The topic of level sets is currently very timely and useful. 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 Professor 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, and the audience is not limited to students, professors, universities, and people 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 too (Cognitech, Siemens, Philips, Focus Imaging).

This book can be suitable for a short professional course related with the processing of visual information.

Contents

• Level set methods & Lagrangian approaches
  • Level set methods
  • Deformable models : Classic, topology-adaptive and generalized formulations
  • Edge detection & boundary extraction
  • Fast edge integration
  • Variational snake theory

• Scalar & vector image reconstruction, restoration
  • Multiplicative denoising and deblurring : Theory and algorithms
  • Total varation minimization for scalar/vector regularization
  • Morphological global reconstruction and levelings : Lattice and PDE approaches

• Grouping
  • Fast marching techniques for visual grouping and segmentation
  • Multiphase object detection and image segmentation
  • Adaptive segmentation of vector-valued images
  • Mumford-Shah for segmentation and stereo

• Shape analysis towards model-based segmentation
  • Shape analysis toward model-based segmentation
  • Joint image registration and segmentation
  • Image alignment

• Motion analysis
  • Variational principles in optical flow estimation and tracking
  • Region matching and tracking under deformations or occlusions

• Computational stereo & implicit surfaces
  • Computational stereo : A variational method
  • Visualization, analysis and shape reconstruction of sparse data
  • Variational problems and partial differential equations on implicit surfaces : Bye bye triangulated surfaces ?

• Medical image analysis
  • Knowledge-based segmentation of medical images
  • Topology preserving geometric deformable models for brain reconstruction

• Simulations & graphics
  • Editing geometric models
  • Simulating natural phenomena

• Bibliography