1. How D.lowe fix the number of octaves?

log2(min(width,height)) is usually used to determine the number of octaves. The "width" and "height" are the resolution of the input image.

2. How they calculate the sigma and K?

sigma=sigma0*2^{o+s/S} where s=0,...,S-1 and o=o_min,...,o_min+O-1.

sigma0 is the base scale (usually set to 1.6), o_min is the first octave index (usually set to 0 to start with the full resolution of the input image), O is the number of octaves, and S is the number of scales per octave (usually set to 3). Note that increasing S usually gives you more keypoints, but may make keypoint detection unstable due to noises.

I am not sure what you mean by "K".

3. Are they passed by all the pixels in the images?

Yes.

4. After a DoG we get a set of images how they merge them to have one image where all candidate key points are on it?

Let Z denote the perpendicular axis of the image plane. DoG images are usually "concatenated" along the Z-axis, resulting in a 3D "image". Given this 3D "image", "pixels" whose 3*3*3 neighbors have all smaller or larger values are determined as local extrema.

5. Why exactly they use the pyramid, scale factor, sigma and K the DoG? What is there effect?

To make keypoint detection invariant to scaling (robust as regards scale changes).

hi go through the following link

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

http://www.icg.tu-graz.ac.at/publications/pdf/fastapproximatedsift.pdf

https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=15&cad=rja&uact=8&ved=0CDUQFjAEOAo&url=http%3A%2F%2Fhuro-sift.googlecode.com%2Fsvn%2Ftrunk%2FResearch%2Fimplementing.the.scale.invariant.feature.transform.sift.method.pdf&ei=b2yOVLC2FtKPuASa64Aw&usg=AFQjCNFCAhV1y2vyfOlKHuxvhaBSBfWfrg&bvm=bv.81828268,d.c2E

http://stackoverflow.com/questions/9211916/sift-implementation-in-matlab-tutorial

Thank you for your help Sir Xiaomeng Wu  and sir Chethankumar Bm

You can read this paper: "Anatomy of the SIFT Method"

http://www.ipol.im/pub/pre/82/

Salam, you can see this link:

https://www.youtube.com/watch?v=NPcMS49V5hg