35 Citations (Scopus)

Abstract

Orthogonal rotation-invariant moments (ORIMs), such as Zernike moments, are introduced and defined on a continuous unit disk and have been proven powerful tools in optics applications. These moments have also been digitized for applications in digital image processing. Unfortunately, digitization compromises the orthogonality of the moments and, therefore, digital ORIMs are incapable of representing subtle details in images and cannot accurately reconstruct images. Typical approaches to alleviate the digitization artifact can be divided into two categories: 1) careful selection of a set of pixels as close approximation to the unit disk and using numerical integration to determine the ORIM values, and 2) representing pixels using circular shapes such that they resemble that of the unit disk and then calculating ORIMs in polar space. These improvements still fall short of preserving the orthogonality of the ORIMs. In this paper, in contrast to the previous methods, we propose a different approach of using numerical optimization techniques to improve the orthogonality. We prove that with the improved orthogonality, image reconstruction becomes more accurate. Our simulation results also show that the optimized digital ORIMs can accurately reconstruct images and can represent subtle image details.

Original languageEnglish (US)
Pages (from-to)272-282
Number of pages11
JournalIEEE Transactions on Image Processing
Volume17
Issue number3
DOIs
StatePublished - Mar 2008

Fingerprint

Digital Image Processing
Rotation Invariant
Image processing
Moment
Orthogonality
Analog to digital conversion
Unit Disk
Digitization
Pixels
Pixel
Zernike Moments
Polar Space
Image reconstruction
Optics
Numerical Optimization
Image Reconstruction
Numerical Techniques
Numerical integration
Optimization Techniques
Approximation

Keywords

  • Image reconstruction
  • Moments
  • Numerical optimization
  • Orthogonality
  • Rotation-invariance
  • Zernike moments

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Orthogonal rotation-invariant moments for digital image processing. / Lin, Huibao; Si, Jennie; Abousleman, Glen P.

In: IEEE Transactions on Image Processing, Vol. 17, No. 3, 03.2008, p. 272-282.

Research output: Contribution to journalArticle

Lin, Huibao ; Si, Jennie ; Abousleman, Glen P. / Orthogonal rotation-invariant moments for digital image processing. In: IEEE Transactions on Image Processing. 2008 ; Vol. 17, No. 3. pp. 272-282.
@article{9631d9eb9f4b48c4910b63b1a8d7e9db,
title = "Orthogonal rotation-invariant moments for digital image processing",
abstract = "Orthogonal rotation-invariant moments (ORIMs), such as Zernike moments, are introduced and defined on a continuous unit disk and have been proven powerful tools in optics applications. These moments have also been digitized for applications in digital image processing. Unfortunately, digitization compromises the orthogonality of the moments and, therefore, digital ORIMs are incapable of representing subtle details in images and cannot accurately reconstruct images. Typical approaches to alleviate the digitization artifact can be divided into two categories: 1) careful selection of a set of pixels as close approximation to the unit disk and using numerical integration to determine the ORIM values, and 2) representing pixels using circular shapes such that they resemble that of the unit disk and then calculating ORIMs in polar space. These improvements still fall short of preserving the orthogonality of the ORIMs. In this paper, in contrast to the previous methods, we propose a different approach of using numerical optimization techniques to improve the orthogonality. We prove that with the improved orthogonality, image reconstruction becomes more accurate. Our simulation results also show that the optimized digital ORIMs can accurately reconstruct images and can represent subtle image details.",
keywords = "Image reconstruction, Moments, Numerical optimization, Orthogonality, Rotation-invariance, Zernike moments",
author = "Huibao Lin and Jennie Si and Abousleman, {Glen P.}",
year = "2008",
month = "3",
doi = "10.1109/TIP.2007.916157",
language = "English (US)",
volume = "17",
pages = "272--282",
journal = "IEEE Transactions on Image Processing",
issn = "1057-7149",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "3",

}

TY - JOUR

T1 - Orthogonal rotation-invariant moments for digital image processing

AU - Lin, Huibao

AU - Si, Jennie

AU - Abousleman, Glen P.

PY - 2008/3

Y1 - 2008/3

N2 - Orthogonal rotation-invariant moments (ORIMs), such as Zernike moments, are introduced and defined on a continuous unit disk and have been proven powerful tools in optics applications. These moments have also been digitized for applications in digital image processing. Unfortunately, digitization compromises the orthogonality of the moments and, therefore, digital ORIMs are incapable of representing subtle details in images and cannot accurately reconstruct images. Typical approaches to alleviate the digitization artifact can be divided into two categories: 1) careful selection of a set of pixels as close approximation to the unit disk and using numerical integration to determine the ORIM values, and 2) representing pixels using circular shapes such that they resemble that of the unit disk and then calculating ORIMs in polar space. These improvements still fall short of preserving the orthogonality of the ORIMs. In this paper, in contrast to the previous methods, we propose a different approach of using numerical optimization techniques to improve the orthogonality. We prove that with the improved orthogonality, image reconstruction becomes more accurate. Our simulation results also show that the optimized digital ORIMs can accurately reconstruct images and can represent subtle image details.

AB - Orthogonal rotation-invariant moments (ORIMs), such as Zernike moments, are introduced and defined on a continuous unit disk and have been proven powerful tools in optics applications. These moments have also been digitized for applications in digital image processing. Unfortunately, digitization compromises the orthogonality of the moments and, therefore, digital ORIMs are incapable of representing subtle details in images and cannot accurately reconstruct images. Typical approaches to alleviate the digitization artifact can be divided into two categories: 1) careful selection of a set of pixels as close approximation to the unit disk and using numerical integration to determine the ORIM values, and 2) representing pixels using circular shapes such that they resemble that of the unit disk and then calculating ORIMs in polar space. These improvements still fall short of preserving the orthogonality of the ORIMs. In this paper, in contrast to the previous methods, we propose a different approach of using numerical optimization techniques to improve the orthogonality. We prove that with the improved orthogonality, image reconstruction becomes more accurate. Our simulation results also show that the optimized digital ORIMs can accurately reconstruct images and can represent subtle image details.

KW - Image reconstruction

KW - Moments

KW - Numerical optimization

KW - Orthogonality

KW - Rotation-invariance

KW - Zernike moments

UR - http://www.scopus.com/inward/record.url?scp=40749102490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=40749102490&partnerID=8YFLogxK

U2 - 10.1109/TIP.2007.916157

DO - 10.1109/TIP.2007.916157

M3 - Article

VL - 17

SP - 272

EP - 282

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 3

ER -