Le comportement des ponderateurs en analyse krigeante. Camparaison avec les filtres classiques utilises en traitement d'images

Y. Z. Ma and Jean-Jacques Royer. ( 1987 )
in: Etudes Geostatisques V, Séminaire C.F.S.G. sur la Géostatistique, Fontainebleau, pages 175--194

Abstract

In this paper, we discuss the behaviour of the weighting function computed by kriging analysis. This theory developed by G. Matheron in 1982, has been extensively used in Earth sciences. In geochemical prospecting, Sandjivy L.(1983,1984) and Wackernagel H. ()1985, 1986) have separated the local anomalies from the background values, similar works from Galli A. and al. (1984), Chiles J.P. and Guillen A. (1984); have been carried out on the separation of local geophysical pattern in magnetic and gravimetry. Recently, this method has been used by Ma Y.Z. and Royer J.J. (1987) to filter away additive noise and detect lineaments in remote sensed images. The kriging analysis (K.A.) technique works in the spatial (or time) domain and is equivalent to the spectral analysis of a second order random stationary process, which works in the frequency space. The advantages of the K.A. is the possibility to work on non-stationary process using the FAI-k concepts. In image processing, local convolution filters are commonly used in the spatial domain, for instance: moving average, Gaussian filter, Laplacien, Gradient, ... What kind of links does it exit between these classical filters and the K.A.? In the following, it is shown that the weighting function computed by K.A. is often similar to these classical filters for a given model of covariance or variogram. The advantages of the K.A. is the possibility of adapting the convolution mask to the underlying structure of the image. Given a theoretical model of the auto-covariance function, the K.A. can build masks for differer :scales corresponding to the nested structures of the image. From this point of view, the K.A. appears as a generalization of the filtering methods. The different filtering methods are compared and discussed in the light of results obtained on two cases studies.

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    BibTeX Reference

    @INPROCEEDINGS{,
        author = { Ma, Y. Z. and Royer, Jean-Jacques },
         title = { Le comportement des ponderateurs en analyse krigeante. Camparaison avec les filtres classiques utilises en traitement d'images },
         month = { "jun" },
     booktitle = { Etudes Geostatisques V },
        series = { Sciences de la Terre },
        number = { 28 },
       chapter = { 0 },
          year = { 1987 },
         pages = { 175--194 },
      location = { Fontainebleau },
    organization = { Séminaire C.F.S.G. sur la Géostatistique },
      abstract = { In this paper, we discuss the behaviour of the weighting function computed by kriging analysis. This theory developed by G. Matheron in 1982, has been extensively used in Earth sciences. In geochemical prospecting, Sandjivy L.(1983,1984) and Wackernagel H. ()1985, 1986) have separated the local anomalies from the background values, similar works from Galli A. and al. (1984), Chiles J.P. and Guillen A. (1984); have been carried out on the separation of local geophysical pattern in magnetic and gravimetry. Recently, this method has been used by Ma Y.Z. and Royer J.J. (1987) to filter away additive noise and detect lineaments in remote sensed images.
    
    The kriging analysis (K.A.) technique works in the spatial (or time) domain and is equivalent to the spectral analysis of a second order random stationary process, which works in the frequency space. The advantages of the K.A. is the possibility to work on non-stationary process using the FAI-k concepts. In image processing, local convolution filters are commonly used in the spatial domain, for instance: moving average, Gaussian filter, Laplacien, Gradient, ... What kind of links does it exit between these classical filters and the K.A.?
    
    In the following, it is shown that the weighting function computed by K.A. is often similar to these classical filters for a given model of covariance or variogram.
    
    The advantages of the K.A. is the possibility of adapting the convolution mask to the underlying structure of the image. Given a theoretical model of the auto-covariance function, the K.A. can build masks for differer :scales corresponding to the nested structures of the image. From this point of view, the K.A. appears as a generalization of the filtering methods.
    
    The different filtering methods are compared and discussed in the light of results obtained on two cases studies. }
    }