Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors

Annals of Statistics

Volumn 33, Issue 6, 2005, Pages 2758-2788

  Dette, Holger ^a   Melas, Viatcheslav B ^b   Pepelyshev, Andrey ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

3D image data; Optimal designs; Principal component analysis; Quadrature formulas; Shape analysis; Spherical harmonic descriptors

Indexed keywords

EID: 33644919113     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000552     Document Type: Article

References (24)

1. ANDREWS, G. E., ASKEY, R. and ROY, R. (1999). Special Functions. Cambridge Univ. Press. MR1688958
2. BOUZITAT, J. (1949). Sur 1'intégration numérique approchée par la méthode de Gauss généralisée et sur une extension de cette méthode. C. R. Acad. Sci. Paris 229 1201-1203. MR0033200
3. Box, G. E. P. and DRAPER, N. R. (1959). A basis for the selection of a response surface design. J. Amer. Statist. Assoc. 54 622-654. MR0108872
4. BRECHBÜHLER, CH., GERIG, G. and KÜBLER, O. (1995). Parametrization of closed surfaces for 3-D shape description. Computer Vision and Image Understanding 61 154-170.
5. DING, W., NESUMI, H., TAKANO, Y. and UKAI, Y. (2000). Quantitative evaluation of the three-dimensional fruit shape and size of Citrus species based on spherical harmonic descriptors. Euphytica 114 103-115.
6. ENGELS, H. (1980). Numerical Quadrature and Cubature. Academic Press, New York. MR0587486
7. FUNKHOUSER, T., MlN, P., KAZHDAN, M., CHEN, J., HALDERMAN, A., DOBKIN, D. and JACOBS, D. (2003). A search engine for 3D models. ACM Transactions on Graphics 22 83-105.
8. GHIZZETTI, A. and OSSICINI, A. (1970). Quadrature Formulae. Birkhäuser, Basel. MR0269116
9. GUNNING, R. C. and ROSSI, H. (1965). Analytic Functions of Several Complex Variables. Prentice-Hall, Englewood Cliffs, NJ. MR0180696
10. HYVÄRINEN, A., KARHUNEN, J. and OJA, E. (2001). Independent Component Analysis. Wiley. New York.
11. KAZHDAN, M., FUNKHOUSER, T. and RUSINKIEWICZ, S. (2003). Rotation invariant spherical harmonic representation of 3D shape descriptors. In Eurographics Symposium on Geometry Processing (L. Kobbelt, P. Schröder and H. Hoppe, eds.) 167-175. Available at www.cs.jhu.edu/~misha/MyPapers/SGP03.pdf.
12. KELEMEN, A., SZÉKELY, G. and GERIG, G. (1999). Elastic model-based segmentation of 3D-neuroradiological data sets. IEEE Transactions on Medical Imaging 18 828-839.
13. KIEFER, J. (1974). General equivalence theory for optimum designs (approximate theory). Ann. Statist. 2 849-879. MR0356386
14. NOVOTNI, M. and KLEIN, R. (2003). 3D Zernike descriptors for content based shape retrieval. In Proc. Eighth ACM Symposium on Solid Modeling and Applications 216-225. ACM Press, New York.
15. PAWLAK, M. and LIAO, S. X. (2002). On the recovery of a function on a circular domain. IEEE Trans. Inform. Theory 48 2736-2753. MR1930340
16. PUKELSHEIM, F. (1993). Optimal Design of Experiments. Wiley, New York. MR1211416
17. PUKELSHEIM, F. and RIEDER, S. (1992). Efficient rounding of approximate designs. Biometrika 79 763-770. MR1209476
18. SACKS, J. and YLVISAKER, D. (1970). Designs for regression problems with correlated errors. III. Ann. Math. Statist. 41 2057-2074. MR0270530
19. SILVEY, S. D. (1980). Optimal Design. Chapman and Hall, London. MR0606742
20. s-optimal designs for polynomial regression using continued fractions. Ann. Statist. 8 1132-1141. MR0585711
21. STUDDEN, W. J. (1982). Optimal designs for weighted polynomial regression using canonical moments. In Statistical Decision Theory and Related Topics III (S. S. Gupta and J. O. Berger, eds.) 2 335-350. Academic Press, New York. MR0705323
22. SZEGÖ, G. (1975). Orthogonal Polynomials, 4th ed. Amer. Math. Soc., Providence, RI.
23. SZÉKELY, G., KELEMEN, A., BRECHBÜHLER, CH. and GERIG, G. (1996). Segmentation of 2D and 3D objects from MRI volume data using constrained elastic deformations of flexible contour and surface models. Medical Image Analysis 1 19-34.
24. WIENS, D. (1998). Minimax robust designs and weights for approximately specified regression with heteroscedastic errors. J. Amer. Statist. Assoc. 93 1440-1450. MR1666639