General Adaptive Neighborhood Image Processing:

The so-called General Adaptive Neighborhood Image Processing (GANIP) approach is presented in a two parts paper dealing respectively with its theoretical and practical aspects.The Adaptive Neighborhood (AN) paradigm allows the building of new image processing transformations using context-dependent analysis. Such operators are no longer spatially invariant, but vary over the whole image with ANs as adaptive operational windows, taking intrinsically into account the local image features. This AN concept is here largely extended, using well-defined mathematical concepts, to that General Adaptive Neighborhood (GAN) in two main ways. Firstly, an analyzing criterion is added within the definition of the ANs in order to consider the radiometric, morphological or geometrical characteristics of the image, allowing a more significant spatial analysis to be addressed. Secondly, general linear image processing frameworks are introduced in the GAN approach, using concepts of abstract linear algebra, so as to develop operators that are consistent with the physical and/or physiological settings of the image to be processed.In this paper, the GANIP approach is more particularly studied in the context of Mathematical Morphology (MM). The structuring elements, required for MM, are substituted by GAN-based structuring elements, fitting to the local contextual details of the studied image. The resulting transforms perform a relevant spatially-adaptive image processing, in an intrinsic manner, that is to say without a priori knowledge needed about the image structures. Moreover, in several important and practical cases, the adaptive morphological operators are connected, which is an overwhelming advantage compared to the usual ones that fail to this property.

[1]  Steven C. Dakin,et al.  The spatial mechanisms mediating symmetry perception , 1997, Vision Research.

[2]  Sanjit K. Mitra,et al.  Nonlinear unsharp masking methods for image contrast enhancement , 1996, J. Electronic Imaging.

[3]  José Crespo,et al.  Theoretical aspects of morphological filters by reconstruction , 1995, Signal Process..

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

[5]  Petros Maragos,et al.  Morphological filters-Part I: Their set-theoretic analysis and relations to linear shift-invariant filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[6]  Etienne Decencière,et al.  Image filtering using morphological amoebas , 2007, Image Vis. Comput..

[7]  D.J. Granrath,et al.  The role of human visual models in image processing , 1981, Proceedings of the IEEE.

[8]  Rangaraj M. Rangayyan,et al.  Adaptive-neighborhood image deblurring , 1994, J. Electronic Imaging.

[9]  J. Pinoli.  Contribution a la modelisation, au traitement et a l'analyse d'image , 1987 .

[10]  J. Pinoli,et al.  Justifications physiques et applications du modèle LIP pour le traitement des images obtenues en lumière transmise , 1996 .

[11]  G. X. Ritter,et al.  Recent Developments in Image Algebra , 1991 .

[12]  Michaël Ropert,et al.  Synthesis of Adaptive Weighted Order Statistic Filters with Gradient Algorithms , 1994, ISMM.

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

[14]  Corinne Vachier.  Morphological scale-space analysis and feature extraction , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[15]  Pierre Soille,et al.  Morphological Image Analysis , 1999 .

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

[17]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[18]  A. Oppenheim.  SUPERPOSITION IN A CLASS OF NONLINEAR SYSTEMS , 1965 .

[19]  J. Astola,et al.  Fundamentals of Nonlinear Digital Filtering , 1997 .

[20]  J. Schwartz,et al.  Linear Operators. Part I: General Theory. , 1960 .

[21]  G. Matheron.  Éléments pour une théorie des milieux poreux , 1967 .

[22]  Serge Beucher,et al.  Use of watersheds in contour detection , 1979 .

[23]  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.

[24]  William A. Pearlman,et al.  Restoration Of Noisy Images With Adaptive Windowing And Nonlinear Filtering , 1986, Other Conferences.

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

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

[27]  Robert C. Vogt.  A Spatially Variant, Locally Adaptive, Background Normalization Operator , 1994, ISMM.

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

[29]  M. Nagao,et al.  Edge preserving smoothing , 1979 .

[30]  John Edward Hafstrom.  Introduction to analysis and abstract algebra , 1967 .

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

[32]  Luc Vincent,et al.  Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Joseph N. Wilson,et al.  Handbook of computer vision algorithms in image algebra , 1996 .

[34]  J. T. Stockham.  The application of generalized linearity to automatic gain control , 1968 .

[35]  M. Grimaud.  La geodesie numerique en morphologie mathematique. Application a la detection des microcalcifications en mammographie numerique , 1991 .

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

[37]  M. Wertheimer.  Laws of organization in perceptual forms. , 1938 .

