Fitting circles to data with correlated noise

Computational Statistics and Data Analysis

Volumn 52, Issue 12, 2008, Pages 5328-5337

  Chernov, N ^a   Sapirstein, P N ^b  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MAXIMUM LIKELIHOOD ESTIMATION;

APPLIED (CO); CORRELATED NOISES; DATA POINTS; ELSEVIER (CO); MAXIMUM LIKELIHOOD ESTIMATES; SCATTERED DATA;

COVARIANCE MATRIX;

EID: 47749111290     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.05.025     Document Type: Article

References (51)

1. Arnold D.E., and Nieves A.L. Factors affecting ceramic standardization. In: Bey G.J., and Pool C.A. (Eds). Ceramic Production and Distribution: An Integrated Approach (1992), Westview Press, Boulder 93-113
2. Atieg A., and Watson G.A. Fitting circular arcs by orthogonal distance regression. Appl. Numer. Anal. Comput. Math. 1 (2004) 66-76
3. Benco, N.L., 1988. Morphological standardization: An approach to the study of craft specialization. In: Kolb, C.C., Lackey, L.M. (Eds.), A Pot for All Reasons: Ceramic Ecology Revisited. Temple University, Philadelphia, pp. 57-72
4. Berman M. The asymptotic statistical behaviour of some estimators for a circular structural model. Statist. Probab. Lett. 7 (1989) 413-416
5. Berman M., and Culpin D. The statistical behavior of some least squares estimators of the center and radius of a circle. J. Roy. Statist. Soc. Ser. B 48 (1986) 183-196
6. Biggerstaff R.H. Three variations in dental arch form estimated by a quadratic equation. J. Dental Res. 51 (1972) 1509
7. Blackman M.J., Stein G.J., and Vandiver P.B. The standardization hypothesis and ceramic mass production: Technological, compositional, and metric indexes of craft specialization at tell leilan. Syria. American Antiquity 58 (1993) 60-80
8. Blinkhorn P. The trials of being a utensil: Pottery function at the medieval hamlet of west cotton, northamptonshire. Mediev. Ceramics 22-23 (1999) 37-46
9. Chan N.N. On circular functional relationships. J. Roy. Statist. Soc. Ser. B 27 (1965) 45-56
10. Chan Y.T., Lee B.H., and Thomas S.M. Approximate maximum likehood estimation of circle parameters. J. Optim. Appl. 125 (2005) 723-733
11. Chan Y.T., and Thomas S.M. Cramer-Rao lower bounds for estimation of a circular arc center and its radius. Graph. Models Image Process. 57 (1995) 527-532
12. Chernov N., and Lesort C. Statistical efficiency of curve fitting algorithms. Comput. Stat. Data Anal. 47 (2004) 713-728
13. Chernov N., and Lesort C. Least squares fitting of circles. J. Math. Imaging. Vision 23 (2005) 239-251
14. Chernov N.I., and Ososkov G.A. Effective algorithms for circle fitting. Comput. Phys. Commun. 33 (1984) 329-333
15. DeBoer W.R. Vessel shape from rim sherds: An experiment on the effect of the individual illustrator. J. Field Archaeology 7 (1980) 133-135
16. di Gironimo, G., Ferrara, B., Patalano, S., 2004. Definition and construction of parametric archtypes of archaeological artefacts by means of cad technologies. In: der Stadt Wien Referat Ulturelles Erbe Stadarchaeologie Wien, M. (Ed.), Enter the Past: The E-Way into the four Dimensions of Cultural Heritage. vol. 1227. BAR International Series, Oxford, pp. 86-89
17. Ericson J.E., and de Atley S.P. Reconstructing ceramic assemblages: An experiment to derive the morphology and capacity of parent vessels from sherds. American Antiquity 41 (1976) 484-489
18. Feller W. An Introduction to Probability Theory and its Applications. 2nd ed. vol. 2 (1971), John Wiley & Sons
19. Frankel D. Pottery production in prehistoric bronze age cyprus: Assessing the problem. J. Mediterranean Archaeology 1 (1988) 27-55
20. Freeman P.R. Note: Thom's survey of the avebury ring. J. Hist. Astron. 8 (1977) 134-136
21. Gilboa A., Karasik A., Sharon I., and Smilansky U. Towards computerized typology and classification of ceramics. J. Archaeological Sci. 31 (2004) 681-694
22. Hagstrum, M.B., 1986. The technology of ceramic production of wanka and inka wares from the yanamarca valley peru. In: Rice, P.M. (Ed.), Ceramic Notes 3. Ceramic Techn. Lab., Florida State Museum, Gainesville, FL, pp. 1-29
23. Hagstrum, M.B., Hildebrand, J.A., 1983. Understanding the curvature measurements of potsherds. Pottery Southwest, 3-7
