Image estimators based on marked bins

Statistics

Volumn 40, Issue 4, 2006, Pages 277-288

  Baíllo, Amparo ^a   Cuevas, Antonio ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Convergence rates; Histogram; Image analysis; Set estimation

Indexed keywords

EID: 33745654571     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880600741723     Document Type: Article

References (24)

1. Cuevas, A. and Rodríguez-Casal, A., 2003, Set estimation: an overview and some recent developments. In: M.G. Akritas and D.N. Politis (Eds) Recent Advances and Trends in Nonparametric Statistics, pp. 251-264 (Amsterdam: Elsevier).
2. Korostelev, A.P. and Tsybakov, A.B., 1993, Minimax Theory of Image Reconstruction (New York: Springer).
3. Rényi, A. and Sulanke, R., 1963, Über die konvexe Hülle von n zufällig gewählten Punkten. Zeitschrift fur Wahrschlinlichkeitstheorie und Verwandte Gebiete, 2, 75-84.
4. Schneider, R., 1988, Random approximation of convex sets. Journal of Microscopy, 151, 211-227.
5. Devroye, L. and Wise, G. L., 1980, Detection of abnormal behavior via nonparametric estimation of the support. SIAM Journal of Applied Mathematics, 38, 480-488.
6. Bafllo, A., Cuevas, A. and Justel, A., 2000, Set estimation and nonparametric detection. Canadian Journal of Statistics, 28, 765-782.
7. Cuevas, A. and Rodríguez-Casal, A., 2004, On boundary estimation. Advances in Applied Probability, 36, 340-354.
8. Hall, P., Park, B.U. and Turlach, B. A., 2002, Rolling-ball method for estimating the boundary of the support of a point-process intensity. Annals Institute of Henri Poincaré Probability and Statistics, 38, 959-971.
9. Rodríguez-Casal, A., 2003, Set estimation under convexity type assumptions, Manuscript.
10. Ray Chaudhuri, A., Basu, A., Bhandari, S.K. and Chaudhuri, B.B., 1999, An efficient approach to consistent set estimation. Sankhyā B, 61, 496-513.
11. Ray Chaudhuri, A., Chaudhuri, B.B. and Parui, S.K., 1997, A novel approach to computation of the shape of a dot pattern and extraction of its perceptual border. Computer Vision and Image Understanding, 68, 257-275.
12. Klemelä, J., 2004, Complexity penalized support estimation. Journal of Multivariate Analysis, 88, 274-297.
13. Stoyan, D., Kendall, W.S. and Mecke, J., 1995, Stochastic Geometry and its Applications (New York: Wiley).
14. 1-View (New York: Wiley).
15. Beirlant, J., Devroye, L., Györfi, L. and Vajda, I., 2001, Large deviations of divergence measures on partitions. Journal of Statistical Planning Inference, 93, 1-16.
16. 1-test statistic of homogeneity. IEEE Transactions on Information Theory, 51, 3965-3973.
17. Devroye, L., Györfi, L. and Lugosi, G., 1996, A Probabilistic Theory of Pattern Recognition (New York: Springer).
18. Walther, G., 1997, Granulometric smoothing. Annals of Statistics, 25, 2273-2299.
19. Györfi, L., Kohler, M., Krzyzac, A. and Walk, H. (2002), A Distribution-Free Theory of Nonparametric Regression. (New York: Springer).
20. Cuevas, A. and Fraiman, R., 1998, On visual distances in density estimation: the Hausdorff choice. Statistics and Probability Letters, 40, 333-341.
21. Gilbarg, D. and Trudinger, N.S., 1983, Elliptic Partial Differential Equations of Second Order (New York: Springer).
22. Upton, G. and Fingleton, B., 1985, Spatial Data Analysis by Example (New York: Wiley).
23. Serra, J., 1982, Image Analysis and Mathematical Morphology (New York: Academic press).
24. Scott, D.W., 1992, Multivariate Density Estimation. Theory, Practice, and Visualization (NewYork: Wiley).