Normal Multi-scale Transforms for Curves

Foundations of Computational Mathematics

Volumn 11, Issue 6, 2011, Pages 617-656

  Harizanov, S ^a   Oswald, P ^b   Shingel, T ^c  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b JACOBS UNIVERSITY BREMEN   (Germany)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Approximating subdivision schemes; Curve representation; Detail decay estimate; Lipschitz smoothness; Nonlinear geometric multi scale transforms

Indexed keywords

EID: 81255199257     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-011-9104-6     Document Type: Article

References (16)

1. R. Baraniuk, M. Janssen, S. Lavu, Multiscale approximation of piecewise smooth two-dimensional functions using normal triangulated meshes, Appl. Comput. Harmon. Anal. 19, 92-130 (2005).
2. M. A. Berger, Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166, 21-27 (1992).
3. P. Binev, N. Dyn, R. A. DeVore, N. Dyn, Adaptive approximation of curves, in Approximation Theory (Acad. Publ. House, Sofia, 2004), pp. 43-57.
4. A. S. Cavaretta, W. Dahmen, C. A. Micchelli, Stationary Subdivision, Memoirs AMS, vol. 93 (Am. Math. Soc., Providence, 1991).
5. I. Daubechies, O. Runborg, W. Sweldens, Normal multiresolution approximation of curves, Constr. Approx. 20, 399-463 (2004).
6. 2 four-point subdivision scheme with fourth order accuracy and its extensions, in Mathematical Methods for Curves and Surfaces, ed. by M. Dæhlen, K. Mørken, L. L. Schumaker (Nashboro Press, Brentwood, 2005), pp. 145-156.
7. N. Dyn, K. Hormann, M. A. Sabin, Z. Shen, Polynomial reproduction by symmetric subdivision schemes, J. Approx. Theory155, 28-42 (2008).
8. N. Dyn, D. Levin, Subdivision schemes in geometric modelling, Acta Numer. 11, 73-144 (2002).
9. I. Friedel, A. Khodakovski, P. Schröder, Variational normal meshes, ACM Trans. Graph. 23, 1061-1073 (2004).
10. P. Grohs, A general proximity analysis of nonlinear subdivision schemes, SIAM J. Math. Anal. 42, 729-750 (2010).
11. I. Guskov, K. Vidimce, W. Sweldens, P. Schröder, Normal meshes, in Computer Graphics (SIGGRAPH'00: Proceedings), ed. by K. Akeley (ACM, New York, 2000), pp. 95-102.
12. A. Khodakovsky, I. Guskov, Compression of normal meshes, in Geometric Modeling for Scientific Visualization (Springer, Berlin, 2003), pp. 189-207.
13. J. M. Lane, R. F. Riesenfeld, A theoretical development for the computer generation and display of piecewise polynomial surfaces, IEEE Trans. Pattern Anal. Mach. Intell. 2, 35-46 (1980).
14. S. Lavu, H. Choi, R. Baraniuk, Geometry compression of normal meshes using rate-distortion algorithms, in Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, ed. by L. Kobbelt, P. Schröder, H. Hoppe (Eurographics Association, Aire-la-Ville, 2003), pp. 52-61.
15. O. Runborg, Introduction to normal multiresolution analysis, in Multiscale Methods in Science and Engineering, ed. by B. Engquist, P. Lötstedt, O. Runborg. Lecture Notes in Computational Science and Engineering, vol. 44 (Springer, Heidelberg, 2005), pp. 205-224.
16. O. Runborg, Fast interface tracking via a multiresolution representation of curves and surfaces, Commun. Math. Sci. 7, 365-389 (2009).