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You have to take the derivative with respect to the vector $x$ and set it equal to zero. For a constant matrix $A$, the derivative of $A^Tx$ is $A$, and the derivative of $\frac12 x^TA^Tx=Ax$. So taking the derivative of $(1)$ gives $$\frac{\partial D}{\partial x}+\frac{\partial^2D}{\partial x^2}x\tag{1}$$ Setting $(1)$ equal to zero results in $(2)$.


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If you remap a local patch around a feature point to log–polar coordinates (with the origin in the point of interest), scale changes correspond to a translation along the log–radial axis, while rotations correspond to translations (with wrap-around) along the angular axis. If you then calculate the two-dimensional Fourier transform, translations in the ...


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