Name
Title | ||
|---|---|---|
Approximation of the Karhunen–Loève transformation and its application to colour images |
Abstract | ||
|---|---|---|
Analysis of colour images in the Red, Green and Blue acquisition space and in the intensity and chrominance spaces shows that colour components are closely correlated (Carron, Ph.D. Thesis, Univ. Savoie, France, 1995; Ocadis, Ph.D. Thesis, Univ. Grenoble, France, 1985). These have to be decorrelated so that each component of the colour image can be studied separately. The Karhunen–Loève transformation provides optimal decorrelation of these colour data. However, this transformation is related to the colour distribution in the image, i.e. to the statistical properties of the colour image and is therefore dependent on the image under analysis. In order to enjoy the advantages of direct, independent and rapid transformation and the advantages of the Karhunen–Loève properties, this paper presents the study of the approximation of the Karhunen–Loève transformation. The approximation is arrived at through exploitation of the properties of Toeplitz matrices. The search for eigenvectors of a Toeplitz matrix shows that complex or real orthogonal mappings such as the discrete Fourier transform and its decompositions approximate the Karhunen–Loève transformation in the case of first-order Markov processes. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1016/S0923-5965(00)00035-7 | Signal Processing: Image Communication |
Keywords | Field | DocType |
Colour analysis,Toeplitz matrix,Toeplitz matrix eigenvalues and vectors,First-order stationary process,Karhunen–Loève transformation,Discrete sine and discrete cosine transformations | Decorrelation,Mathematical analysis,Matrix (mathematics),Artificial intelligence,Eigenvalues and eigenvectors,Color image,Computer vision,Karhunen–Loève theorem,Chrominance,Algorithm,Toeplitz matrix,Discrete Fourier transform,Mathematics | Journal |
Volume | Issue | ISSN |
16 | 6 | 0923-5965 |
Citations | PageRank | References |
7 | 0.94 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rémi Kouassi | 1 | 7 | 1.28 |
| Pierre Gouton | 2 | 85 | 16.94 |
| Michel Paindavoine | 3 | 115 | 21.70 |