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.


Markov Process Image Sequence Observation Process Markovian Assumption Noisy Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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    H. Maître, 1980 Elements of Picture Processing. Cours ENST ,1980.Google Scholar
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    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

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