Thank you very much Prof. April for the useful information.

Dear Dr. April would you please give me a little bit more explanation of the following paragraph ( in a simple manner):

"texture is comprised of space-localized frequency events. Multiresolutional analysis (via the discrete wavelet transform (DWT)) is a logical choice, since the wavelet basis have excellent joint space frequency resolution"

In fact, I know that via DWT we can determine which frequency occurs where in the image. But I cannot still understand why this property makes it a good choice for feature extraction. I also cannot understand what do we mean by the term "joint space frequency resolution".

and also what do we mean by "textural events" ( Is it textural features?)

Many thanks again.

It is in general quite difficult to say in advance what method will work well in a specific application. If I were you, I'd have a try with Local Binary Patterns (LBP). It works generally quite well, it's simple and computationally light. Code available at: http://www.cse.oulu.fi/CMV/Downloads/LBPMatlab

Dear Dr. April

Can I use the following matlab code in order to implement shift invariant DWT as you described in your book chapter?

http://www.mathworks.com/help/wavelet/ug/translation-invariant-denoising-with-cyclespinning.html

Please accept my appreciation in advance.

The meaning of this sentence: "the wavelet basis have excellent joint space frequency resolution"

The limitation of Fourier Transform is that it gives only the global frequency content of a signal. This limitation is overcome by Short Time Fourier Transform which is able to retrieve both frequency and time (or position in case of image) information from a signal. It calculates the FT of a windowed part of the original signal, where the window shifts along the time (or position) axis.

Low frequency components often last a long period of time, so a high frequency resolution is required. High frequency components often appear as short bursts, invoking the need for a higher time resolution.

The problem of Short Time Fourier Transform is that it is not possible to get both a good time resolution and a good frequency resolution.

The basic difference between the Wavelet Transform and Short Time Fourier Transform is that in WT, the window width (space resolution) can be changed as the function of the analyzing frequency. In high frequencies we have small window width (high space resolution) and in low frequency we have big window width (low space resolution).

Thank you very much Dr. April

Is it possible for you to share the code you've written for Shift Invariant DWT with me? I want to compare the result of this method with other ones and for sure I will cite your works wherever I use it.