I am at the moment reading a paper (SURF) and trying to understand what is happening here and how the things works as it does....
a non maximum supression is performed on the scale space representation of the image. This give us a list the local maxima within +-1 neighborhood. These are den used here which i don't quite understand.
The final step in localising the points involves interpolating the nearby data to find the location in both space and scale to sub-pixel accuracy. This is done by fitting a 3D quadratic as proposed by Brown [3]. In order to do this we express the determinant of the Hessian function, H(x,y,$\sigma$), as a Taylor expansion up to quadratic terms centered at detected location. This is expressed as: $$H(\textbf{x}) = H \frac{\partial H^T}{\partial \textbf{x}}\textbf{x} + \frac{1}{2}\textbf{x}^T\frac{\partial^2 H}{\partial \textbf{x}^2}\textbf{x}$$ $\textbf{x}=(x,y)$
As I understand has there been made a taylor expansion based on some points.. is that even possible?
This is taken from this paper https://code.google.com/p/opensurf1/downloads/detail?name=opensurf.pdf
My question is this