Quantization by Dummies

Every time it happens to me, I remember the episode in The Simpsons where Homer wants to get a raise when he was working at Bowlarama, he proposes to Al to triple the business, then you can see Homer reading “Advanced Marketing”, next scene the book is in trash bin and Homer is reading “Basic Marketing”, after that you can see a pile of books in the trash and Homer looking for the word “marketing” at the dictionary…

I had to read an technical article related to Quantization and present an explanation for the Digital Image Processing class in a workshop session. The teacher gave us a list of articles related to quantization and she asked us to choose one of them. The first problem we faced was the availability of the papers, although the university has some kind of subscription with IEEE and ScienceDirect, the number of articles available for us to download was very limited and the date of them was quite old.

While looking at the titles of the papers “the” question was arisen, which article should I choose? First of all looked at the articles that sounded good to me, then I realized that none of them were available from IEEE, and couldn’t connect to ScienceDirect from school. Then I started searching any article from the list available from IEEE was “Generalized Scalar Quantizer Design Using Dynamic Programming” (bear in mind that if you don’t have a subscription you can’t see the article). The article is three pages long, but I couldn’t get to understand it enough to make a presentation.

I gave up searching the articles from the list and started surfing with Saint Google, I don’t remember the keywords I used to search, but I came up with “Optimal Entropy-Constrained Scalar Quantization of a Uniform Source”. It’s funny because while writing this post I was looking for the link to this file and found that the one of the coauthors of the article, ANDRÁS GYÖRGY,  has a bunch of his papers published listed in his publication's page, are available to download and some of them are about quantization.

After that, troubles has just begun, I started reading the article, and realized that most of the ideas were unclear to me, then I had to go to the books to search for the definition of the term I was stuck with, but while reading the definition I found also some things that for the moment I wasn’t able to understand, besides that I couldn’t found any ‘for dummies’ book about digital image processing, go figure, and it’s obvious there is no such thing. So I was reading in circles, finally, I put some kind of order in my ideas and made a presentation with the concepts I got. Still, it wasn’t enough to be clear the concept proposed in the paper, at least for me.

The best thing that I recall from this exercise is that it helped me to understand that research is not easy, but reading and sharing the little knowledge acquired, is the only way to start learning new things, it opens the mind to a different level, because we can see the work other people involved in the same field is doing, and also get fresh ideas from our peers, remember that feedback is always good and there is no such thing as “constructive nor destructive” critics.

The feared Discrete Fourier Transform (aka:DFT)

Why we should care about the Discrete Fourier Transform?

I will start talking about the applications in which DFT is used, as Gonzalez says in his image processing book, besides being the cornerstone in linear filtering, it offers considerable flexibility in the design and implementation of filtering solutions in areas as image compression, image restoration, image enhancement, and many other applications of practical interest. Now, we are ready to cheerfully start studying the DFT in deep. (Yeah, right)  

By definition, the DFT is represented as follows:

Mmmm, and as you easily can see from the equation above, :P, we have:

• X(k) = Is the Discrete Fourier Transform of our signal, is its representation in the frequency domain (what?)

• x(n) = Is our signal in the spatial domain, ie. an audio signal

So, if we see the equation, each sample X(k) will be the sum of the multiplication of all the input signal values by the frequency components of the signal.  Yes, is that e raised to two pi divided by N times minus i times k times n.

Without looking for more troubles with efficiency measurement algorithms, we can see (not so clearly) that while we have more samples in our signal, the amount of multiplications and additions is raised exponentially, that inconvenience was solved with the FFT, but that is something that I will not touch so far.

Here I stop with this little explanation of the DFT, but I will continue with an example of it coded in MATLAB in a later post.

(So far I can’t get to understand this)

I need the same thing that Fourier was smoking…

Definitely I don’t understand the Discrete Fourier Transform, and even more, the troubles are elevated to square when I try to comprehend it applied to an image, ha!

As Mr. Marley used to say…

Begining

to Ivonne

Time to begin.

The objective of this blog is to share ideas, homework, articles, essays, events, links and any thing related to the development of my thesis in Master of Science in Electrical Engineering at the University of Juarez. This is meant to make available in a global manner the knowledge that could be generated at some point, and to create also a hub of discussion regarding topics related to digital image processing.

The main idea of the thesis is based on the Wavelet transform. The main purpose of a transform in the digital signal processing world, is to change in domain a signal, this is, represent in a “different” way a signal; with the objective of being able to see characteristics that would not be noticeable otherwise into the original domain. There are a bunch of transforms available; among them is the Fourier Transform, the Discrete Cosine Transform, the Wavelet, the Contourlet, etc.

Based on the fact that a domain transform an alternative approach can be achieved to the analysis of the signal, in comparison with the representation in the original domain. A characterization of images is pretended (based on the fact that an image is indeed a 2D signal) in the transformed domain, using in this particular case the Wavelet transform and be able to obtain in a systematic manner information that could be used in the different fields of digital image processing, like in the patter recognition as an example.

This blog is born due to the response of a personal need of clarify all the ideas that are brought in the way towards the making of the thesis project, perhaps the focus of this blog is oriented to the academic world, but it is obvious that can not be limited only to serve that purpose. I want to thank deeply to the love of my life, which always gives me her support and with out herself I would not never think about writing this Blog.