You do not need to implement KAZE descriptor, because an open source implementation is available from:

http://www.robesafe.com/personal/pablo.alcantarilla/kaze.html

I hope that this code helps you in your research!

Dear Robert

I have downloaded that Open CV code already. I want an implementation in MATLAB.

Dear Hossein,

Sorry, I did not know that you have previously downloaded the OpenCV code and that you need a Matlab implementation. Unfortunately, as far as I know there is not an open source version of the code for Matlab, so you would have to implement this code by taking as reference the OpenCV code.

Apart from original KAZE implementation, an accelerated version was recently proposed (A-KAZE), I attach you the paper where it is presented because it could help you to better understand the description methodology.

Good luck with your research!

Conference Paper Fast Explicit Diffusion for Accelerated Features in Nonlinea...