### Abstract

Adaptation of an opening possessing a multiparameter structuring element is studied in the context of Markov chains by treating the multiple parameters as a vector r defining the state of the system and considering the operative filter Λ _{r} to be opening by reconstruction. Adaptation of Λ _{r} (transition of r) is in accordance to whether or not Λ _{r} correctly or incorrectly passes signal and noise grains sampled from the image. Signal and noise are modeled as unions of randomly parameterized and randomly translated primary grains. Transition probabilities are discussed for two adaptation protocols and the state-probability increment equations are deduced from the appropriate Chapman-Kolmogorov equations. Adaptation convergence is characterized by the steady-state distributions of the Markov chains and these are computed numerically.

Original language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | Edward R. Dougherty, Jaakko T. Astola, Harold G. Longbotham, Nasser M. Nasrabadi, Aggelos K. Katsaggelos |

Pages | 37-47 |

Number of pages | 11 |

State | Published - Dec 1 1995 |

Event | Nonlinear Image Processing VI - San Jose, CA, USA Duration: Feb 6 1995 → Feb 9 1995 |

### Publication series

Name | Proceedings of SPIE - The International Society for Optical Engineering |
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Volume | 2424 |

ISSN (Print) | 0277-786X |

### Other

Other | Nonlinear Image Processing VI |
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City | San Jose, CA, USA |

Period | 2/6/95 → 2/9/95 |

### Fingerprint

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(pp. 37-47). (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 2424).