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2008 | 18 | 1 | 49-61
Tytuł artykułu

Nonlinear image processing and filtering: A unified approach based on vertically weighted regression

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A class of nonparametric smoothing kernel methods for image processing and filtering that possess edge-preserving properties is examined. The proposed approach is a nonlinearly modified version of the classical nonparametric regression estimates utilizing the concept of vertical weighting. The method unifies a number of known nonlinear image filtering and denoising algorithms such as bilateral and steering kernel filters. It is shown that vertically weighted filters can be realized by a structure of three interconnected radial basis function (RBF) networks. We also assess the performance of the algorithm by studying industrial images.
Rocznik
Tom
18
Numer
1
Strony
49-61
Opis fizyczny
Daty
wydano
2008
Twórcy
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  • Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, R3T5V6, Canada
  • RWTH Aachen University, Aachen, Germany
Bibliografia
  • Barash D. (2002). A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation, IEEE Transactions on Pattern Analysis and Machine Intelligence 24(6): 844-847.
  • Barner K., Sarham A. and Hadie R. (1999). Partition-based weighted sum filters for image restoration, IEEE Transactions on Image Procedings 8(5): 740-745.
  • Barner K.E. and Arce G.R. (2004). Nonlinear Signal and Image Processing: Theory, Methods, and Applications, CRC Press, Boca Raton, FL.
  • Buades A., Coll B. and Morel J. (2005). A review of image denoising algorithms, with a new one, SIAM Journal on Multiscale Modeling and Simulation 4(2): 490-530.
  • Chiu C., Glad K., Godtliebsen F. and Marron J. (1998). Edgepreserving smoother for image processing, Journal of the American Statistical Association 93(442): 526-541.
  • Efromovich S. (1999). Nonparametric Curve Estimation: Methods, Theory and Applications, Springer-Verlag, New York.
  • Elad M. (2002): On the origin of the bilateral filter and ways to improve it, IEEE Transactions on Image Processing 11(10): 1141-1150.
  • Hall P. and Koch S. (1992). On the feasibility of cross-validation in image analysis, SIAM Journal on Applied Mathematics 52(1): 292-313.
  • Jain A. (1989): Fundamentals of Digital Image Processing, Prentice Hall, New York.
  • Krzyżak A., Rafajłowicz E. and Skubalska-Rafajłowicz E. (2001). Clipped median and space-filling curves in image filtering, Nonlinear Analysis 47(1): 303--314.
  • Lee J. (1983). Digital image smoothing and the sigma filter, Computer Vision, Graphics and Image Processing 24(2): 255-269.
  • Mitra S. and Sicuranza G. (2001). Nonlinear Image Processing, Academic Press, San Diego.
  • 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 Intelligence 13(6): 514-529.
  • Pawlak M. and Liao S. X. (2002). On the recovery of a function on a circular domain, IEEE Transactions on Information Theory 48(10): 2736-2753.
  • Pawlak M. and Rafajłowicz E. (1999). Vertically weighted regression - A tool for nonlinear data anlysis and constructing control charts, Statistical Archives 84: 367-388.
  • Pawlak M. and Rafajłowicz E. (2001). Jump preserving signal reconstruction using vertical weighting, Nonlinear Analysis 47(1): 327-338.
  • Pawlak M., Rafajłowicz E. and Steland A. (2004). On detecting jumps in time series: Nonparametric setting, Nonparametric Statistics 16(3-4): 329-347.
  • Polzehl J. and Spokoiny V. (2000). Adaptive weights smoothing with applications to image restoration, Journal of the Royal Statistical Society B 62(2): 335-354.
  • Smith S. and Brady J. M. (1997). SUSAN - A new approach to low level image processing, International Journal of Computer Vision 23(1): 45-78.
  • Steland A. (2003). Jump-preserving monitoring of dependent processes using pilot estimators, Statistics and Decision 21(4): 343-366.
  • Steland A. (2005). On the distribution of the clipping median under a mixture model, Statistics and Probability Letters 71(1): 1-13.
  • Takeda H., Farsiu S., and Milanfar P. (2007). Kernel regression for image processing and reconstruction, IEEE Transactions on Image Processing 16(2): 349-366.
  • Tomasi C. and Manduchi R. (1998). Bilateral filtering for gray and color images, IEEE International Conference on Computer Vision, pp. 839-845.
  • van der Vaart A. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge, 1998.
  • Wasserman L. (2006). All of Nonparametric Statistics, Springer-Verlag, New York.
  • Yaroslavsky L. (1985). Digital Picture Processing, Springer-Verlag, New York.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv18i1p49bwm
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