations. They are powerful numerical techniques for analyzing and computing interface motion in a host of application settings. In computer vision, it has been applied to stereo and segmentation, whereas in graphics it has been applied to the postproduction process of in-painting and 3-D model construction. Osher is co-inventor of the Level Set Methods, a pioneering framework introduced jointly with James Sethian from the University of Berkeley in 1998. This methodology has been used up to now to provide solutions to a wide application range not limited to image processing, computer vision, robotics, fluid mechanics, crystallography, lithography, and computer graphics. The topic is of great interest to advanced students, professors, and R&D professionals working in the areas of graphics (post-production), video-based surveillance, visual inspection, augmented reality, document image processing, and medical image processing. These techniques are already employed to provide solutions and products in the industry (Cognitech, Siemens, Philips, Focus Imaging). An essential compilation of survey chapters from the leading researchers in the field, emphasizing the applications of the methods. This book can be suitable for a short professional course related with the processing of visual information.

Table of Contents

Preface	xv
List of Contributors	xxi
I Level set Methods & Lagrangian Approaches	1	(40)
1 Level set Methods	3	(18)
Stanley Osher
1.1 Introduction	3	(2)
1.2 Level set Dictionary and Technology	5	(2)
1.3 Numerical Methods	7	(5)
1.4 Imaging Science Applications	12	(8)
1.4.1 Dynamic Visibility	13	(1)
1.4.2 Interpolation from Unorganized Points via the Level Set Method	14	(1)
1.4.3 PDE's on Implicit Surfaces	14	(1)
1.4.4 The Level Set Method Links Active Contours, Mumford-Shah Segmentation and Total Variation Restoration	14	(2)
1.4.5 Modeling Textures with Total Variation Minimization and Oscillating Patterns	16	(4)
1.5 Conclusion	20	(1)
2 Deformable Models: Classic, Topology-Adaptive and Generaliz\d Formulations	21	(20)
Demetri Terzopoulos
2.1 Introduction	21	(2)
2.2 Classic Deformable Models	23	(7)
2.2.1 Energy-Minimizing Snakes	23	(2)
2.2.2 Dynamic Snakes	25	(1)
2.2.3 Discretization and Numerical Simulation	26	(1)
2.2.4 Probabilistic Interpretation	27	(1)
2.2.5 Higher-Dimensional Generalizations	28	(1)
2.2.6 Connections to Curve Evolution	29	(1)
2.3 Topology-Adaptive Deformable Models	30	(3)
2.3.1 Topology-Adaptive snakes	30	(2)
2.3.2 Topology-Adaptive Deformable Surfaces	32	(1)
2.4 Generalized Deformable Models	33	(7)
2.4.1 Dynamic NURES	33	(3)
2.4.2 Deformable Superquadrics	36	(4)
2.5 Conclusion	40	(1)
II Edge Detection & Boundary Ext\action	41	(60)
3 Fast Methods for Implicit Active Contour Models	43	(16)
Joachim Weickert and Gerald Kühne
3.1 Introduction	43	(2)
3.2 Implicit Active Contour Models	45	(1)
3.3 Numerical Implementation	46	(5)
3.4 Experimental Results	51	(3)
3.4.1 Accuracy Evaluation in Case of Mean Curvature Motion	51	(1)
3.4.2 Efficiency Gain for Implicit Active Contour Models	51	(3)
3.5 Conclusions	54	(1)
3.6 Appendix: The Thomas Algorithm	55	(4)
4 Fast Edge Integration	59	(20)
Ron Kimmel
4.1 Introduction	59	(1)
4.2 Mathematical Notations	60	(1)
4.3 Geometric Integral Measures for Active Contours	61	(3)
4.3.1 Alignment Term	62	(1)