24. Hagstrum M.B., and Hildebrand J.A. The two-curvature method for reconstructing ceramic morphology. Amer. Antiquity 55 (1990) 388-403
25. Haliř R., and Flusser J. Numerically stable direct least squares fitting of ellipses. Sixth Conf. Cent. Europe Comput. Graph. Vis., WSCG'98, Conf. Proc. Plzen, Czech Rep. vol. 1 (1998) 125-132
26. Haliř, R., Menard, C., 1996. Diameter estimation for archaeological pottery using active vision. In: Pinz, A. (Ed.), Proc. 20th Workshop Austrian Assoc. Pattern Recognition, ÖAGM'96 (Schloss Seggau, Leibnitz) pp. 251-261
27. Kanatani K. Cramer-Rao lower bounds for curve fitting. Graph. Models Image Process. 60 (1998) 93-99
28. Karimäki V. Effective circle fitting for particle trajectories. Nuclear Instrum. Methods Phys. Res. A 305 (1991) 187-191
29. Landau U.M. Estimation of a circular arc center and its radius. Comput. Vis. Graph. Image Process. 38 (1987) 317-326
30. Longacre W.A., Kvamme K.L., and Kobayashi M. Southwestern pottery standardization: An ethnoarchaeological view from the Philippines. The Kiva 53 (1988) 101-112
31. Millet, M., 1979. An approach to the functional interpretation of pottery. In: Millet, M. (Ed.), Pottery and the Archaeologist. Inst. Archaeology, London, pp. 35-48
32. Mounier R.A. Estimation of capacity in aboriginal conoidal vessels. J. Middle Atlantic Archaeology 3 (1987) 95-102
33. Nievergelt Y. A finite algorithm to fit geometrically all midrange lines, circles, planes, spheres, hyperplanes, and hyperspheres. J. Numer. Math. 91 (2002) 257-303
34. Pei S.-C., and Horng J.-H. Optimum approximation of digital planar curves using circular arcs. Pattern Recogn. 29 (1996) 383-388
35. Ph J., and Arnold I. Dimensional standardization and production scale in mesoamerican ceramics. Latin Amer. Antiquity 2 (1991) 363-370
36. Ph J., and Arnold I. Working without a net: Recent trends in ceramic ethnoarchaeology. J. Archaeological Res. 8 (2000) 105-133
37. Plog S. Estimating vessel orifice diameters: Measurement methods and measurement error. In: Nelson B.A. (Ed). Decoding Prehistoric Ceramics (1985) 243-254
38. Plog S., Plog F., and Wait W. Decision Making in Modern Surveys. Advances in Archaeological Method and Theory vol. 1 (1978)
39. Poblome, J., 1999. Sagalassos Red Slip Ware: Typology and Chronology. In: Waelkens, M. (Ed.), Studies in Eastern Mediterranean Archaeology. vol. 2. Brepols
40. Polak M. South Gaulish Terra Sigillata with Potters' Stamps from Vechten. Rei Cretariae Romanae Fautorum Acta Supplementum vol. 9 (2000)
41. Pot T., and de Groot H.L. An analysis of rim fragments from 14th-century globular pots excavated in utrecht. Mediev. Ceramics 13 (1989) 31-42
42. Rice P.M. Recent ceramic analysis: 2. composition, production, and theory. J. Archaeological Res. 4 (1996) 165-202
43. Roux V. Ceramic standardization and intensity of production: Quantifying degrees of specialization. American Antiquity 68 (2003) 768-782
44. Späth H. Least-squares fitting by circles. Computing 57 (1996) 179-185
45. Stark B.L. Problems in the analysis of standardization and specialization in pottery. In: Mills B.J., and Crown P.L. (Eds). Ceramic Production in the American Southwest (1995), Univ. Arizona Press, Tuscon 231-267
46. Thom A. A statistical examination of the megalithic sites in britain. J. Roy. Statist. Soc. Ser. A 118 (1955) 275-295
47. Thomas S.M., and Chan Y.T. A simple approach for the estimation of circular arc center and its radius. Comput. Vis. Graph. Image Process. 45 (1989) 362-370
48. Whalen M.E. Ceramic vessel size estimation from sherds: An experiment and a case study. J. Field Archaeology 25 (1998) 219-227
49. Yin S.J., and Wang S.G. Estimating the parameters of a circle by heteroscedastic regression models. J. Statist. Plann. Inference. 124 (2004) 439-451
50. Zelniker E., and Clarkson V. A statistical analysis of the Delogne-Kåsa method for fitting circles. Digit. Signal Process. 16 (2006) 498-522
51. Zhang, S., Xie, L., Adams, M.D., 2006. Feature extraction for outdoor mobile robot navigation based on a modified gaussnewton optimization approach 54, 277-287