Geometric Curve Evolution and Image Processing

• Main Author: Cao, Frédéric (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1805
• Subjects: Partial differential equations.; Optical data processing.; Differential geometry.; Partial Differential Equations.; Image Processing and Computer Vision.; Differential Geometry.

In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous...

Table of Contents:

• Preface
• Part I. The curve smoothing problem: 1. Curve evolution and image processing; 2. Rudimentary bases of curve geometry
• Part II. Theoretical curve evolution: 3. Geometric curve shortening flow; 4. Curve evolution and level sets
• Part III. Numerical curve evolution: 5. Classical numerical methods for curve evolution; 6. A geometrical scheme for curve evolution
• Conclusion and perspectives
• A. Proof of Thm. 4.3.4
• References
• Index.