Jump detection in regression surfaces

Journal of Computational and Graphical Statistics

Volumn 6, Issue 3, 1997, Pages 332-354

  Qru, Peihua ^a   Yandell, Brian ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

Image processing; Jump detection criterion; Jump location curves; Jump surfaces; Least squares plane; Modification procedure; Slopes; Threshold value

Indexed keywords

EID: 0031321648     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.1997.10474746     Document Type: Article

References (43)

1. Besag, J. (1986), “On the Statistical Analysis of Dirty Pictures” (with discussion), Journal of the Royal Statistical Society, Ser. B, 48, 259-302.
2. Bhandarkar, S.M., Zhang, Y., and Potter, W.D. (1994), "An Edge Detection Technique Using Genetic Algorithm-Based Optimization,” Pattern Recognition, 27, 1159-1180.
3. Brodsky, B.E., and Dharkhovsky, B.S. (1993), Nonparametric Methods in Change-Point Problems, The Netherlands: Kluwer Academic Publishers.
4. Canny, J. (1986), “A Computational Approach to Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 679-698.
5. Chen, X.R. (1988), “Hypothesis Testing and Interval Estimation About the Model Which has Only One ChangePoint,” Scientia Sinica, 8A, 1-13.
6. Chen, M.H., Lee, D., and Pavlidis, T. (1991), “Residual Analysis for Feature Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 30-40.
7. Chu, C.K. (1994), “Estimation of Change-Points in a Nonparametric Regression Function Through Kernel Density Estimation,” Communications in Statistics-Theory and Methods, 23, 3037-3062.
8. Eubank, R.L., and Speckman, P.L. (1994), “Nonparametric Estimation of Functions With Jump Discontinuities,” in IMS Lecture Notes Change-Point Problems, vol. 23, eds. E. Carlstein, H.G. Muller, and D. Siegmund, Hayward, CA: IMS, 130-144.
9. Geman, S., and Geman, D. (1984), “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
10. Godtliebsen, F„ and Chu, C.K. (1995), “Estimation of the Number of True Gray Levels, Their Values, and Relative Frequencies in a Noisy Image,” Journal of the American Statistical Association, 90, 890-899.
11. Gonzalez, R.C., and Woods, R.E. (1992), Digital Image Processing, Reading, MA: Addison-Wesley.
12. Hall, P., and Titterington, M. (1992), “Edge-Preserving and Peak-Preserving Smoothing,” Technometrics, 34. 429-440.
13. Haralick, R.M. (1984), “Digital Step Edges From Zero Crossing of Second Directional Derivatives,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 58-68.
14. Johnson, R.P. (1990), “Contrast Based Edge Detection,” Pattern Recognition, 23, 311-318.
15. Korostelev, A.P., and Tsybakov, A.B. (1993). Minimax Theory of Image Reconstruction, Lecture Notes in Statistics, vol. 82, New York: Springer-Verlag.
16. Lai, T.L., Robbins, H., and Wei, C.Z. (1979), “Strong Consistency of Least Squares Estimates in Multiple Regression II,” Journal of Multivariate Analysis, 9, 343-362.
17. Loader, C.R. (1994), “Change Point Estimation Using Nonparametric Regression,” AT&T Bell Laboratories.
18. Marr, D., and Hildreth, E. (1980), “Theory of Edge Detection,” Proceedings of the Royal Statistical Society of London, 207, 187-217.
19. McDonald, J.A., and Owen, A.B. (1986), “Smoothing With Split Linear Fits,” Technometrics, 28, 195-208.
20. Müller, H.G. (1992), “Change-Points in Nonparametric Regression Analysis,” The Annals of Statistics, 20, 737-761.
21. Müller, H.G., and Song, K.S. (1994), “Maximin Estimation of Multidimensional Boundaries,” Journal of Multivariate Analysis, 50, 265-281.
22. O’Sullivan, F., and Qian, M. (1994), “A Regularized Contrast Statistic for Object Boundary Estimation- Implementation and Statistical Evaluation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 561-570.
23. Perona, P., and Malik, J. (1990), “Scale Space and Edge Detection Using Anisotropic Diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 629-639.
24. Qiu, P. (1994), “Estimation of the Number of Jumps of the Jump Regression Functions,” Communications in Statistics-Theory and Methods, 23, 2141-2155.
25. Qiu, P. (1997), “Nonparametric Estimation of Jump Surface,” Sankhya, Series A, June issue.
26. Qiu, P., and Bhandarkar, S.M. (1996), “An Edge Detection Technique Using Local Smoothing and Statistical Hypothesis Testing,” Pattern Recognition Letters, 17, 849-872.
27. Qiu, P., and Yandell, B. (1994), “A Local Polynomial Jump Detection Algorithm in Nonparametric Regression,” University of Wisconsin-Madison, Dept, of Statistics (tentatively accepted by Technometrics).
28. Rosenfeld, A., and Kak, A.C. (1982), Digital Picture Processing, (vols. 1 and 2), New York: Academic Press.
29. Rudemo, M., and Stryhn, H. (1994), “Approximating the Distribution of Maximum Likelihood Contour Estimators in Two-Region Images,” Scandinavian Journal of Statistics, 21, 41-55.
30. Saint-Marc, P., Chen, J., and Medioni, G. (1991), “Adaptive Smoothing: A General Tool for Early Vision,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 514-529.
31. Sarkar, S.S., and Boyer, K.L. (1990), “On Optimal Infinite Impulse Response Edge Detection Filters,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 1154-1171.
32. Shiau, J.H. (1985), “Smoothing Spline Estimation of Functions With Discontinuities,” technical report 768, University of Wisconsin-Madison, Dept, of Statistics.
33. Shiau, J.H. (1987), “A Note on MSE Coverage Intervals in a Partial Spline Model,” Communications in Statistics-Theory and Methods, 16, 1851-1866.
34. Shiau, J.H., Wahba, G., and Johnson, D.R. (1986), “Partial Spline Models for the Inclusion of Tropopause and Frontal Boundary Information in Otherwise Smooth Two- and Three-Dimensional Objective Analysis,” Journal of Atmospheric and Oceanic Technology, 3, 714-725.
35. Sinha, S.S., and Schunk, B.G. (1992), “A Two-Stage Algorithm for Discontinuity-Preserving Surface Reconstruction,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 36-55.
36. Speckman, P.L. (1993), “Detection of Change-Points in Nonparametric Regression,” University of Missouri, Dept, of Statistics.
37. Tan, H.L., Gelfand, S.B., and Delp, E.J. (1989), “A Comparative Cost Function Approach to Edge Detection,” IEEE Transaction on Systems, Man, and Cybernetics, 19, 1337-1349.
38. Tan, H.L., Gelfand, S.B., and Delp, E.J. (1991), “A Cost Minimization Approach to Edge Detection Using Simulated Annealing,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 3-18.
39. Torre, V., and Poggio, T.A. (1986), “On Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 147-163.
40. Wang, Y. (1995), “Jump and Sharp Cusp Detection by Wavelets,” Biometrika, 82, 385-397.
41. Wu, J.S., and Chu, C.K. (1993a), “Kemel Type Estimators of Jump Points and Values of a Regression Function,” The Annals of Statistics, 21, 1545-1566.
42. Wu, J.S., and Chu, C.K. (1993b), “Nonparametric Function Estimation and Bandwidth Selection for Discontinuous Regression Functions,” Statistica Sinica, 3, 557-576.
43. Yin, Y.Q. (1988), “Detecting of the Number, Locations and Magnitudes of Jumps,” Communications in Statistics-Stochastic Models, 4, 445-155.