A variational approach for exact histogram specification

Raymond CHAN; Mila NIKOLOVA; You Wei WEN

doi:10.1007/978-3-642-24785-9_8

A variational approach for exact histogram specification

Raymond CHAN^*, Mila NIKOLOVA, You Wei WEN

^*Corresponding author for this work

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

4 Citations (Scopus)

Abstract

We focus on exact histogram specification when the input image is quantified. The goal is to transform this input image into an output image whose histogram is exactly the same as a prescribed one. In order to match the prescribed histogram, pixels with the same intensity level in the input image will have to be assigned to different intensity levels in the output image. An approach to classify pixels with the same intensity value is to construct a strict ordering on all pixel values by using auxiliary attributes. Local average intensities and wavelet coefficients have been used by the past as the second attribute. However, these methods cannot enable strict-ordering without degrading the image. In this paper, we propose a variational approach to establish an image preserving strict-ordering of the pixel values. We show that strict-ordering is achieved with probability one. Our method is image preserving in the sense that it reduces the quantization noise in the input quantified image. Numerical results show that our method gives better quality images than the preexisting methods.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers
Editors	Alfred M. BRUCKSTEIN, Bart M. Haar ROMENY, Alexander M. BRONSTEIN, Michael M. BRONSTEIN
Publisher	Springer Berlin Heidelberg
Pages	86-97
Number of pages	12
ISBN (Electronic)	9783642247859
ISBN (Print)	9783642247842
DOIs	https://doi.org/10.1007/978-3-642-24785-9_8
Publication status	Published - 2012
Externally published	Yes
Event	3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011 - Ein-Gedi, Israel Duration: 29 May 2011 → 2 Jun 2011

Publication series

Name	Lecture Notes in Computer Science
Volume	6667
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011
Country/Territory	Israel
City	Ein-Gedi
Period	29/05/11 → 2/06/11

Funding

The research was supported in part by HKRGC Grant CUHK400510 and DAG Grant 2060408.

Keywords

convex minimization
Exact histogram specification
restoration from quantization noise
smooth nonlinear optimization
strict-ordering
variational methods

Access to Document

10.1007/978-3-642-24785-9_8

Cite this

CHAN, R., NIKOLOVA, M., & WEN, Y. W. (2012). A variational approach for exact histogram specification. In A. M. BRUCKSTEIN, B. M. H. ROMENY, A. M. BRONSTEIN, & M. M. BRONSTEIN (Eds.), Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers (pp. 86-97). (Lecture Notes in Computer Science; Vol. 6667). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_8

CHAN, Raymond ; NIKOLOVA, Mila ; WEN, You Wei. / A variational approach for exact histogram specification. Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers. editor / Alfred M. BRUCKSTEIN ; Bart M. Haar ROMENY ; Alexander M. BRONSTEIN ; Michael M. BRONSTEIN. Springer Berlin Heidelberg, 2012. pp. 86-97 (Lecture Notes in Computer Science).

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abstract = "We focus on exact histogram specification when the input image is quantified. The goal is to transform this input image into an output image whose histogram is exactly the same as a prescribed one. In order to match the prescribed histogram, pixels with the same intensity level in the input image will have to be assigned to different intensity levels in the output image. An approach to classify pixels with the same intensity value is to construct a strict ordering on all pixel values by using auxiliary attributes. Local average intensities and wavelet coefficients have been used by the past as the second attribute. However, these methods cannot enable strict-ordering without degrading the image. In this paper, we propose a variational approach to establish an image preserving strict-ordering of the pixel values. We show that strict-ordering is achieved with probability one. Our method is image preserving in the sense that it reduces the quantization noise in the input quantified image. Numerical results show that our method gives better quality images than the preexisting methods.",

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author = "Raymond CHAN and Mila NIKOLOVA and WEN, {You Wei}",

year = "2012",

doi = "10.1007/978-3-642-24785-9_8",

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isbn = "9783642247842",

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booktitle = "Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers",

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CHAN, R, NIKOLOVA, M & WEN, YW 2012, A variational approach for exact histogram specification. in AM BRUCKSTEIN, BMH ROMENY, AM BRONSTEIN & MM BRONSTEIN (eds), Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers. Lecture Notes in Computer Science, vol. 6667, Springer Berlin Heidelberg, pp. 86-97, 3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011, Ein-Gedi, Israel, 29/05/11. https://doi.org/10.1007/978-3-642-24785-9_8

A variational approach for exact histogram specification. / CHAN, Raymond; NIKOLOVA, Mila; WEN, You Wei.
Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers. ed. / Alfred M. BRUCKSTEIN; Bart M. Haar ROMENY; Alexander M. BRONSTEIN; Michael M. BRONSTEIN. Springer Berlin Heidelberg, 2012. p. 86-97 (Lecture Notes in Computer Science; Vol. 6667).

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

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AU - NIKOLOVA, Mila

AU - WEN, You Wei

PY - 2012

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N2 - We focus on exact histogram specification when the input image is quantified. The goal is to transform this input image into an output image whose histogram is exactly the same as a prescribed one. In order to match the prescribed histogram, pixels with the same intensity level in the input image will have to be assigned to different intensity levels in the output image. An approach to classify pixels with the same intensity value is to construct a strict ordering on all pixel values by using auxiliary attributes. Local average intensities and wavelet coefficients have been used by the past as the second attribute. However, these methods cannot enable strict-ordering without degrading the image. In this paper, we propose a variational approach to establish an image preserving strict-ordering of the pixel values. We show that strict-ordering is achieved with probability one. Our method is image preserving in the sense that it reduces the quantization noise in the input quantified image. Numerical results show that our method gives better quality images than the preexisting methods.

AB - We focus on exact histogram specification when the input image is quantified. The goal is to transform this input image into an output image whose histogram is exactly the same as a prescribed one. In order to match the prescribed histogram, pixels with the same intensity level in the input image will have to be assigned to different intensity levels in the output image. An approach to classify pixels with the same intensity value is to construct a strict ordering on all pixel values by using auxiliary attributes. Local average intensities and wavelet coefficients have been used by the past as the second attribute. However, these methods cannot enable strict-ordering without degrading the image. In this paper, we propose a variational approach to establish an image preserving strict-ordering of the pixel values. We show that strict-ordering is achieved with probability one. Our method is image preserving in the sense that it reduces the quantization noise in the input quantified image. Numerical results show that our method gives better quality images than the preexisting methods.

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KW - strict-ordering

KW - variational methods

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SN - 9783642247842

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BT - Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers

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A2 - BRONSTEIN, Alexander M.

A2 - BRONSTEIN, Michael M.

PB - Springer Berlin Heidelberg

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Y2 - 29 May 2011 through 2 June 2011

ER -

CHAN R, NIKOLOVA M, WEN YW. A variational approach for exact histogram specification. In BRUCKSTEIN AM, ROMENY BMH, BRONSTEIN AM, BRONSTEIN MM, editors, Scale Space and Variational Methods in Computer Vision: Third International Conference, SSVM 2011, Revised Selected Papers. Springer Berlin Heidelberg. 2012. p. 86-97. (Lecture Notes in Computer Science). doi: 10.1007/978-3-642-24785-9_8

A variational approach for exact histogram specification

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Keywords

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