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

Ewaryst Rafajłowicz; Mirosław Pawlak; Angsar Steland

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 1, page 49-61
  • ISSN: 1641-876X

Abstract

top
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.

How to cite

top

Ewaryst Rafajłowicz, Mirosław Pawlak, and Angsar Steland. "Nonlinear image processing and filtering: A unified approach based on vertically weighted regression." International Journal of Applied Mathematics and Computer Science 18.1 (2008): 49-61. <http://eudml.org/doc/207864>.

@article{EwarystRafajłowicz2008,
abstract = {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.},
author = {Ewaryst Rafajłowicz, Mirosław Pawlak, Angsar Steland},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {image filtering; vertically weighted regression; nonlinear filters},
language = {eng},
number = {1},
pages = {49-61},
title = {Nonlinear image processing and filtering: A unified approach based on vertically weighted regression},
url = {http://eudml.org/doc/207864},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Ewaryst Rafajłowicz
AU - Mirosław Pawlak
AU - Angsar Steland
TI - Nonlinear image processing and filtering: A unified approach based on vertically weighted regression
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 1
SP - 49
EP - 61
AB - 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.
LA - eng
KW - image filtering; vertically weighted regression; nonlinear filters
UR - http://eudml.org/doc/207864
ER -

References

top
  1. 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. 
  2. 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. 
  3. Barner K.E. and Arce G.R. (2004). Nonlinear Signal and Image Processing: Theory, Methods, and Applications, CRC Press, Boca Raton, FL. 
  4. 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. Zbl1108.94004
  5. 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. 
  6. Efromovich S. (1999). Nonparametric Curve Estimation: Methods, Theory and Applications, Springer-Verlag, New York. Zbl0935.62039
  7. Elad M. (2002): On the origin of the bilateral filter and ways to improve it, IEEE Transactions on Image Processing 11(10): 1141-1150. 
  8. Hall P. and Koch S. (1992). On the feasibility of cross-validation in image analysis, SIAM Journal on Applied Mathematics 52(1): 292-313. Zbl0743.60041
  9. Jain A. (1989): Fundamentals of Digital Image Processing, Prentice Hall, New York. Zbl0744.68134
  10. Krzyżak A., Rafajłowicz E. and Skubalska-Rafajłowicz E. (2001). Clipped median and space-filling curves in image filtering, Nonlinear Analysis 47(1): 303--314. Zbl1042.94503
  11. Lee J. (1983). Digital image smoothing and the sigma filter, Computer Vision, Graphics and Image Processing 24(2): 255-269. 
  12. Mitra S. and Sicuranza G. (2001). Nonlinear Image Processing, Academic Press, San Diego. 
  13. 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. 
  14. 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. Zbl1062.94002
  15. Pawlak M. and Rafajłowicz E. (1999). Vertically weighted regression - A tool for nonlinear data anlysis and constructing control charts, Statistical Archives 84: 367-388. Zbl1117.62499
  16. Pawlak M. and Rafajłowicz E. (2001). Jump preserving signal reconstruction using vertical weighting, Nonlinear Analysis 47(1): 327-338. Zbl1043.94521
  17. Pawlak M., Rafajłowicz E. and Steland A. (2004). On detecting jumps in time series: Nonparametric setting, Nonparametric Statistics 16(3-4): 329-347. Zbl1065.62200
  18. 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. 
  19. 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. 
  20. Steland A. (2003). Jump-preserving monitoring of dependent processes using pilot estimators, Statistics and Decision 21(4): 343-366. Zbl1041.62076
  21. Steland A. (2005). On the distribution of the clipping median under a mixture model, Statistics and Probability Letters 71(1): 1-13. Zbl1058.62018
  22. Takeda H., Farsiu S., and Milanfar P. (2007). Kernel regression for image processing and reconstruction, IEEE Transactions on Image Processing 16(2): 349-366. 
  23. Tomasi C. and Manduchi R. (1998). Bilateral filtering for gray and color images, IEEE International Conference on Computer Vision, pp. 839-845. 
  24. van der Vaart A. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge, 1998. Zbl0910.62001
  25. Wasserman L. (2006). All of Nonparametric Statistics, Springer-Verlag, New York. Zbl1099.62029
  26. Yaroslavsky L. (1985). Digital Picture Processing, Springer-Verlag, New York. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.