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Nonlinear Image Processing and Filtering: A Unified Approach Based on Vertically Weighted Regression

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Applied Image Processing (special issue), Anton Kummert and Ewaryst Rafajłowicz (Eds.)

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Barash D. (2002). A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation, IEEE Transactions on Pattern Analysis and Machine Intelligence24(6): 844-847.10.1109/TPAMI.2002.1008390Search in Google Scholar

Barner K., Sarham A. and Hadie R. (1999). Partition-based weighted sum filters for image restoration, IEEE Transactions on Image Procedings8(5): 740-745.10.1109/83.760341Search in Google Scholar

Barner K.E. and Arce G.R. (2004). Nonlinear Signal and Image Processing: Theory, Methods, and Applications, CRC Press, Boca Raton, FL.10.1201/9780203010419Search in Google Scholar

Buades A., Coll B. and Morel J. (2005). A review of image denoising algorithms, with a new one, SIAM Journal on Multiscale Modeling and Simulation4(2): 490-530.10.1137/040616024Search in Google Scholar

Chiu C., Glad K., Godtliebsen F. and Marron J. (1998). Edgepreserving smoother for image processing, Journal of the American Statistical Association93(442): 526-541.10.1080/01621459.1998.10473702Search in Google Scholar

Efromovich S. (1999). Nonparametric Curve Estimation: Methods, Theory and Applications, Springer-Verlag, New York.Search in Google Scholar

Elad M. (2002): On the origin of the bilateral filter and ways to improve it, IEEE Transactions on Image Processing11(10): 1141-1150.10.1109/TIP.2002.801126Search in Google Scholar

Hall P. and Koch S. (1992). On the feasibility of cross-validation in image analysis, SIAM Journal on Applied Mathematics52(1): 292-313.10.1137/0152015Search in Google Scholar

Jain A. (1989): Fundamentals of Digital Image Processing, Prentice Hall, New York.Search in Google Scholar

Krzyżak A., Rafajłowicz E. and Skubalska-Rafajłowicz E. (2001). Clipped median and space-filling curves in image filtering, Nonlinear Analysis47(1): 303-314.10.1016/S0362-546X(01)00178-XSearch in Google Scholar

Lee J. (1983). Digital image smoothing and the sigma filter, Computer Vision, Graphics and Image Processing24(2): 255-269.10.1016/0734-189X(83)90047-6Search in Google Scholar

Mitra S. and Sicuranza G. (2001). Nonlinear Image Processing, Academic Press, San Diego.Search in Google Scholar

P. Saint-Marc J.S., and Medioni G. C. (1991). Adaptive smoothing: A general tool for early vision, IEEE Transations on Pattern Analysis and Machine Intelligence13(6): 514-529.10.1109/34.87339Search in Google Scholar

Pawlak M. and Liao S. X. (2002). On the recovery of a function on a circular domain, IEEE Transactions on Information Theory48(10): 2736-2753.10.1109/TIT.2002.802627Search in Google Scholar

Pawlak M. and Rafajłowicz E. (1999). Vertically weighted regression - A tool for nonlinear data anlysis and constructing control charts, Statistical Archives84: 367-388.10.1007/s101820000039Search in Google Scholar

Pawlak M. and Rafajłowicz E. (2001). Jump preserving signal reconstruction using vertical weighting, Nonlinear Analysis47(1): 327-338.10.1016/S0362-546X(01)00180-8Search in Google Scholar

Pawlak M., Rafajłowicz E. and Steland A. (2004). On detecting jumps in time series: Nonparametric setting, Nonparametric Statistics16(3-4): 329-347.10.1080/10485250410001656435Search in Google Scholar

Polzehl J. and Spokoiny V. (2000). Adaptive weights smoothing with applications to image restoration, Journal of the Royal Statistical Society B62(2): 335-354.10.1111/1467-9868.00235Search in Google Scholar

Smith S. and Brady J. M. (1997). SUSAN - A new approach to low level image processing, International Journal of Computer Vision23(1): 45-78.10.1023/A:1007963824710Search in Google Scholar

Steland A. (2003). Jump-preserving monitoring of dependent processes using pilot estimators, Statistics and Decision21(4): 343-366.10.1524/stnd.21.4.343.25348Search in Google Scholar

Steland A. (2005). On the distribution of the clipping median under a mixture model, Statistics and Probability Letters71(1): 1-13.10.1016/j.spl.2004.10.016Search in Google Scholar

Takeda H., Farsiu S., and Milanfar P. (2007). Kernel regression for image processing and reconstruction, IEEE Transactions on Image Processing16(2): 349-366.10.1109/TIP.2006.88833017269630Search in Google Scholar

Tomasi C. and Manduchi R. (1998). Bilateral filtering for gray and color images, IEEE International Conference on Computer Vision, pp. 839-845.Search in Google Scholar

van der Vaart A. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge, 1998.10.1017/CBO9780511802256Search in Google Scholar

Wasserman L. (2006). All of Nonparametric Statistics, Springer-Verlag, New York.Search in Google Scholar

Yaroslavsky L. (1985). Digital Picture Processing, Springer-Verlag, New York.10.1007/978-3-642-81929-2Search in Google Scholar

ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics