On global performance of approximations to smooth curves using gridded data

Annals of Statistics

Volumn 26, Issue 6, 1998, Pages 2206-2217

  Hall, Peter ^a   Raimondo, Marc ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Digital image; Image analysis; L1 metric; Lattice; Local linear smoothing; Local polynomial smoothing; Metric number theory; Numerical analysis; Pixel grid

Indexed keywords

EID: 0032243953     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1024691467     Document Type: Article

References (9)

1. BAKER, R. C. (1986). Diophantine Inequalities. Oxford Univ. Press.
2. FREEMAN, H. (1970). Boundary encoding and processing. In Picture Processing and Psychopictorics (B. S. Lipkin and A. Rosenfeld, eds.) Academic Press, New York.
3. HALL, P. and RAIMONDO, M. (1997). Approximating a line thrown at random onto a grid. Ann. Appl. Probab. 7 648-665.
4. KHINTCHINE, A. YA. (1963). Continued Fractions. Noordhoff, Groningen.
5. KOROSTELEV, A. P. and TSYBAKOV, A. B. (1993). Minimax Theory of Image Reconstruction. Lecture Notes in Statist. 82. Springer, Berlin.
6. LEVEQUE, W. J. (1956) Topics in Number Theory I. Addison-Wesley, Reading, MA.
7. SCHMIDT, W. M. (1980). Diophantine Approximation. Springer, Berlin.
8. WAND, M. P. and JONES, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.
9. WORRING, M. and SMEULDERS, W. M. (1995). Digitized circular arcs: characterization and parameter estimation. IEEE Trans. Pattern Anal. Machine Intell. 17 587-598.