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.
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.