CRISP-contourlets: A critically sampled directional multiresolution image representation

Yue Lu, Minh N. Do

Research output: Contribution to journalConference article

Abstract

Directional multiresolution image representations have lately attracted much attention. A number of new systems, such as the curvelet transform and the more recent contourlet transform, have been proposed. A common issue of these transforms is the redundancy in representation, an undesirable feature for certain applications (e.g. compression). Though some critically sampled transforms have also been proposed in the past, they can only provide limited directionality or limited flexibility in the frequency decomposition. In this paper, we propose a filter bank structure achieving a nonredundant multiresolution and multidirectional expansion of images. It can be seen as a critically sampled version of the original contourlet transform (hence the name CRISP-contourets) in the sense that the corresponding frequency decomposition is similar to that of contourlets, which divides the whole spectrum both angularly and radially. However, instead of performing the multiscale and directional decomposition steps separately as is done in contourlets, the key idea here is to use a combined iterated nonseparable filter bank for both steps. Aside from critical sampling, the proposed transform possesses other useful properties including perfect reconstruction, flexible configuration of the number of directions at each scale, and an efficient tree-structured implementation.

Original languageEnglish (US)
Pages (from-to)655-665
Number of pages11
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume5207
Issue number2
StatePublished - Dec 1 2003
EventWavelets: Applications in Signal and Image Processing X - San Diego, CA, United States
Duration: Aug 4 2003Aug 8 2003

Fingerprint

Image Representation
Multiresolution
Contourlet Transform
Filter Banks
Filter banks
Transform
Decomposition
decomposition
Decompose
Curvelet Transform
filters
Nonseparable
redundancy
Redundancy
Divides
flexibility
Compression
Flexibility
sampling
Sampling

Keywords

  • Filter banks
  • Image representation
  • Maximal decimation
  • Multidirectional
  • Multiresolution

ASJC Scopus subject areas

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

Cite this

CRISP-contourlets : A critically sampled directional multiresolution image representation. / Lu, Yue; Do, Minh N.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 5207, No. 2, 01.12.2003, p. 655-665.

Research output: Contribution to journalConference article

@article{619bca9df5da4c448149802e7f5b511e,
title = "CRISP-contourlets: A critically sampled directional multiresolution image representation",
abstract = "Directional multiresolution image representations have lately attracted much attention. A number of new systems, such as the curvelet transform and the more recent contourlet transform, have been proposed. A common issue of these transforms is the redundancy in representation, an undesirable feature for certain applications (e.g. compression). Though some critically sampled transforms have also been proposed in the past, they can only provide limited directionality or limited flexibility in the frequency decomposition. In this paper, we propose a filter bank structure achieving a nonredundant multiresolution and multidirectional expansion of images. It can be seen as a critically sampled version of the original contourlet transform (hence the name CRISP-contourets) in the sense that the corresponding frequency decomposition is similar to that of contourlets, which divides the whole spectrum both angularly and radially. However, instead of performing the multiscale and directional decomposition steps separately as is done in contourlets, the key idea here is to use a combined iterated nonseparable filter bank for both steps. Aside from critical sampling, the proposed transform possesses other useful properties including perfect reconstruction, flexible configuration of the number of directions at each scale, and an efficient tree-structured implementation.",
keywords = "Filter banks, Image representation, Maximal decimation, Multidirectional, Multiresolution",
author = "Yue Lu and Do, {Minh N.}",
year = "2003",
month = "12",
day = "1",
language = "English (US)",
volume = "5207",
pages = "655--665",
journal = "Proceedings of SPIE - The International Society for Optical Engineering",
issn = "0277-786X",
publisher = "SPIE",
number = "2",

}

TY - JOUR

T1 - CRISP-contourlets

T2 - A critically sampled directional multiresolution image representation

AU - Lu, Yue

AU - Do, Minh N.

PY - 2003/12/1

Y1 - 2003/12/1

N2 - Directional multiresolution image representations have lately attracted much attention. A number of new systems, such as the curvelet transform and the more recent contourlet transform, have been proposed. A common issue of these transforms is the redundancy in representation, an undesirable feature for certain applications (e.g. compression). Though some critically sampled transforms have also been proposed in the past, they can only provide limited directionality or limited flexibility in the frequency decomposition. In this paper, we propose a filter bank structure achieving a nonredundant multiresolution and multidirectional expansion of images. It can be seen as a critically sampled version of the original contourlet transform (hence the name CRISP-contourets) in the sense that the corresponding frequency decomposition is similar to that of contourlets, which divides the whole spectrum both angularly and radially. However, instead of performing the multiscale and directional decomposition steps separately as is done in contourlets, the key idea here is to use a combined iterated nonseparable filter bank for both steps. Aside from critical sampling, the proposed transform possesses other useful properties including perfect reconstruction, flexible configuration of the number of directions at each scale, and an efficient tree-structured implementation.

AB - Directional multiresolution image representations have lately attracted much attention. A number of new systems, such as the curvelet transform and the more recent contourlet transform, have been proposed. A common issue of these transforms is the redundancy in representation, an undesirable feature for certain applications (e.g. compression). Though some critically sampled transforms have also been proposed in the past, they can only provide limited directionality or limited flexibility in the frequency decomposition. In this paper, we propose a filter bank structure achieving a nonredundant multiresolution and multidirectional expansion of images. It can be seen as a critically sampled version of the original contourlet transform (hence the name CRISP-contourets) in the sense that the corresponding frequency decomposition is similar to that of contourlets, which divides the whole spectrum both angularly and radially. However, instead of performing the multiscale and directional decomposition steps separately as is done in contourlets, the key idea here is to use a combined iterated nonseparable filter bank for both steps. Aside from critical sampling, the proposed transform possesses other useful properties including perfect reconstruction, flexible configuration of the number of directions at each scale, and an efficient tree-structured implementation.

KW - Filter banks

KW - Image representation

KW - Maximal decimation

KW - Multidirectional

KW - Multiresolution

UR - http://www.scopus.com/inward/record.url?scp=1242263472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1242263472&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:1242263472

VL - 5207

SP - 655

EP - 665

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

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

SN - 0277-786X

IS - 2

ER -