[38]  L. Shen,et al.  Linear Algebra , 1968 .

[39]  Shmuel Peleg,et al.  PICTURES AS ELEMENTS IN VECTOR SPACE. , 1983, CVPR 1983.

[40]  Ulisses De Mendonça Braga Neto,et al.  Alternating Sequential Filters by Adaptive-Neighborhood Structuring Functions , 1996 .

[41]  Jae S. Lim,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[42]  A. Venetsanopoulos,et al.  Order statistics in digital image processing , 1992, Proc. IEEE.

[43]  L. S. Pontryagin,et al.  General Topology I , 1990 .

[44]  Mihai Ciuc.  Traitement d'images multicomposantes : application à l'imagerie couleur et radar , 2002 .

[45]  Pierre Soille,et al.  Morphological Image Analysis: Principles and Applications , 2003 .

[46]  Henk J. A. M. Heijmans,et al.  Algebraic Framework for Linear and Morphological Scale-Spaces , 2002, J. Vis. Commun. Image Represent..

[47]  Petros Maragos,et al.  Experiments on Image Compression Using Morphological Pyramids , 1989, Other Conferences.

[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]  William F. Schreiber,et al.  Fundamentals of electronic imaging systems : some aspects of image processing , 1986 .

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

[51]  M Jourlin,et al.  LIP‐model‐based three‐dimensional reconstruction and visualization of HIV‐infected entire cells , 1994, Journal of microscopy.

[52]  Jacques Verly,et al.  Some principles and applications of adaptive mathematical morphology for range imagery , 1993 .

[53]  Rangaraj M. Rangayyan,et al.  Adaptive neighborhood mean and median image filtering , 1994, J. Electronic Imaging.

[54]  Jean-Charles Pinoli,et al.  Multiscale image filtering and segmentation by means of adaptive neighborhood mathematical morphology , 2005, IEEE International Conference on Image Processing 2005.

[55]  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.

[56]  S. Beucher,et al.  Morphological segmentation , 1990, J. Vis. Commun. Image Represent..

[57]  Olivier Cuisenaire.  Locally adaptable mathematical morphology , 2005, IEEE International Conference on Image Processing 2005.

[58]  Jean-Charles Pinoli,et al.  Image dynamic range enhancement and stabilization in the context of the logarithmic image processing model , 1995, Signal Process..

[59]  A.K. Jain,et al.  Advances in mathematical models for image processing , 1981, Proceedings of the IEEE.

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

[61]  Petros Maragos,et al.  Morphological filters-Part II: Their relations to median, order-statistic, and stack filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[62]  Philippe Salembier.  Structuring element adaptation for morphological filters , 1992, J. Vis. Commun. Image Represent..

[63]  Jaakko Astola,et al.  An Introduction to Nonlinear Image Processing , 1994 .

[64]  Philippe Salembier,et al.  Connected operators and pyramids , 1993, Optics & Photonics.

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

[66]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

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

[68]  R M Rangayyan,et al.  Adaptive-neighborhood filtering of images corrupted by signal-dependent noise. , 1998, Applied optics.

[69]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[70]  Dan Schonfeld,et al.  Spatially-variant mathematical morphology , 1994, Proceedings of 1st International Conference on Image Processing.

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

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

[73]  J. W. Modestino,et al.  Flat Zones Filtering, Connected Operators, and Filters by Reconstruction , 1995 .

[74]  Jong-Sen Lee,et al.  Refined filtering of image noise using local statistics , 1981 .

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

[76]  J. N. Wilson,et al.  Image Algebra: An Overview , 1990, Comput. Vis. Graph. Image Process..

[77]  Shmuel Peleg,et al.  Inversion of picture operators , 1987, Pattern Recognit. Lett..

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

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

[80]  Rangaraj M. Rangayyan,et al.  Adaptive-neighborhood histogram equalization of color images , 2001, J. Electronic Imaging.

[81]  P. W. Hawkes.  IMAGE ALGEBRA AND RANK-ORDER FILTERS , 2003 .

[82]  Rangaraj M. Rangayyan,et al.  Filtering multiplicative noise in images using adaptive region-based statistics , 1998, J. Electronic Imaging.

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

[84]  David Marr,et al.  VISION A Computational Investigation into the Human Representation and Processing of Visual Information , 2009 .

[85]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[86]  Rangaraj M. Rangayyan,et al.  Filtering noise in color images using adaptive-neighborhood statistics , 2000, J. Electronic Imaging.