3D Kalman Filtering of Image Sequences

  • D. Cano
  • M. Bénard
Part of the NATO ASI Series book series (volume 2)


The authors are currently engaged in processing time-series of satellite imagery. Processing includes noise elimination and in this context, a 3D Kalman filtering has been developped and is presented here.

The first step is the definition of a class of two and three-parameter Markov discrete processes. The linear filtering of such stochastic processes reduces to a one-parameter vectorial Markov process recursive filtering, described by Kalman's equations. The 3D filter is then broken down into a two-dimensional spatial filter and a one-dimensional time filter. Some more stationnarity hypothesis allows a very simplified algorithm. The CPU time required is about 4 minutes on a middle range computer, for a 512 × 512 pixels picture.

The results are exposed on one-image sequence, which is assumed to verify the Markovian assumptions.


fIlterIng Covariance 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Korezlioglu, 1978 Filtrage lineaire récursif des processus à 2 indices discrets, Markoviens au sens large. Rapport ENST - D -78004, Fév. 1978.Google Scholar
  2. [2]
    S. Attasi, 1975 Modelisation et traitement des suites à2 indices. These d’Etat ,Université Paris-VI.Google Scholar
  3. [3]
    Huang, 1975 Topics in applied physics, Vol. 42, 2D Digital Signal Processing. springer V erlag, Berlin.Google Scholar
  4. [4]
    H. Maître, 1980 Elements of Picture Processing. Cours ENST ,1980.Google Scholar
  5. [5]
    J.W. Woods, 1981 Kalman filtering in two dimensions. Further results. IEEE -ASSP ,Vol. 29, n° 2, April 1981, pp. 188–197.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • D. Cano
    • 1
    • 2
  • M. Bénard
    • 1
    • 2
  1. 1.Centre de Télédétection et d’Analyse des Milieux Naturels (C.T.A.M.N.)Ecole Nationale Supérieure des Mines de ParisValbonne CédexFrance
  2. 2.Laboratoire ImageEcole Nationale Supérieure des TélécommunicationsParis Cédex 13France

Personalised recommendations