General Adaptive Neighborhood Choquet Image Filtering

A novel framework entitled General Adaptive Neighborhood Image Processing (GANIP) has been recently introduced in order to propose an original image representation and mathematical structure for adaptive image processing and analysis. The central idea is based on the key notion of adaptivity which is simultaneously associated with the analyzing scales, the spatial structures and the intensity values of the image to be addressed. In this paper, the GANIP framework is briefly exposed and particularly studied in the context of Choquet filtering (using fuzzy measures), which generalizes a large class of image filters. The resulting spatially-adaptive operators are studied with respect to the general GANIP framework and illustrated in both the biomedical and materials application areas. In addition, the proposed GAN-based filters are practically applied and compared to several other denoising methods through experiments on image restoration, showing a high performance of the GAN-based Choquet filters.

[1]  Jean-Charles Pinoli,et al.  The Logarithmic Image Processing Model: Connections with Human Brightness Perception and Contrast Estimators , 1997, Journal of Mathematical Imaging and Vision.

[2]  Alberto Prieto,et al.  General Logarithmic Image Processing Convolution , 2006, IEEE Transactions on Image Processing.

[3]  Jean-Charles Pinoli,et al.  Logarithmic Adaptive Neighborhood Image Processing (LANIP): Introduction, Connections to Human Brightness Perception, and Application Issues , 2007, EURASIP J. Adv. Signal Process..

[4]  Jean-Charles Pinoli,et al.  A model for logarithmic image processing , 1988 .

[5]  M. Sugeno,et al.  An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[6]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Azriel Rosenfeld,et al.  Picture Processing by Computer , 1969, CSUR.

[8]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

[9]  G. Deng,et al.  An Entropy Interpretation of the Logarithmic Image Processing Model With Application to Contrast Enhancement , 2009, IEEE Trans. Image Process..

[10]  D. R. K. Brownrigg,et al.  The weighted median filter , 1984, CACM.

[11]  M Jourlin,et al.  Contrast definition and contour detection for logarithmic images , 1989, Journal of microscopy.

[12]  T. Lindeberg.  Scale-Space Theory : A Basic Tool for Analysing Structures at Different Scales , 1994 .

[13]  R. Weale.  Vision. A Computational Investigation Into the Human Representation and Processing of Visual Information. David Marr , 1983 .

[14]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[15]  J. Debayle.  General Adaptive Neighborhood Image Processing Part II : Practical Application Examples , 2009 .

[16]  Guang Deng,et al.  Differentiation-Based Edge Detection Using the Logarithmic Image Processing Model , 1998, Journal of Mathematical Imaging and Vision.

[17]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[18]  Alan V. Oppenheim,et al.  Generalized Superposition , 1967, Information and Control.

[19]  Ergun Erçelebi,et al.  Image restoration by lifting-based wavelet domain E-median filter , 2006 .

[20]  Jean-Charles Pinoli,et al.  A general comparative study of the multiplicative homomorphic, log-ratio and logarithmic image processing approaches , 1997, Signal Process..

[21]  Maryellen L. Giger,et al.  Quantitative performance evaluation of the EM algorithm applied to radiographic images , 1991, Electronic Imaging.

[22]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[23]  J. Michel,et al.  Logarithmic image processing: additive contrast, multiplicative contrast, and associated metrics , 2001 .

[24]  J. Morel,et al.  On image denoising methods , 2004 .

[25]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[26]  Gonzalo R. Arce,et al.  Detail-preserving ranked-order based filters for image processing , 1989, IEEE Trans. Acoust. Speech Signal Process..

[27]  G. Choquet.  Theory of capacities , 1954 .

[28]  Stefan Friedrich,et al.  Topology , 2019, Arch. Formal Proofs.

[29]  R M Rangayyan,et al.  Feature enhancement of film mammograms using fixed and adaptive neighborhoods. , 1984, Applied optics.

[30]  William K. Pratt,et al.  Digital image processing (2nd ed.) , 1991 .

[31]  Jr. Thomas G. Stockham,et al.  Image processing in the context of a visual model , 1972 .

[32]  M. Jourlin,et al.  Logarithmic image processing: The mathematical and physical framework for the representation and processing of transmitted images , 2001 .

[33]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  Michel Grabisch,et al.  Fuzzy integrals as a generalized class of order filters , 1994, Remote Sensing.

[35]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[36]  Guang Deng,et al.  Multiscale image enhancement using the logarithmic image processing model , 1993 .

[37]  Jean-Charles Pinoli,et al.  General Adaptive Neighborhood Image Processing: , 2006, Journal of Mathematical Imaging and Vision.

[38]  M. Jourlin,et al.  Logarithmic Image Processing for Color Images , 2011 .

[39]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[40]  Xiangchu Feng,et al.  Variational Image Restoration and Decomposition with Curvelet Shrinkage , 2008, Journal of Mathematical Imaging and Vision.

[41]  A. Oppenheim,et al.  Nonlinear filtering of multiplied and convolved signals , 1968 .

[42]  J. Pinoli,et al.  SPATIALLY ADAPTIVE MORPHOLOGICAL IMAGE FILTERING USING INTRINSIC STRUCTURING ELEMENTS , 2011 .

[43]  Maryellen L. Giger,et al.  Evaluating the EM algorithm for image processing using a human visual fidelity criterion , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[44]  D. L. Donoho,et al.  Ideal spacial adaptation via wavelet shrinkage , 1994 .

[45]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[46]  J. Pinoli.  A contrast definition for logarithmic images in the continuous setting , 1991 .

[47]  Alan C. Bovik,et al.  A Statistical Evaluation of Recent Full Reference Image Quality Assessment Algorithms , 2006, IEEE Transactions on Image Processing.

[48]  G. R. Tobin,et al.  The study of logarithmic image processing model and its application to image enhancement , 1995, IEEE Trans. Image Process..

[49]  J. K. Hunter,et al.  Measure Theory , 2007 .