Filters involving derivatives with application to reconstruction from scanned halftone images

Søren Forchhammer; Kim S. Jensen

doi:10.1109/83.370673

Filters involving derivatives with application to reconstruction from scanned halftone images

Søren Forchhammer, Kim S. Jensen

Technical University of Denmark

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Abstract

This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters

Original language	English
Journal	I E E E Transactions on Image Processing
Volume	4
Issue number	4
Pages (from-to)	448-459
ISSN	1057-7149
DOIs	https://doi.org/10.1109/83.370673
Publication status	Published - 1995

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Copyright: 1995 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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title = "Filters involving derivatives with application to reconstruction from scanned halftone images",

abstract = "This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters",

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note = "Copyright: 1995 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE",

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AU - Jensen, Kim S.

N1 - Copyright: 1995 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 1995

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N2 - This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters

AB - This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters

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JO - I E E E Transactions on Image Processing

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Filters involving derivatives with application to reconstruction from scanned halftone images

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