Today we finished the construction of Daubechies’ maxflat filters. For those who are anxious to know what is wavelet – infinite repetition of LP/HP filter pair H0 and H1would lead to scaling and wavelet functions in continuous-space wavelet theory. So conceptually discrete filters H0/H1 and continuous scaling/wavelet functions carry exactly identical information because one is [...]
Archive for September, 2008
From First-Generation to Second-Generation Wavelets
Posted in wavelets on September 25, 2008 | Leave a Comment »
The Validity of Markovian Assumption
Posted in ee565 on September 25, 2008 | Leave a Comment »
As I have shown in the class, a critical assumption made by the class of so-called local models is that the conditional pdf of a pixel is only determined by the pixels in its surrounding neighborhood. Such assumption is the key to overcome the curse of dimensionality in modeling image signals (whose dimensionality is in [...]
What is Texture?
Posted in ee565 on September 18, 2008 | Leave a Comment »
We have moved to the application so-called “texture synthesis”. But I have not given a formal definition of texture and I don’t think I will be able to do so in this class because it never exists in the literature. Like many other terms in image processing such as “edge” or “object”, texture is a [...]
EMD vs. AFR
Posted in wavelets on September 18, 2008 | 1 Comment »
This Friday Ms. Wu and Mr. Chen are going to tell us two interesting stories: one is about empirical mode decomposition (EMD) and the other is about automatic face recognition (AFR). I made arrangements about Friday student presentations in a random fashion but it happened that EMD and AFR are two topics of very different [...]
How good do you need to be at mathematics?
Posted in wavelets on September 15, 2008 | 2 Comments »
When I read Ingrid’s ground-breaking paper in 1998, I was truly impressed by how she managed to combine her mathematical talent and physical intuition. Then I cannot help wondering about others including myself – apparently every individual’s mathematical talent differs. Does EE people really need a lot of mathematics? Which subfield of mathematics (analysis, geometry, [...]
From Research (Ideas) to Development (Products)
Posted in ee565 on September 15, 2008 | Leave a Comment »
Today we discussed various potential applications of image denoising into MRI, Ultrasound, infrared and microscopic imaging. I think you all have got the general impression of how image quality CAN be improved by image processing algorithms. You might be wondering: if these fancy denoising algorithms (GSM, NLmean and BM3D) are so powerful, how come we [...]
Patch Everywhere
Posted in ee565 on September 10, 2008 | Leave a Comment »
After we have learned wavelet-based denoising, you might have got the impression that the heavy-tail law of wavelet coefficients is end of the story. That is so striking – that must be the ultimate solution to separating image signals from the Gaussian noise. For a long while, I thought so too and the community of [...]
Symmetry(Invariance) Everywhere
Posted in wavelets on September 10, 2008 | 1 Comment »
Mathematical definition of symmetry is fairly broad. You can refer to http://en.wikipedia.org/wiki/Symmetry to take a look. Symmetry is a fundamental concept in both algebra and geometry. A large body of mathematical literature can be related to symmetry defined in the broadest sense. For example, if we consider congruent traingles as symmetric objects (scale-invariance), we can [...]
Why do we want Translation Invariance in denoising?
Posted in ee565 on September 8, 2008 | Leave a Comment »
Some student A came up with a super-splendid image denoising algorithm and claimed his algorithm beats all the available ones. How would I respond? Yes, congrulations – after I have verified that his experiments are all legitimate. But how do I know if his algorithm is optimal even without understanding the technical details? Here is [...]
What is randomness?
Posted in wavelets on September 8, 2008 | 1 Comment »
Our intuition often tells us randomness is on the opposite side of determinism. However, if you consider the following deterministic mapping (you can start with arbitrary x_0, but set parameter a to vary from 1 to 4)
x_{n+1}=a*x_n*(1-x_n)
The sequence {x_1,x_2,…,} will start to look very much random after a is above 3.57. This is an example [...]
