### Abstract

New class of nonlinear filters called Vector Median Rational Hybrid Filters (VMRHF) for multispectral image processing was introduced and applied to color image filtering problem. These filters are based on Rational Functions (RF). There are several advantages to the use of this function. First, it is a universal approximator and a good extrapolator. Second, it can be trained by a linear adaptive algorithm. Third, it has a best approximation for a specified function. The output is the result of vector rational operation taking into account three sub-functions, such as two vector median (VM) sub-filters and one center weighted vector median filter (CWVMF). It was shown that every sub-function will preserve details within its sub-window. These filters exhibit desirable properties, such as, edge and details preservation and accurate chromaticity estimation. The performance of the proposed filter is compared against widely known nonlinear filters for multispectral image processing such as: Vector median filters (VMF) introduced by Astola et al, which are derived as maximum likelihood (ML) estimates from exponential distributions, the class of directional-distance filters (DDF) introduced to study the processing of color image data using directional information. Experimental and comparative results in color image filtering show very good performance measures when the error is measured in the L*a*b* space. L*a*b* is known as a space where equal color differences result in equal distances, and therefore, it is close to the human perception of colors.

Original language | English |
---|---|

Pages (from-to) | 400-408 |

Number of pages | 9 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 3516 |

Issue number | I |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*3516*(I), 400-408.

**Vector Median-Rational Hybrid Filters.** / Khriji, Lazhar; Gabbouj, Moncef.

Research output: Contribution to journal › Article

*Proceedings of SPIE - The International Society for Optical Engineering*, vol. 3516, no. I, pp. 400-408.

}

TY - JOUR

T1 - Vector Median-Rational Hybrid Filters

AU - Khriji, Lazhar

AU - Gabbouj, Moncef

PY - 1999

Y1 - 1999

N2 - New class of nonlinear filters called Vector Median Rational Hybrid Filters (VMRHF) for multispectral image processing was introduced and applied to color image filtering problem. These filters are based on Rational Functions (RF). There are several advantages to the use of this function. First, it is a universal approximator and a good extrapolator. Second, it can be trained by a linear adaptive algorithm. Third, it has a best approximation for a specified function. The output is the result of vector rational operation taking into account three sub-functions, such as two vector median (VM) sub-filters and one center weighted vector median filter (CWVMF). It was shown that every sub-function will preserve details within its sub-window. These filters exhibit desirable properties, such as, edge and details preservation and accurate chromaticity estimation. The performance of the proposed filter is compared against widely known nonlinear filters for multispectral image processing such as: Vector median filters (VMF) introduced by Astola et al, which are derived as maximum likelihood (ML) estimates from exponential distributions, the class of directional-distance filters (DDF) introduced to study the processing of color image data using directional information. Experimental and comparative results in color image filtering show very good performance measures when the error is measured in the L*a*b* space. L*a*b* is known as a space where equal color differences result in equal distances, and therefore, it is close to the human perception of colors.

AB - New class of nonlinear filters called Vector Median Rational Hybrid Filters (VMRHF) for multispectral image processing was introduced and applied to color image filtering problem. These filters are based on Rational Functions (RF). There are several advantages to the use of this function. First, it is a universal approximator and a good extrapolator. Second, it can be trained by a linear adaptive algorithm. Third, it has a best approximation for a specified function. The output is the result of vector rational operation taking into account three sub-functions, such as two vector median (VM) sub-filters and one center weighted vector median filter (CWVMF). It was shown that every sub-function will preserve details within its sub-window. These filters exhibit desirable properties, such as, edge and details preservation and accurate chromaticity estimation. The performance of the proposed filter is compared against widely known nonlinear filters for multispectral image processing such as: Vector median filters (VMF) introduced by Astola et al, which are derived as maximum likelihood (ML) estimates from exponential distributions, the class of directional-distance filters (DDF) introduced to study the processing of color image data using directional information. Experimental and comparative results in color image filtering show very good performance measures when the error is measured in the L*a*b* space. L*a*b* is known as a space where equal color differences result in equal distances, and therefore, it is close to the human perception of colors.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032674637&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032674637

VL - 3516

SP - 400

EP - 408

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

SN - 0277-786X

IS - I

ER -