How to do 2-D Karhunen-Loeve(K-L) transform in matlab?

[chang]

Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!

Michael

[Novae]

Hi Michael

I saw this transform (KLT) once used as a dimension reduction technique for feature spaces. I believe its closely related to principal component analysis.

"FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets" from Faloutsos and Lin uses the KLT.

Sorry not to be able to help you more but I hope I could point you in a good direction.

Igor

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!
Michael

[Greg Heath]

CORRECTED FOR THE HEINOUS SIN OF TOP-POSTING!

Post by Novae

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!

I saw this transform (KLT) once used as a dimension reduction technique for feature spaces. I believe its closely related to principal component analysis.
"FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets" from Faloutsos and Lin uses the KLT.
Sorry not to be able to help you more but I hope I could point you in a good direction.

I 'm pretty sure that the KL Transform is exactly the PC Transform.

Hope this helps.

Greg

[Novae]

Hi Greg

Most probably they are. Anyway this article may bring some extra light on the subject if one's more interested in this subject:

"On the relationships between SVD, KLT and PCA " by Jan J. Gerbrands

Igor

Post by Greg Heath
CORRECTED FOR THE HEINOUS SIN OF TOP-POSTING!

Post by Novae

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!

I saw this transform (KLT) once used as a dimension reduction technique for feature spaces. I believe its closely related to principal component analysis.
"FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets" from Faloutsos and Lin uses the KLT.
Sorry not to be able to help you more but I hope I could point you in a good direction.

I 'm pretty sure that the KL Transform is exactly the PC Transform.
Hope this helps.
Greg

[Novae]

Hi again

From "Automatic human face location in a complex background using motion and color information" by Choong Hwan LEE, Jun Sung Kim and Kyu Ho Park - Pattern Recognition, Volume 29, Issue 11, November 1996, Pages 1877-1889

"The principal component coordinates (KL space) are obtained from the eigenvalues and eigenvectors of the covariance matrix of the color image values. This process is the well-known Karhunen-Loeve transformation of the RGB tristimulus values. This
space is said to have a large discriminant power since the principal coordinates are an orthogonal coordinate system in which the components are uncorrelated."

Is your goal to convert RGB color space into KL space? Maybe this will help a little more.

Igor

Post by Novae
Hi Greg
"On the relationships between SVD, KLT and PCA " by Jan J. Gerbrands
Igor

Post by Greg Heath
CORRECTED FOR THE HEINOUS SIN OF TOP-POSTING!

Post by Novae

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!

I saw this transform (KLT) once used as a dimension reduction technique for feature spaces. I believe its closely related to principal component analysis.
"FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets" from Faloutsos and Lin uses the KLT.
Sorry not to be able to help you more but I hope I could point you in a good direction.

I 'm pretty sure that the KL Transform is exactly the PC Transform.
Hope this helps.
Greg

[chang]

Thanks a lot, guys.
I believe the k-l transform is the PCA. But it seems that all the PCA kind of research is base on the vectors...
I've found how to do k-l transform on a block of an image,but it is not what I want...
Basically, they first partition the image into blocks such as 8x8 (it is a matrix), then they
rewrite these matrices as the vector (row by row for instance). Finally, they do the 1D K-L transform.
What I want is use the 8x8 matrix directly (not change it into a vector) and then do a 2D K-L transform (just like a 2D DCT used in the image coding and video coding standards). So can you guys give me a hint of this?
Thanks again!
Michael

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!
Michael

[p***@gmail.com]

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...

Please send the KL Transform for 2D image having more pixel value.

Post by chang
Thanks in advance!
Michael

[数亿开户]

chang於 2009年12月13日星期日 UTC+8上午3時00分06秒寫道：

Post by chang
Hi everyone,
do you guys know how to do 2 dimensional K-L transform? I know how to do a 1-D one. But I really have no idea about how 2-D transform works. And I have google a lot and find nothing on 2-D case...
Thanks in advance!
Michael

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