Quaternion in Image Processing - Learn How to Represent 3D Space

[tavoos]

Hi everyone
I have question about Arithmetic quaternion. this concept is used in image processing for representing R G B color channel as a hyper complex number or single unit.how can it is possible? can I represent every things in 3D space as a hyper complex number by quaternion?
Please help me
Thanks a lot

 

[mfb]

Quaternions have 4 degrees of freedom (you need 4 real values to describe a quaternion) - if you fix their magnitude to 1, you have three left, those can encode R G B.
I have no idea if/why/when this is useful for colors. It is used for rotations in 3D spaces.

 

[D H]

Typical usage for colors is to use non-unitary pure quaternions. The scalar ("real") part is zero. The imaginary parts correspond to red, green, and blue.

Why do this? One reason is that the concept of Fourier transforms has been extended to the quaternions. This representation let's one analyze a color image as a whole in the frequency domain. Edge detection can also be extended to the quaternions, once again letting one analyze a color image as a whole. You don't get this with three separate real channels, one each for red, green, and blue.

 

[mfb]

Typical usage for colors is to use non-unitary pure quaternions. The scalar ("real") part is zero. The imaginary parts correspond to red, green, and blue.

Ah, that makes more sense, thanks.

 

[tavoos]

Dears
Thanks for replying
I read some papers that use quaternion to fuse multi features like intensity ,motion ,colors.how can it is possible?
2- You said that we can use Quaternion to process color components as whole or single point, it means that each single point in 4D space(Quaternion) has all properties of (R G B) ?
Please help me .
Thanks

 

[D H]

You've read the papers, and that is the correct approach for understanding something new. Since this approach is fairly new, you're not going to find it in textbooks. This is indeed a fairly new approach; the earliest reference I can find is 1996, and the concept apparently didn't really take hold until the mid-2000s.

Do you know the basics of k-means clustering, 2 dimensional FFT, wavelet transformations, edge detection, digital filtering, principal components analysis, etc. as applied to gray scale images? Do you know what quaternions are? If you don't know these basic concepts (all of which can be found in texts and are taught in classes), you are doing the equivalent of diving into the deep end of the pool with having first learned to swim.

 

[tavoos]

You've read the papers, and that is the correct approach for understanding something new. Since this approach is fairly new, you're not going to find it in textbooks. This is indeed a fairly new approach; the earliest reference I can find is 1996, and the concept apparently didn't really take hold until the mid-2000s.

Do you know the basics of k-means clustering, 2 dimensional FFT, wavelet transformations, edge detection, digital filtering, principal components analysis, etc. as applied to gray scale images? Do you know what quaternions are? If you don't know these basic concepts (all of which can be found in texts and are taught in classes), you are doing the equivalent of diving into the deep end of the pool with having first learned to swim.

Thanks for replying as you mentioned there is not enough textbook about this subject.but I know that the concept of such basics.what do you means?you want to say I am wrong. if yes? please clear for me what I am wrong about Quaternion
Thanks

 

[D H]

I'm not saying you're wrong about anything. I don't understand what it is you are asking. If you are asking us to write a book on how quaternions are useful in image processing (which is what you appear to be asking), this isn't the place to ask. An internet forum isn't the right place for such questions.

What we can help you with is where you have specific questions about specific issues, something where the answer might take a few paragraphs, maybe a page.

 

[D H]

Asking for help by email is even worse than asking for help in the open forums. Others with similar questions may be able to take advantage of the answers when you ask for help in the open forums. I (and others) are quite willing to take the time to answer such questions freely (i.e., no money involved) because we're potentially benefiting a number of people at once.

You are the only one who can possibly benefit when you ask for help by email. That means I should charge you consulting rates for my help. Note well: The going rate for short term engineering consulting work in the US is well in excess of $100/hour ($200+/hour is more likely for short term work), with an eight hour minimum.

 

[D H]

Your questions need to be better formulated. Ask specific questions. Don't ask us to write a book. That's a general unwritten rule for internet forums.

I was not asking to set up a consultancy. You most likely cannot afford the rates my employer charges other companies for my time, and if you could, I would probably balk.We obviously have a language issue here. What is it that is troubling you? What don't you understand? What do you need help with? Try to be precise, and try to keep in mind that I don't have time to write a book. (And if I did, it wouldn't be on this subject. I am not an expert, at least not anymore -- particular with respect to color imagery. Gray scale imagery is so much easier to deal with.)