# What transformations have been applied to this image to yield four derivatives?

In a few days I have an exam of image processing. I'm currently having a look at the example exam and I came across this question. "Which transformation of this image is being done here. Explain the components in the quadrants NA (second image)."  Na

Can anyone help me with this ?

• Had this question on my exam. And the answer given here was that answer that i used. The answer was correct – Olivier_s_j Feb 18 '12 at 11:15

## 1 Answer

This to me looks exactly like the two-dimensional Haar wavelet transform. All four quadrants are a part of the transform, even though different operations have been performed on them. Upper left quadrant is a result of low-pass filtering with a 2x2 two-dimensional rect function (Haar wavelet) and decimation be a factor of 2, upper right is the output of a horizontal high-pass filter, lower left is the output of a vertical high-pass filter, and lower right is the output of a diagonal high-pass filter.

• I had this question on my exam. I really hope you are correct :p – Olivier_s_j Jan 17 '12 at 9:01
• Well, that's what I would have put down. On the other hand, I have no idea what your professor might have called it. Haar wavelet transform, however, is the most common name. Let me know how it goes! = ) Also, what is the subject you're studying? – Phonon Jan 17 '12 at 14:21
• Engineering with multimedia and information technology major. We saw the haar wavelet transform. And from what I've studied, this seems to be correct. :D – Olivier_s_j Jan 18 '12 at 9:11