An efficient set estimator in high dimensions: Consistency and applications to fast data visualization

Computer Vision and Image Understanding

Volumn 93, Issue 3, 2004, Pages 260-287

  Ray Chaudhuri, A ^a   Basu, A ^b   Tan, K ^c   Bhandari, S ^b   Chaudhuri, B B ^b  

^a JADAVPUR UNIVERSITY   (India)

^b INDIAN STATISTICAL INSTITUTE   (India)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Consistency; High dimensional data; Point set; Set estimation; Shape descriptors; Visualization

Indexed keywords

COMPUTATIONAL METHODS; DATA REDUCTION; IDENTIFICATION (CONTROL SYSTEMS); PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); SPURIOUS SIGNAL NOISE; VISUALIZATION;

CONSISTENCY; DATA VISUALIZATION; HIGH-DIMENSIONAL DATA; POINT SET; SET ESTIMATION; SHAPE DESCRIPTORS;

MOTION ESTIMATION;

EID: 1642414281     PISSN: 10773142     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cviu.2003.10.002     Document Type: Article

References (25)

1. H. Edelsbrunner, E.P. Mücke, Three-dimensional alpha shapes, ACM Trans. Graphics 13 (1994) 43-72.
2. P. Bajcsy, A. Ray Chaudhuri, Benefits of high resolution SAR for ATR of targets in proximity, Radar Conf. Proc. of the IEEE (2002) 29-34.
3. A. Okabe, B. Boots, K. Sugihara, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Wiley, New York, 1992.
4. J.C. Russ, Image Processing HandBook, CRC Press, Ann Arbar, 1995.
5. U. Grenander, Abstract Inference, Wiley, New York, 1975.
6. P.L. Combettes, Foundations of set theoretic estimation, Proc. IEEE 81 (2) (1993) 182-208.
7. A. Ray Chaudhuri, B.B. Chaudhuri, S.K. Parui, A novel approach to computation of the shape of dot pattern and extraction of its perceptual border, Comput. Vision Image Understanding 68 (3) (1997) 257-275 (doi: 10.1006/cviu.1997.0550).
8. A. Ray Chaudhuri, A. Basu, S. Bhandari, B.B. Chaudhuri, An efficient approach to consistent set estimation, Sankhya-B 61 (1999) 496-513.
9. J.G. Postaire, R.D. Zhang, C.L. Botte, Cluster Analysis by binary morphology, IEEE Trans. Pattern Anal. Mach. Intell. 15 (2) (1993) 170-180.
10. R. Haralick, L. Shapiro, Computer and Robot Vision, vol. 1, Chapter 5, Addison-Wesley, 1992.
11. 2, Int. J. Gen. Syst. 20 (1992) 307-339.
12. 2 in the context of cluster analysis, Ph.D. thesis, Indian Statistical Institute, Calcutta, 1988.
13. T.M. Apostal, Mathematical Analysis, Addision-Wesley, 1971.
14. H. Edelsbrunner, D.G. Kirkpatrick, R. Seidel, On the shape of a set of points in the plane, IEEE Trans. Informat. Theory IT-29 (1983) 551-559.
15. N. Ahuja, M. Tuceryan, Extraction of early perceptual structure in dot patterns: integrating region, boundary, and component Gestalt, Comput. Vision, Graphics, Image Process. 48 (1989) 304-356.
16. 2, J. Math. Imaging Vision 4 (2) (1994) 151-170.
17. D.R. Cox, D.V. Hinkley, Theoretical Statistics, Chapman & Hall, London, 1974.
18. N. Amenta, M. Bern, M. Kamvysselis, A new Voronoi-based surface reconstruction algoritm, in: Proc. SIG-GRAPH '98 (1998).
19. D. Attali, r-Regular shape reconstruction from unorganized points, in: 13th ACM Symp. on Computational GeometryissuenrJune (1997) 248-253.
20. M. Melkemi, L. Chen, D. Vandorpe, Shapes of weighted sets of points, in: ICPR 2000, Barcelone, Espagne, September 2000.
21. A. Ray Chaudhuri, A. Basu, S. Bhandari, B.B. Chaudhuri, Consistent set estimation in k-dimensions: an efficient approach, in: Lecture Notes in Computer Science Series, vol. 1451, Springer-Verlag, Berlin, 1998, pp. 667-676.
22. n, Int. J. Pattern Recog. Artif. Intell. 5 (1991) 797-808.
23. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, New York, NY, 1982.
24. R.M. Haralick, S.R. Sternberg, X. Zhuang, Image analysis using mathematical morphology, IEEE Trans. Pattern Anal. Mach. Intell. 9 (1987) 523-550.
25. X. Zhou, R. Gordon, Generation of noise in binary images, CVGIP: Graphical Models and Image Processing 53 (5) (1991) 476-478.