| Geometric Curve Evolution and Image Processing 2003 Edition Contributor(s): Cao, Frédéric (Author) |
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ISBN: 3540004025 ISBN-13: 9783540004028 Publisher: Springer OUR PRICE: $47.45 Product Type: Paperback - Other Formats Published: February 2003 Annotation: 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 and self-contained exposition of the techniques of "motion by curvature." The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Geometry - Differential - Computers | Computer Graphics |
| Dewey: 516.362 |
| LCCN: 2003041554 |
| Series: Lecture Notes |
| Physical Information: 0.43" H x 6.14" W x 9.21" (0.64 lbs) 194 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved. |