I am studying SIFT. I am a little confused in some of Lowe's algorithm.
In order to have a descriptor invariant to translations like scaling, we must get rid of the scaling factor in LoG (Laplacian of Gaussian). I know that the LoG is represented like this:
Then the scale invariant LoG would look like this:
But how the DoG can be like this?:
In other words, how by approximation,using DoG, we get rid of that scale factor in SIFT. I know how DoG is computed, but the thing is I cannot understand how we get rid of that factor to have a invariant-to-scale LoG approximation. Any precise explanation is really appreciated.
EDIT: some more questions, Please answer precisely. Thanks :-) 1- At the final step of SIFT, we calculate feature vector using Gradient Orientation. to do do, the keypoint's rotation is subtracted from each orientation. I cannot understand why we subtract them?
2- What about Illumination dependence?
Anyone can explain how we remove Illumination and Orientation dependency?