Comments on "optimal approximation of uniformly rotated images: relationship between Karhumen-Loeve expansion and discrete cosine transform"

Author

Rae-Hong Park

Author_Institution

Dept. of Electron. Eng., Sogang Univ., Seoul, South Korea

Volume

11

Issue

3

fYear

2002

fDate

3/1/2002 12:00:00 AM

Firstpage

332

Lastpage

334

Abstract

This paper points out the incorrect expressions of Uenohara and Kanade (see ibid., vol.7, p.116-19, 1998), in the context of the representation of the eigenvectors based on the discrete cosine transform (DCT). With the repeated eigenvalues, the eigenvector matrix of the P/spl times/P real symmetric circulant matrix can be constructed using the singular value decomposition (SVD), where P denotes the number of uniformly rotated images. Or equivalently it can be formulated in terms of the discrete Hartley transform (DHT). An example with P=4 is presented to show the correctness of our analysis.

Keywords

Karhunen-Loeve transforms; approximation theory; discrete Hartley transforms; discrete cosine transforms; eigenvalues and eigenfunctions; image representation; optimisation; singular value decomposition; DCT; DHT; Karhunen-Loeve expansion; SVD; discrete Hartley transform; discrete cosine transform; eigenvalues; eigenvector matrix; eigenvectors; image representation; optimal approximation; real symmetric circulant matrix; singular value decomposition; uniformly rotated images; Covariance matrix; Discrete Fourier transforms; Discrete cosine transforms; Discrete transforms; Eigenvalues and eigenfunctions; Filters; Matrix decomposition; Singular value decomposition; Symmetric matrices; Vectors;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.988965

Filename

988965