A keypoint descriptor is created by first computing the gradient magnitude and orientation at each image sample point in a region around the keypoint location. But i confused about the meaning of "region". what is the size of it? depends on the keypoint's magnitude ? or kernel size of Gaussian in the scale level which the keypoint found ? or else ?
It depends on "kernel size of Gaussian in the scale level" - in sense "what region from original image we take". Also it depends on SIFT parameter - PatchSize (usually=41) to which size window in pixels we reproject region from the original image.