You could try the Scholarpedia article on SIFT:

http://www.scholarpedia.org/article/Scale_Invariant_Feature_Transform

SIFT are quite standard in computer vision, though there are many types of features that are in use: histograms of gradients, wavelets, LESH, GLOH, ORB, SURF, to mention a few... You might want to check them out if working on image analysis.

As for the descriptor in SIFT, it is simply a set of binned orientation histograms computed on some pixel neighborhoods around the keypoint. The descriptor size may vary (it's not necessarily 128, you can make it smaller or wider) - and you could also use PCA/SVD for some dimensionality reduction, unless I am mistaken

Look at the SIFT section of this MATLAB Tutorial by Gonzalo Vaca-Castano: http://www.cs.ucf.edu/~gvaca/REU2012/

The tutorial references this blog series: http://www.aishack.in/2010/05/sift-scale-invariant-feature-transform/

Salam Hadjer,http://www.vlfeat.org/~vedaldi/code/sift.html

the link contains document about SIFT and a matlab C implementation

http://web.eecs.umich.edu/~silvio/teaching/EECS598/lectures/lecture10_1.pdf

Thank you ahmed barak allaho fik

wa fiki baraka Allah, you are welcome Hadjer, good luck.

Here is a simple document regarding your subject- bonne chance

There is a good blog on this, which explains these feature detection algorithm step by step , which you can easily follow.

http://www.aishack.in/2010/05/sift-scale-invariant-feature-transform/

Good luck.