Quaternion principal component analysis of color images

@article{Bihan2003QuaternionPC,
  title={Quaternion principal component analysis of color images},
  author={N. L. Bihan and S. Sangwine},
  journal={Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)},
  year={2003},
  volume={1},
  pages={I-809}
}
  • N. L. Bihan, S. Sangwine
  • Published 2003
  • Mathematics, Computer Science
  • Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)
In this paper, we present quaternion matrix algebra techniques that can be used to process the eigen analysis of a color image. Applications of principal component analysis (PCA) in image processing are numerous, and the proposed tools aim to give material for color image processing, that take into account their particular nature. For this purpose, we use the quaternion model for color images and introduce the extension of two classical techniques to their quaternionic case: singular value… Expand
Color Image Analysis by Quaternion-Type Moments
In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holisticExpand
Quaternion higher-order spectra and their invariants for color image recognition
This paper describes an invariants generation method for color images, which could be a useful tool in color object recognition tasks. First, by using the algebra of quaternions, we introduce theExpand
Local quaternion Fourier transform and color image texture analysis
Color images can be treated as two-dimensional quaternion functions. For analysis of quaternion images, a joint space-wavenumber localized quaternion S transform (QS) is presented in this study for aExpand
Assessment of color image fusion algorithms based on quaternion singular value decomposition
  • Yuqing Wang, Ming Zhu, Haochen Pang, Yong Wang
  • Mathematics, Engineering
  • International Symposium on Multispectral Image Processing and Pattern Recognition
  • 2009
In this paper, a new approach to objectively assess the performance of image fusion algorithms is proposed. It is based on the quaternion representation for the structural information of colorExpand
Assessment of color image fusion algorithms based on quaternion singular value decomposition
  • Yuqing Wang, Ming Zhu, Haochen Pang, Yong Wang
  • Mathematics, Engineering
  • International Symposium on Multispectral Image Processing and Pattern Recognition
  • 2009
In this paper, a new approach to objectively assess the performance of image fusion algorithms is proposed. It is based on the quaternion representation for the structural information of colorExpand
Vector Sparse Representation of Color Image Using Quaternion Matrix Analysis
Traditional sparse image models treat color image pixel as a scalar, which represents color channels separately or concatenate color channels as a monochrome image. In this paper, we propose a vectorExpand
EXPLORATION IN QUATERNION COLOUR
Quaternions have been a subject for research in mathematics, physical, and engineering for decades. Using quaternions to represent colours, however, has recently been proposed and studied. In thisExpand
Quaternion angular radial transform and properties transformation for color-based object recognition
Nowadays, with the increased use of digital images, almost all of which are in color format. Conventional methods process color images by converting them into gray scale, which is definitely notExpand
Applying Quaternion Fourier Transforms for Enhancing Color Images
The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use theExpand
Quaternion-based sparse representation of color image
In this paper, we propose a quaternion-based sparse representation model for color images and its corresponding dictionary learning algorithm. Differing from traditional sparse image models, whichExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 20 REFERENCES
Hypercomplex auto- and cross-correlation of color images
  • S. Sangwine, T. Ell
  • Mathematics, Computer Science
  • Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348)
  • 1999
TLDR
This paper presents for the first time a definition of correlation applicable to color images, based on quaternions or hypercomplex numbers, and devised a visualization of the result using the polar form of a quaternion in which color denotes quaternional eigenaxis and phase, and a grayscale image represents the modulus. Expand
Fourier transforms of colour images using quaternion or hypercomplex, numbers
The 2D quaternion, or hypercomplex, Fourier transform is introduced. This transform makes possible the handling of colour images in the frequency domain in a holistic manner, without separateExpand
Quaternion subspace method for vector-sensor wave separation
  • N. L. Bihan, J. Mars
  • Computer Science, Mathematics
  • 2002 11th European Signal Processing Conference
  • 2002
TLDR
The way quaternions allows to characterize signals collected on vector-sensor array is introduced and the way it can be computed is exposed, and a quaternionic subspace method for polarized wave separation is developed using this new tool based on quaternion matrix algebra. Expand
A novel block truncation coding of color images by using quaternion-moment-preserving principle
  • S. Pei, C. Cheng
  • Mathematics
  • 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96
  • 1996
To compress color-pixel blocks, a novel color BTC algorithm, called the quaternion-moment block truncation coding (QMBTC), is presented in this paper. The QMBTC are derived by using the quaternionExpand
Hypercomplex operators and vector correlation
TLDR
The necessity of carefully choosing the form of the correlation function is identified, the set of equivalent forms for hypercomplex correlation is presented and how these can be validated using hypercomplex operator algebra is demonstrated. Expand
Quaternions and matrices of quaternions
Abstract We give a brief survey on quaternions and matrices of quaternions, present new proofs for certain known results, and discuss the quaternionic analogues of complex matrices. The methods ofExpand
Colour-sensitive edge detection using hypercomplex filters
TLDR
This paper presents a colour edge detection procedure designed to find edges between homogeneous regions of particular colours and demonstrates that this procedure can successfully find particular coloured edges in both synthetic and natural images. Expand
On left eigenvalues of a quaternionic matrix
Abstract In this paper, we introduce the concept of left and right eigenvalues for a quaternionic matrix, and investigate their properties, quantities and relationship.
Statistical Signal Processing: Detection, Estimation, and Time Series Analysis
1. Introduction. 2. Rudiments of Linear Algebra and Multivariate Normal Theory. 3. Sufficiency and MVUB Estimators. 4. Neyman-Pearson Detectors. 5. Bayes Detectors. 6. Maximum Likelihood Estimators.Expand
On left eigenvalues of a qnatemioiiic matrix,“ Linear algebra and ifs applicarinirs
  • 2001
...
1
2
...