SINGULAR VALUE DECOMPOSITION IN DIGITAL IMAGE ANALYSIS
Abstract
The paper describes new properties of the singular matrix decomposition. It is shown that permutation of rows or columns of the matrix or matrix rotation by 90 degrees does not change the set of its singular numbers. However, variation the value of at least one matrix element or permutation of any two matrix elements leads to a modification of the whole set of the singular numbers. Examples of image sharpening and contrast enhancement by modification of the singular numbers are given.
About the Author
V. V. Starovoitov
Объединенный институт проблем информатики НАН Беларуси
Russian Federation
Russian Federation
References
1. Golub, G. Calculating the singular values and pseudo-inverse of a matrix / G. Golub, W. Kahan // Journal of the Society for Industrial and Applied Mathematics. Series B: Numerical Analysis.– 1965. – Vol 2, no. 2. – P. 205–224.
2. Demmel, J. Accurate singular values of bidiagonal matrices / J. Demmel, W. Kahan // SIAM Journal on Scientific and Statistical Computing. – 1990. – Vol. 11, no. 5. – P. 873–912.
3. Gerbrands, J.J. On the relationships between SVD, KLT and PCA / J.J. Gerbrands // Pattern Recognition. – 1981. – Vol. 14, no. 1–6. – P. 375–381.
4. Moonen, M. SVD and signal processing: algorithms, applications and architectures /M. Moonen, B. De Moor. – Elsevier Science, 1995. – 485 р.
5. Хорн, Р. Матричный анализ / Р. Хорн, Ч. Джонсон ; пер. с англ. – М. : Мир, 1989. – 655 с.
6. Jha, S.K. Denoising by singular value decomposition and its application to electronic nose data processing / S.K. Jha, R.D.S. Yadava // IEEE Sensors Journal. – 2011. – Vol. 11, no. 1. – P. 35–44.
7. Liu, R. An SVD-based watermarking scheme for protecting rightful ownership / R. Liu, T. Tan // IEEE transactions on multimedia. – 2002. – Vol. 4, no. 1. – P. 121–128.
8. Andrews, H. Singular value decomposition (SVD) image coding / H. Andrews, C. Patterson // IEEE transactions on Communications. – 1976. – Vol. 24, no. 4. – P. 425–432.
9. Narwaria, M. SVD-based quality metric for image and video using machine learning / M. Narwaria, W. Lin // IEEE Trans. on Systems, Man, and Cybernetics. Part B. – 2012. – Vol. 42, no. 2. – P. 347–364.
10. Targhi, A.T. Clustering of singular value decomposition of image data with applications to texture classification / A.T. Targhi, A. Shademan // Proc. of Intern. Conf. on Visual Communications and Image Processing. – Lugano, Switzerland, 2003. – Vol. 5150. – P. 972–979.
11. Zhang, D. A new face recognition method based on svd perturbation for single example image per person / D. Zhang, S. Chen, Z.-H. Zhou // Applied Mathematics and Computation. – 2005. – Vol. 163, no. 2. – P. 95–907.
12. No-reference image blur index based on singular value curve / Q. Sang [et al.] // Journal of Visual Communication and Image Representation. – 2014. – Vol. 25, no. 7. – P. 1625–1630.
13. Singular value decomposition based sample diversity and adaptive weighted fusion for face recognition / G. Zhang [et al.] // Digital Signal Processing. – 2017. – Vol. 62, no. 3. – P. 150–156.
14. Карчевский, Е.М. Лекции по линейной алгебре и аналитической геометрии /Е.М. Карчевский, М.М. Карчевский. – Казань : Казанский гос. ун-т, 2014. – 352 с.
15. Белоусов, И.В. Матрицы и определители : учеб. пособие по линейной алгебре. – 2-е изд. – Кишинев : Изд-во Ин-та прикладной физики АН Республики Молдова, 2006. – 101 с.
Review
For citations:
Starovoitov V.V. SINGULAR VALUE DECOMPOSITION IN DIGITAL IMAGE ANALYSIS. Informatics. 2017;(2(54)):70-83. (In Russ.)
Views: 916
Email this article 